In this research, the extreme SuperHyperNotion, namely, extreme SuperHyperGirth, is up. $E_1$ and $E_3$ are some empty extreme SuperHyperEdges but $E_2$ is a loop extreme SuperHyperEdge and $E_4$ is an extreme SuperHyperEdge. Thus in the terms of extreme SuperHyperNeighbor, there's only one extreme SuperHyperEdge, namely, $E_4.$ The extreme SuperHyperVertex, $V_3$ is extreme isolated means that there's no extreme SuperHyperEdge has it as an extreme endpoint. Thus the extreme SuperHyperVertex, $V_3,$ is excluded in every given extreme SuperHyperGirth. $ \mathcal{C}(NSHG)=\{E_i\}~\text{is an extreme SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^i~\text{is an extreme SuperHyperGirth SuperHyperPolynomial.} \ \ \mathcal{C}(NSHG)=\{V_i\}~\text{is an extreme R-SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^I~{\small\text{is an extreme R-SuperHyperGirth SuperHyperPolynomial.}} $ The following extreme SuperHyperSet of extreme SuperHyperEdges[SuperHyperVertices] is the extreme type-SuperHyperSet of the extreme SuperHyperGirth. The extreme SuperHyperSet of extreme SuperHyperEdges[SuperHyperVertices], is the extreme type-SuperHyperSet of the extreme SuperHyperGirth. The extreme SuperHyperSet of the extreme SuperHyperEdges[SuperHyperVertices], is an extreme SuperHyperGirth $\mathcal{C}(ESHG)$ for an extreme SuperHyperGraph $ESHG:(V,E)$ is an extreme type-SuperHyperSet with the maximum extreme cardinality of an extreme SuperHyperSet $S$ of extreme SuperHyperEdges[SuperHyperVertices] such that there's only one extreme consecutive sequence of the extreme SuperHyperVertices and the extreme SuperHyperEdges form only one extreme SuperHyperCycle. There are not only four extreme SuperHyperVertices inside the intended extreme SuperHyperSet. Thus the non-obvious extreme SuperHyperGirth isn't up. The obvious simple extreme type-SuperHyperSet called the extreme SuperHyperGirth is an extreme SuperHyperSet includes only less than four extreme SuperHyperVertices. But the extreme SuperHyperSet of the extreme SuperHyperEdges[SuperHyperVertices], doesn't have less than four SuperHyperVertices inside the intended extreme SuperHyperSet. Thus the non-obvious simple extreme type-SuperHyperSet of the extreme SuperHyperGirth isn't up. To sum them up, the extreme SuperHyperSet of the extreme SuperHyperEdges[SuperHyperVertices], isn't the non-obvious simple extreme type-SuperHyperSet of the extreme SuperHyperGirth. Since the extreme SuperHyperSet of the extreme SuperHyperEdges[SuperHyperVertices], is an extreme SuperHyperGirth $\mathcal{C}(ESHG)$ for an extreme SuperHyperGraph $ESHG:(V,E)$ is the extreme SuperHyperSet $S$ of extreme SuperHyperVertices[SuperHyperEdges] such that there's only one extreme consecutive extreme sequence of extreme SuperHyperVertices and extreme SuperHyperEdges form only one extreme SuperHyperCycle given by that extreme type-SuperHyperSet called the extreme SuperHyperGirth and it's an extreme SuperHyperGirth . Since it 's the maximum extreme cardinality of an extreme SuperHyperSet $S$ of extreme SuperHyperEdges[SuperHyperVertices] such that there's only one extreme consecutive extreme sequence of extreme SuperHyperVertices and extreme SuperHyperEdges form only one extreme SuperHyperCycle. There are only less than four extreme SuperHyperVertices inside the intended extreme SuperHyperSet, thus the obvious extreme SuperHyperGirth, is up. The obvious simple extreme type-SuperHyperSet of the extreme SuperHyperGirth, is: ,is the extreme SuperHyperSet, is: does includes only less than four SuperHyperVertices in a connected extreme SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only simple extreme type-SuperHyperSet called the extreme SuperHyperGirth amid those obvious[non-obvious] simple extreme type-SuperHyperSets called the neutrosophic SuperHyperGirth , is only and only. A basic familiarity with extreme SuperHyperGirth theory, SuperHyperGraphs, and extreme SuperHyperGraphs theory are proposed.

In this research, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperGirth, is up. $E_1$ and $E_3$ are some empty neutrosophic SuperHyperEdges but $E_2$ is a loop neutrosophic SuperHyperEdge and $E_4$ is an neutrosophic SuperHyperEdge. Thus in the terms of neutrosophic SuperHyperNeighbor, there's only one neutrosophic SuperHyperEdge, namely, $E_4.$ The neutrosophic SuperHyperVertex, $V_3$ is neutrosophic isolated means that there's no neutrosophic SuperHyperEdge has it as an neutrosophic endpoint. Thus the neutrosophic SuperHyperVertex, $V_3,$ is excluded in every given neutrosophic SuperHyperGirth. $ \mathcal{C}(NSHG)=\{E_i\}~\text{is an neutrosophic SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^i~\text{is an neutrosophic SuperHyperGirth SuperHyperPolynomial.} \ \ \mathcal{C}(NSHG)=\{V_i\}~\text{is an neutrosophic R-SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^I~{\small\text{is an neutrosophic R-SuperHyperGirth SuperHyperPolynomial.}} $ The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices], is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], is an neutrosophic SuperHyperGirth $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is an neutrosophic type-SuperHyperSet with the maximum neutrosophic cardinality of an neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are not only four neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperGirth isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperGirth is an neutrosophic SuperHyperSet includes only less than four neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], doesn't have less than four SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth isn't up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], isn't the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], is an neutrosophic SuperHyperGirth $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperGirth and it's an neutrosophic SuperHyperGirth . Since it 's the maximum neutrosophic cardinality of an neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are only less than four neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, thus the obvious neutrosophic SuperHyperGirth, is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth, is: ,is the neutrosophic SuperHyperSet, is: does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperGirth amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the neutrosophic SuperHyperGirth , is only and only. A basic familiarity with neutrosophic SuperHyperGirth theory, SuperHyperGraphs, and neutrosophic SuperHyperGraphs theory are proposed.

The research is on the SuperHyperGirth and the neutrosophic SuperHyperGirth. A SuperHyperGraph has SuperHyperGirth where it’s the longest SuperHyperCycle. To get structural examples and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph based on SuperHyperGirth. It’s the main. It’ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. This SuperHyperClass is officially called “SuperHyperFlower”. If there’s a need to have all SuperHyperCycles until the SuperHyperGirth, then it’s officially called “SuperHyperOrder” but otherwise, it isn’t SuperHyperOrder. There are two instances about the clarifications for the main definition titled “SuperHyperGirth”. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on SuperHyperGirth and they’re called “SuperHyperFlower.” A SuperHyperGraph has “neutrosophic SuperHyperGirth” where it’s the strongest [the maximum value from all SuperHyperCycles amid the minimum value amid all SuperHyperEdges from a SuperHyperCycle.] SuperHyperCycle. In “Cancer’s Recognitions”, the aim is to find either the longest SuperHyperCycle or the strongest SuperHyperCycle in those neutrosophic SuperHyperModels. For the longest SuperHyperCycle, called SuperHyperGirth, and the strongest SuperHyperCycle, called neutrosophic SuperHyperGirth, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it’s not enough since it’s essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, assume a SuperHyperGraph. Then a “SuperHyperForcing” Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex; a “neutrosophic SuperHyperForcing” Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum neutrosophic cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. Assume a SuperHyperGraph. Then a “SuperHyperForcing” Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex; a “neutrosophic SuperHyperForcing” Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum neutrosophic cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. Assume a SuperHyperGraph. Then an “δ−SuperHyperForcing” is a minimal SuperHyperForcing of SuperHyperVertices with minimum cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of s ∈ S : |S∩N(s)|>|S∩(V \N(s))|+δ, |S∩N(s)|<|S∩(V \N(s))|+δ.Thefirst Expression, holds if S is an “δ−SuperHyperOffensive”. And the second Expression, holds if S is an “δ−SuperHyperDefensive”; a“neutrosophic δ−SuperHyperForcing” is a minimal neutrosophic SuperHyperForcing of SuperHyperVertices with minimum neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of s ∈ S : |S ∩ N(s)|neutrosophic > |S ∩ (V \ N (s))|neutrosophic + δ, |S ∩ N (s)|neutrosophic < |S ∩ (V \ N (s))|neutrosophic + δ. The first Expression, holds if S is a “neutrosophic δ−SuperHyperOffensive”. And the second Expression, holds if S is a “neutrosophic δ−SuperHyperDefensive”. It’s useful to define “neutrosophic” version of SuperHyperForcing. Since there’s more ways to get type-results to make SuperHyperForcing more understandable. For the sake of having neutrosophic SuperHyperForcing, there’s a need to “redefine” the notion of “SuperHyperForcing”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotions, namely, SuperHyperAlliances and Neutrosophic SuperHyperAlliances. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The “Cancer’s Recognitions” are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called “SuperHyperVertex” but the relations amid them all officially called “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic SuperHyperGraph” are chosen and elected to research about “Cancer’s Recognitions”. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and “Cancer’s Recognitions”. Some avenues are posed to pursue this research. It’s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. An “SuperHyperAlliance” is a minimal SuperHyperSet of SuperHyperVertices with minimum cardinality such that either of the following expressions hold for the cardinalities of SuperHyperNeighbors of s∈S:,|S∩N(s)|>|S∩(V \N(s))|,and|S∩N(s)|<|S∩(V \N(s))|.Thefirst Expression, holds if S is SuperHyperOffensive. And the second Expression, holds if S is “SuperHyperDefensive”. It’s useful to define “neutrosophic” version of SuperHyperAlliances. Since there’s more ways to get type-results to make SuperHyperAlliances more understandable. For the sake of having neutrosophic SuperHyperAlliances, there’s a need to “redefine” the notion of “SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a SuperHyperAlliance. It’s redefined neutrosophic SuperHyperAlliance if the mentioned Table holds, concerning, “The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph” with the key points, “The Values of The Vertices & The Number of Position in Alphabet”, “The Values of The SuperVertices&The Minimum Values of Its Vertices”, “The Values of The Edges&The Minimum Values of Its Vertices”, “The Values of The HyperEdges&The Minimum Values of Its Vertices”, “The Values of The SuperHyperEdges&The Minimum Values of Its Endpoints”. To get structural examples and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph based on SuperHyperAlliances. It’s the main. It’ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there’s a need to have all SuperHyperConnectivities until the SuperHyperAlliances, then it’s officially called “SuperHyperAlliances” but otherwise, it isn’t SuperHyperAlliances. There are some instances about the clarifications for the main definition titled “SuperHyperAlliances”. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on SuperHyperAlliances. For the sake of having neutrosophic SuperHyperAlliances, there’s a need to “redefine” the notion of “neutrosophic SuperHyperAlliances” and “neutrosophic SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. It’s redefined “neutrosophic SuperHyperGraph” if the intended Table holds. And SuperHyperAlliances are redefined “neutrosophic SuperHyperAlliances” if the intended Table holds. It’s useful to define “neutrosophic” version of SuperHyperClasses. Since there’s more ways to get neutrosophic type-results to make neutrosophic SuperHyperAlliances more understandable. Assume a neutrosophic SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are “neutrosophic SuperHyperPath”, “neutrosophic SuperHyperCycle”, “neutrosophic SuperHyperStar”, “neutrosophic SuperHyperBipartite”, “neutrosophic SuperHyperMultiPartite”, and “neutrosophic SuperHyperWheel” if the intended Table holds. A SuperHyperGraph has “neutrosophic SuperHyperAlliances” where it’s the strongest [the maximum neutrosophic value from all SuperHyperAlliances amid the maximum value amid all SuperHyperVertices from a SuperHyperAlliances.] SuperHyperAlliances. A graph is SuperHyperUniform if it’s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s only one SuperVertex as intersection amid all SuperHyperEdges; it’s SuperHyperBipartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this SuperHyperModel, The “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperVertices” and the common and intended properties between “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called “neutrosophic”. In the future research, the foundation will be based on the “Cancer’s Recognitions” and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it’s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn’t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it’s said to be neutrosophic SuperHyperGraph] to have convenient perception on what’s happened and what’s done. There are some specific models, which are well-known and they’ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). The aim is to find either the longest SuperHyperAlliances or the strongest SuperHyperAlliances in those neutrosophic SuperHyperModels. For the longest SuperHyperAlliances, called SuperHyperAlliances, and the strongest SuperHyperCycle, called neutrosophic SuperHyperAlliances, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it’s not enough since it’s essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotions, namely, SuperHyperDefensive SuperHyperAlliances and Neutrosophic SuperHyperDefensive SuperHyperAlliances. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The “Cancer’s Recognitions” are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called “SuperHyperVertex” but the relations amid them all officially called “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic SuperHyperGraph” are chosen and elected to research about “Cancer’s Recognitions”. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and “Cancer’s Recognitions”. Some avenues are posed to pursue this research. It’s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. An “SuperHyperAlliance” is a minimal SuperHyperSet of SuperHyperVertices with minimum cardinality such that either of the following expressions hold for the cardinalities of SuperHyperNeighbors of s∈S:,|S∩N(s)|>|S∩(V \N(s))|,and|S∩N(s)|<|S∩(V \N(s))|.Thefirst Expression, holds if S is SuperHyperOffensive. And the second Expression, holds if S is “SuperHyperDefensive”. It’s useful to define “neutrosophic” version of SuperHyperDefensive SuperHyperAlliances. Since there’s more ways to get type-results to make SuperHyperDefensive SuperHyperAlliances more understandable. For the sake of having neutrosophic SuperHyperDefensive SuperHyperAlliances, there’s a need to “redefine” the notion of “SuperHyperDefensive SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a SuperHyperAlliance. It’s redefined neutrosophic SuperHyperAlliance if the mentioned Table holds, concerning, “The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph” with the key points, “The Values of The Vertices & The Number of Position in Alphabet”, “The Values of The SuperVertices&The Minimum Values of Its Vertices”, “The Values of The Edges&The Minimum Values of Its Vertices”, “The Values of The HyperEdges&The Minimum Values of Its Vertices”, “The Values of The SuperHyperEdges&The Minimum Values of Its Endpoints”. To get structural examples and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph based on SuperHyperDefensive SuperHyperAlliances. It’s the main. It’ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there’s a need to have all SuperHyperConnectivities until the SuperHyperDefensive SuperHyperAlliances, then it’s officially called “SuperHyperDefensive SuperHyperAlliances” but otherwise, it isn’t SuperHyperDefensive SuperHyperAlliances. There are some instances about the clarifications for the main definition titled “SuperHyperDefensive SuperHyperAlliances”. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on SuperHyperDefensive SuperHyperAlliances. For the sake of having neutrosophic SuperHyperDefensive SuperHyperAlliances, there’s a need to “redefine” the notion of “neutrosophic SuperHyperDefensive SuperHyperAlliances” and “neutrosophic SuperHyperDefensive SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. It’s redefined “neutrosophic SuperHyperGraph” if the intended Table holds. And SuperHyperDefensive SuperHyperAlliances are redefined “neutrosophic SuperHyperDefensive SuperHyperAlliances” if the intended Table holds. It’s useful to define “neutrosophic” version of SuperHyperClasses. Since there’s more ways to get neutrosophic type-results to make neutrosophic SuperHyperDefensive SuperHyperAlliances more understandable. Assume a neutrosophic SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are “neutrosophic SuperHyperPath”, “neutrosophic SuperHyperCycle”, “neutrosophic SuperHyperStar”, “neutrosophic SuperHyperBipartite”, “neutrosophic SuperHyperMultiPartite”, and “neutrosophic SuperHyperWheel” if the intended Table holds. A SuperHyperGraph has “neutrosophic SuperHyperDefensive SuperHyperAlliances” where it’s the strongest [the maximum neutrosophic value from all SuperHyperDefensive SuperHyperAlliances amid the maximum value amid all SuperHyperVertices from a SuperHyperDefensive SuperHyperAlliances.] SuperHyperDefensive SuperHyperAlliances. A graph is SuperHyperUniform if it’s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s only one SuperVertex as intersection amid all SuperHyperEdges; it’s SuperHyperBipartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this SuperHyperModel, The “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperVertices” and the common and intended properties between “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called “neutrosophic”. In the future research, the foundation will be based on the “Cancer’s Recognitions” and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it’s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn’t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it’s said to be neutrosophic SuperHyperGraph] to have convenient perception on what’s happened and what’s done. There are some specific models, which are well-known and they’ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). The aim is to find either the longest SuperHyperDefensive SuperHyperAlliances or the strongest SuperHyperDefensive SuperHyperAlliances in those neutrosophic SuperHyperModels. For the longest SuperHyperDefensive SuperHyperAlliances, called SuperHyperDefensive SuperHyperAlliances, and the strongest SuperHyperCycle, called neutrosophic SuperHyperDefensive SuperHyperAlliances, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it’s not enough since it’s essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

in this research, new setting is introduced for new SuperHyperNotion, namely, Neutrosophic SuperHyperStable. In this research article, there are some research segments for ``Neutrosophic SuperHyperStable'' about some researches on neutrosophic SuperHyperStable. With researches on the basic properties, the research article starts to make neutrosophic SuperHyperStable theory more understandable. Assume a neutrosophic SuperHyperGraph. Then a ``neutrosophic SuperHyperStable'' $\mathcal{I}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotion, namely, 11 Neutrosophic 1-failed SuperHyperForcing. Two different types of SuperHyperDefinitions 12 are debut for them but the research goes further and the SuperHyperNotion, 13 SuperHyperUniform, and SuperHyperClass based on that are well-defined and 14 well-reviewed. The literature review is implemented in the whole of this research. For 15 shining the elegancy and the significancy of this research, the comparison between this 16 SuperHyperNotion with other SuperHyperNotions and fundamental 17 SuperHyperNumbers are featured. The definitions are followed by the examples and the 18 instances thus the clarifications are driven with different tools. The applications are 19 figured out to make sense about the theoretical aspect of this ongoing research. The 20 “Cancer’s Neutrosophic Recognition” are the under research to figure out the challenges 21 make sense about ongoing and upcoming research. The special case is up. The cells are 22 viewed in the deemed ways. There are different types of them. Some of them are 23 individuals and some of them are well-modeled by the group of cells. These types are all 24 officially called “SuperHyperVertex” but the relations amid them all officially called 25 “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic 26 SuperHyperGraph” are chosen and elected to research about “Cancer’s Neutrosophic 27 Recognition”. Thus these complex and dense SuperHyperModels open up some avenues 28 to research on theoretical segments and “Cancer’s Neutrosophic Recognition”. Some 29 avenues are posed to pursue this research. It’s also officially collected in the form of 30 some questions and some problems. Assume a SuperHyperGraph. Then a “1-failed 31 SuperHyperForcing” Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) 32 is the maximum cardinality of a SuperHyperSet S of black SuperHyperVertices 33 (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) isn’t 34 turned black after finitely many applications of “the color-change rule”: a white 35 SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white 36 SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred 37 by “1-” about the usage of any black SuperHyperVertex only once to act on white 38 SuperHyperVertex to be black SuperHyperVertex; a “neutrosophic 1-failed 39 SuperHyperForcing” Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) 40 is the maximum neutrosophic cardinality of a SuperHyperSet S of black 41 SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such 42 that V (G) isn’t turned black after finitely many applications of “the color-change rule”: 43 a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only 44 1/128 white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is 45 referred by “1-” about the usage of any black SuperHyperVertex only once to act on 46 white SuperHyperVertex to be black SuperHyperVertex. Assume a SuperHyperGraph. 47 Then an “δ−1-failed SuperHyperForcing” is a maximal 1-failed SuperHyperForcing of 48 SuperHyperVertices with maximum cardinality such that either of the following 49 expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of s ∈ S : 50 |S ∩N(s)| > |S ∩(V \N(s))|+δ, |S ∩N(s)| < |S ∩(V \N(s))|+δ. The first Expression, 51 holds if S is an “δ−SuperHyperOffensive”. And the second Expression, holds if S is an 52 “δ−SuperHyperDefensive”; a“neutrosophic δ−1-failed SuperHyperForcing” is a maximal 53 neutrosophic 1-failed SuperHyperForcing of SuperHyperVertices with maximum 54 neutrosophic cardinality such that either of the following expressions hold for the 55 neutrosophic cardinalities of SuperHyperNeighbors of s ∈ S : |S ∩ N(s)|neutrosophic > 56 |S ∩ (V \ N (s))|neutrosophic + δ, |S ∩ N (s)|neutrosophic < |S ∩ (V \ N (s))|neutrosophic + δ. 57 The first Expression, holds if S is a “neutrosophic δ−SuperHyperOffensive”. And the 58 second Expression, holds if S is a “neutrosophic δ−SuperHyperDefensive”. It’s useful to 59 define “neutrosophic” version of 1-failed SuperHyperForcing. Since there’s more ways to 60 get type-results to make 1-failed SuperHyperForcing more understandable. For the sake 61 of having neutrosophic 1-failed SuperHyperForcing, there’s a need to “redefine” the 62 notion of “1-failed SuperHyperForcing”. The SuperHyperVertices and the 63 SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this 64 procedure, there’s the usage of the position of labels to assign to the values. Assume a 65 1-failed SuperHyperForcing. It’s redefined neutrosophic 1-failed SuperHyperForcing if 66 the mentioned Table holds, concerning, “The Values of Vertices, SuperVertices, Edges, 67 HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph” 68 with the key points, “The Values of The Vertices & The Number of Position in 69 Alphabet”, “The Values of The SuperVertices&The maximum Values of Its Vertices”, 70 “The Values of The Edges&The maximum Values of Its Vertices”, “The Values of The 71 HyperEdges&The maximum Values of Its Vertices”, “The Values of The 72 SuperHyperEdges&The maximum Values of Its Endpoints”. To get structural examples 73 and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph 74 based on 1-failed SuperHyperForcing. It’s the main. It’ll be disciplinary to have the 75 foundation of previous definition in the kind of SuperHyperClass. If there’s a need to 76 have all SuperHyperConnectivities until the 1-failed SuperHyperForcing, then it’s 77 officially called “1-failed SuperHyperForcing” but otherwise, it isn’t 1-failed 78 SuperHyperForcing. There are some instances about the clarifications for the main 79 definition titled “1-failed SuperHyperForcing”. These two examples get more scrutiny 80 and discernment since there are characterized in the disciplinary ways of the 81 SuperHyperClass based on 1-failed SuperHyperForcing. For the sake of having 82 neutrosophic 1-failed SuperHyperForcing, there’s a need to “redefine” the notion of 83 “neutrosophic 1-failed SuperHyperForcing” and “neutrosophic 1-failed 84 SuperHyperForcing”. The SuperHyperVertices and the SuperHyperEdges are assigned 85 by the labels from the letters of the alphabets. In this procedure, there’s the usage of 86 the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. 87 It’s redefined “neutrosophic SuperHyperGraph” if the intended Table holds. And 88 1-failed SuperHyperForcing are redefined “neutrosophic 1-failed SuperHyperForcing” if 89 the intended Table holds. It’s useful to define “neutrosophic” version of 90 SuperHyperClasses. Since there’s more ways to get neutrosophic type-results to make 91 neutrosophic 1-failed SuperHyperForcing more understandable. Assume a neutrosophic 92 SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended 93 Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, 94 SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are 95 “neutrosophic SuperHyperPath”, “neutrosophic SuperHyperCycle”, “neutrosophic 96 SuperHyperStar”, “neutrosophic SuperHyperBipartite”, “neutrosophic 97 2/128 SuperHyperMultiPartite”, and “neutrosophic SuperHyperWheel” if the intended Table 98 holds. A SuperHyperGraph has “neutrosophic 1-failed SuperHyperForcing” where it’s 99 the strongest [the maximum neutrosophic value from all 1-failed SuperHyperForcing 100 amid the maximum value amid all SuperHyperVertices from a 1-failed 101 SuperHyperForcing.] 1-failed SuperHyperForcing. A graph is SuperHyperUniform if it’s 102 SuperHyperGraph and the number of elements of SuperHyperEdges are the same. 103 Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as 104 follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given 105 SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one 106 SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s 107 only one SuperVertex as intersection amid all SuperHyperEdges; it’s 108 SuperHyperBipartite it’s only one SuperVertex as intersection amid two given 109 SuperHyperEdges and these SuperVertices, forming two separate sets, has no 110 SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as 111 intersection amid two given SuperHyperEdges and these SuperVertices, forming multi 112 separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one 113 SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has 114 one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes 115 the specific designs and the specific architectures. The SuperHyperModel is officially 116 called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this 117 SuperHyperModel, The “specific” cells and “specific group” of cells are 118 SuperHyperModeled as “SuperHyperVertices” and the common and intended properties 119 between “specific” cells and “specific group” of cells are SuperHyperModeled as 120 “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, 121 indeterminacy, and neutrality to have more precise SuperHyperModel which in this case 122 the SuperHyperModel is called “neutrosophic”. In the future research, the foundation 123 will be based on the “Cancer’s Neutrosophic Recognition” and the results and the 124 definitions will be introduced in redeemed ways. The neutrosophic recognition of the 125 cancer in the long-term function. The specific region has been assigned by the model 126 [it’s called SuperHyperGraph] and the long cycle of the move from the cancer is 127 identified by this research. Sometimes the move of the cancer hasn’t be easily identified 128 since there are some determinacy, indeterminacy and neutrality about the moves and 129 the effects of the cancer on that region; this event leads us to choose another model [it’s 130 said to be neutrosophic SuperHyperGraph] to have convenient perception on what’s 131 happened and what’s done. There are some specific models, which are well-known and 132 they’ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves 133 and the traces of the cancer on the complex tracks and between complicated groups of 134 cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, 135 SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). 136 The aim is to find either the longest 1-failed SuperHyperForcing or the strongest 137 1-failed SuperHyperForcing in those neutrosophic SuperHyperModels. For the longest 138 1-failed SuperHyperForcing, called 1-failed SuperHyperForcing, and the strongest 139 SuperHyperCycle, called neutrosophic 1-failed SuperHyperForcing, some general results 140 are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have 141 only two SuperHyperEdges but it’s not enough since it’s essential to have at least three 142 SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of 143 any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, 144 literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph 145 theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotions, namely, an 1-failed SuperHyperForcing and Neutrosophic 1-failed SuperHyperForcing. Assume a SuperHyperGraph. Then an ``1-failed SuperHyperForcing'' $\mathcal{Z}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of black SuperHyperVertices (whereas SuperHyperVertices in $V(G) \setminus S$ are colored white) such that $V(G)$ isn't turned black after finitely many applications of ``the color-change rule'': a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred by ``1-'' about the usage of any black SuperHyperVertex only once to act on white SuperHyperVertex to be black SuperHyperVertex; a ``neutrosophic 1-failed SuperHyperForcing'' $\mathcal{Z}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a SuperHyperSet $S$ of black SuperHyperVertices (whereas SuperHyperVertices in $V(G) \setminus S$ are colored white) such that $V(G)$ isn't turned black after finitely many applications of ``the color-change rule'': a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred by ``1-'' about the usage of any black SuperHyperVertex only once to act on white SuperHyperVertex to be black SuperHyperVertex. Assume a SuperHyperGraph. Then an ``$\delta-$1-failed SuperHyperForcing'' is a \underline{maximal} 1-failed SuperHyperForcing of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$1-failed SuperHyperForcing'' is a \underline{maximal} neutrosophic 1-failed SuperHyperForcing of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotions, namely, an SuperHyperStable and Neutrosophic SuperHyperStable. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer's Recognitions'' are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex'' but the relations amid them all officially called ``SuperHyperEdge''. The frameworks ``SuperHyperGraph'' and ``neutrosophic SuperHyperGraph'' are chosen and elected to research about ``Cancer's Recognitions''. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer's Recognitions''. Some avenues are posed to pursue this research. It's also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Then a``SuperHyperStable'' $\mathcal{I}(NSHG)$ for a SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's no SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$SuperHyperStable'' is a \underline{maximal} SuperHyperStable of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$SuperHyperStable'' is a \underline{maximal} neutrosophic SuperHyperStable of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. It's useful to define a ``neutrosophic'' version of an SuperHyperStable. Since there's more ways to get type-results to make an SuperHyperStable more understandable. For the sake of having neutrosophic SuperHyperStable, there's a need to ``redefine'' the notion of an ``SuperHyperStable''. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there's the usage of the position of labels to assign to the values. Assume an SuperHyperStable. It's redefined a neutrosophic SuperHyperStable if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph'' with the key points, ``The Values of The Vertices \& The Number of Position in Alphabet'', ``The Values of The SuperVertices\&The maximum Values of Its Vertices'', ``The Values of The Edges\&The maximum Values of Its Vertices'', ``The Values of The HyperEdges\&The maximum Values of Its Vertices'', ``The Values of The SuperHyperEdges\&The maximum Values of Its Endpoints''. To get structural examples and instances, I'm going to introduce the next SuperHyperClass of SuperHyperGraph based on an SuperHyperStable. It's the main. It'll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there's a need to have all SuperHyperConnectivities until the SuperHyperStable, then it's officially called an ``SuperHyperStable'' but otherwise, it isn't an SuperHyperStable. There are some instances about the clarifications for the main definition titled an ``SuperHyperStable''. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on an SuperHyperStable. For the sake of having a neutrosophic SuperHyperStable, there's a need to ``redefine'' the notion of a ``neutrosophic SuperHyperStable'' and a ``neutrosophic SuperHyperStable''. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there's the usage of the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. It's redefined ``neutrosophic SuperHyperGraph'' if the intended Table holds. And an SuperHyperStable are redefined to an ``neutrosophic SuperHyperStable'' if the intended Table holds. It's useful to define ``neutrosophic'' version of SuperHyperClasses. Since there's more ways to get neutrosophic type-results to make a neutrosophic SuperHyperStable more understandable. Assume a neutrosophic SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are ``neutrosophic SuperHyperPath'', ``neutrosophic SuperHyperCycle'', ``neutrosophic SuperHyperStar'', ``neutrosophic SuperHyperBipartite'', ``neutrosophic SuperHyperMultiPartite'', and ``neutrosophic SuperHyperWheel'' if the intended Table holds. A SuperHyperGraph has a ``neutrosophic SuperHyperStable'' where it's the strongest [the maximum neutrosophic value from all the SuperHyperStable amid the maximum value amid all SuperHyperVertices from an SuperHyperStable.] SuperHyperStable. A graph is a SuperHyperUniform if it's a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It's SuperHyperPath if it's only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it's SuperHyperCycle if it's only one SuperVertex as intersection amid two given SuperHyperEdges; it's SuperHyperStar it's only one SuperVertex as intersection amid all SuperHyperEdges; it's SuperHyperBipartite it's only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it's SuperHyperMultiPartite it's only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it's a SuperHyperWheel if it's only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph'' and ``Neutrosophic SuperHyperGraph''. In this SuperHyperModel, The ``specific'' cells and ``specific group'' of cells are SuperHyperModeled as ``SuperHyperVertices'' and the common and intended properties between ``specific'' cells and ``specific group'' of cells are SuperHyperModeled as ``SuperHyperEdges''. Sometimes, it's useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``neutrosophic''. In the future research, the foundation will be based on the ``Cancer's Recognitions'' and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it's called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn't be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it's said to be neutrosophic SuperHyperGraph] to have convenient perception on what's happened and what's done. There are some specific models, which are well-known and they've got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). The aim is to find either the longest SuperHyperStable or the strongest SuperHyperStable in those neutrosophic SuperHyperModels. For the longest SuperHyperStable, called SuperHyperStable, and the strongest SuperHyperCycle, called neutrosophic SuperHyperStable, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it's not enough since it's essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn't any formation of any SuperHyperCycle but literarily, it's the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn't form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

I introduce now for the first time the neutrosophic modal logic. The Neutrosophic Modal Logic includes the neutrosophic operators that express the modalities. It is an extension of neutrosophic predicate logic, and of neutrosophic propositional logic. In order for the paper to be self-contained, I also recall the etymology and definition of neutrosophy and of neutrosophic logic. Several examples are presented as well.

In this research, Assume a neutrosophic SuperHyperGraph. Then a ``Failed SuperHyperStable $\mathcal{I}(NSHG)$ for a SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common; a ``neutrosophic Failed SuperHyperStable'' $\mathcal{I}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's a neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperStable'' is a \underline{maximal} Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperStable'' is a \underline{maximal} neutrosophic Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme Failed SuperHyperClique theory, Neutrosophic Failed SuperHyperClique theory, and (Neutrosophic) SuperHyperGraphs theory are proposed.

In this research, assume a SuperHyperGraph. Then a neutrosophic SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; a neutrosophic SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient; a neutrosophic R-SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; a neutrosophic R-SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient. It's useful to define a ``neutrosophic'' version of a SuperHyperMatching . Since there's more ways to get type-results to make a SuperHyperMatching more understandable. For the sake of having neutrosophic SuperHyperMatching, there's a need to ``redefine'' the notion of a ``SuperHyperMatching ''. A basic familiarity with neutrosophic SuperHyperMatching theory, SuperHyperGraphs theory, and neutrosophic SuperHyperGraphs theory are proposed.

New setting is introduced to study neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhood of different vertices. Neighbor is a key term to have these notions. Having all possible edges amid vertices in a set is a key type of approach to have these notions namely neutrosophic failed-independent number and failed independent neutrosophic-number. Two numbers are obtained but now both settings leads to approach is on demand which is finding biggest set which have all vertices which are neighbors. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then failed independent number I(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum cardinality of a set S of vertices such that every two vertices of S are endpoints for an edge, simultaneously; failed independent neutrosophic-number In(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum neutrosophic cardinality of a set S of vertices such that every two vertices of S are endpoints for an edge, simultaneously. As concluding results, there are some statements, remarks, examples and clarifications about some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, complete-bipartite-neutrosophic graphs and complete-t-partite-neutrosophic graphs. The clarifications are also presented in both sections “Setting of Neutrosophic Failed-Independent Number,” and “Setting of Failed Independent Neutrosophic-Number,” for introduced results and used classes. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhoods of vertices. In path-neutrosophic graphs, two neighbors, form maximal set but with slightly differences, in cycle-neutrosophic graphs, two neighbors forms maximal set. Other classes have same approaches. In complete-neutrosophic graphs, a set of all vertices leads us to neutrosophic failed-independent number and failed independent neutrosophic-number. In star-neutrosophic graphs, a set of vertices containing only center and one other vertex, makes maximal set. In complete-bipartite-neutrosophic graphs, a set of vertices including two vertices from different parts makes intended set but with slightly differences, in complete-t-partite-neutrosophic graphs, a set of t vertices from different parts makes intended set. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. Using basic set to extend this set to set of all vertices has key role to have these notions in the form of neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhood of vertices. The cardinality of a set has eligibility to neutrosophic failed-independent number but the neutrosophic cardinality of a set has eligibility to call failed independent neutrosophic-number. Some results get more frameworks and perspective about these definitions. The way in that, two vertices have connections amid each other, opens the way to do some approaches. A vertex could affect on other vertex but there’s no usage of edges. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New setting is introduced to study quasi-degree and quasi-co-degree arising from co-neighborhood. quasi-degree and quasi-co-degree is about a vertex which are applied into the setting of neutrosophic graphs. . The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs and star-neutrosophic graphs, complete-bipartite-neutrosophic graphs and complete-multipartite-neutrosophic graphs are investigated in the terms of a vertex which is called either quasi-degree or quasi-co-degree. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form quasi-degree and quasi-co-degree. Quasi-degree is a value of a vertex which is maximum amid all values of vertices which are neighbors to a fixed vertex. Quasi-co-degree is a value of an edge which is maximum amid all values of edges which are neighbors to a fixed vertex but corresponded vertex is representative for this notion. Using different values which are related to a vertex inspire us to focus on edge and vertices which are corresponded to a fixed vertex. The notion of neighborhood is used to collect either vertices are titled neighbors or edges are incident to fixed vertex. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definitions are provided. Using fixed vertex has key role to have these notions in the form of vertex or edge. The value of an edge has eligibility to call quasi-co-degree but the value of a vertex has eligibility to call quasi-degree. Some results get more frameworks and perspective about these definitions. The way in that, two vertices have connection together, open the way to define neighborhood and co-neighborhood. The maximum values in neighborhood and co-neighborhood introduces quasi-degree and quasi-co-degree, respectively. New name is chosen from degree. Since amid all vertices with different degrees, one vertex is chosen. In other words, one vertex is fixed and its degree turns out quasi-degree where two degrees could be assigned to a vertex. Degree of edges and degree of vertices. The number of edges which are incident to the vertex and the number of vertices which are neighbors to the vertex. Degree and co-degree are the notions which are transformed to use in quasi-style. Two neutrosophic values introduce two neutrosophic vertices separately in each settings. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to purse this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

Many various using of this new-born fuzzy model for solving real-world problems and urgent requirements involve introducing new concept for analyzing the situations which leads to solve them by proper, quick and ecient method based on statistical data. This gap between the model and its solution cause that we introduce nikfar domination in neutrosophic graphs as creative and eective tool for studying a few selective vertices of this model instead of all ones by using special edges. Being special selection of these edges aect to achieve quick and proper solution to these problems. Domination hasn't ever been introduced. So we don't have any comparison with another de nitions. The most used graphs which have properties of being complete, empty, bipartite, tree and like stu and they also achieve the names for themselves, are studied as fuzzy models for getting nikfar dominating set or at least becoming so close to it. We also get the relations between this special edge which plays main role in doing dominating with other special types of edges of graph like bridges. Finally, the relation between this number with other special numbers and characteristic of graph like order are discussed.

In this research article, the notions of SuperHyperDominating and SuperHyperResolving are defined in the setting of neutrosophic SuperHyperGraphs. Some ideas are introduced on both notions of SuperHyperDominating and SuperHyperResolving, simultaneously and as the same with each other. Some neutrosophic SuperHyperClasses are defined based on the notion, SuperHyperResolving. The terms of duality, totality, perfectness, connectedness, and stable, are added to basic framework and initial notions, SuperHyperDominating and SuperHyperResolving but the concentration is on the “perfectness” to figure out what’s going on when for all targeted SuperHyperVertices, there’s only one SuperHyperVertex in the intended set. There are some instances and some clarifications to make sense about what’s happened and what’s done in the starting definitions. The key point is about the minimum sets. There are some questions and some problems to be taken as some avenues to pursue this study and this research. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

New setting is introduced to study chromatic number. Different types of chromatic numbers and neutrosophic chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different types of edges from connectedness in same neutrosophic graphs and in modified neutrosophic graphs to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute types of chromatic numbers. This specific relation amid edges is necessary to compute both types of chromatic number concerning the number of representative in the set of representatives and types of neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no intended edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study chromatic number. vital chromatic number and n-vital chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using vital edge from connectedness to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute vital chromatic number. This specific relation amid edges is necessary to compute both vital chromatic number concerning the number of representative in the set of representatives and n-vital chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no vital edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study chromatic number. Neutrosophic chromatic number and chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assigns to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using strong edge to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute neutrosophic chromatic number. This specific relation amid edges is necessary to compute both chromatic number concerning the number of representative in the set of representatives and neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no strong edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study co-neighborhood, neutrosophic t-neighborhood, neutrosophic quasi-vertex set, neutrosophic quasi-order, neutrosophic neighborhood, neutrosophic co-t-neighborhood, neutrosophic quasi-edge set, neutrosophic quasi-size, Neutrosophic number, neutrosophic co-neighborhood, co-neutrosophic number, quasi-number and quasi-co-number. Some classes of neutrosophic graphs are investigated.

New setting is introduced to study failed zero-forcing number and failed zero-forcing neutrosophic-number. Leaf-like is a key term to have these notions. Forcing a vertex to change its color is a type of approach to force that vertex to be zero-like. Forcing a vertex which is only neighbor for zero-like vertex to be zero-like vertex but now reverse approach is on demand which is finding biggest set which doesn’t force. LetNTG : (V,E,σ,μ) be a neutrosophic graph. Then failed zero-forcing number Z(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximal cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) isn’t turned black after finitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Failed zero-forcing neutrosophic-number Zn(NTG) for a neutrosophic graphNTG : (V,E,σ,μ) is maximal neutrosophic cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) isn’t turned black afterfinitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Failed zero-forcing number and failed zero-forcing neutrosophic-number are about a set of vertices which are applied into the setting of neutrosophic graphs. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, bipartite-neutrosophic graphs, and t-partite-neutrosophic graphs are investigated in the terms of maximal set which forms both of failed zero-forcing number and failed zero-forcing neutrosophic-number. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form failed zero-forcing number and failed zero-forcing neutrosophic-number. In path-neutrosophic graphs, the set of vertices such that every given two vertices in the set, have distance at least two, forms maximal set but with slightly differences, in cycle-neutrosophic graphs, the set of vertices such that every given two vertices in the set, have distance at least two, forms maximal set. Other classes have same approaches. In complete-neutrosophic graphs, a set of vertices excluding two vertices leads us to failed zero-forcing number and failed zero-forcing neutrosophic-number. In star-neutrosophic graphs, a set of vertices excluding only two vertices and containing center, makes maximal set. In complete-bipartite-neutrosophic graphs, a set of vertices excluding two vertices from same parts makes intended set but with slightly differences, in complete-t-partite-neutrosophic graphs, a set of vertices excluding two vertices from same parts makes intended set. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. Using basic set not to extend this set to set of all vertices has key role to have these notions in the form of failed zero-forcing number and failed zero-forcing neutrosophic-number. The cardinality of a set has eligibility to form failed zero-forcing number but the neutrosophic cardinality of a set has eligibility to call failed zero-forcing neutrosophic-number. Some results get more frameworks and perspective about these definitions. The way in that, two vertices don’t have unique connection together, opens the way to do some approaches. A vertex could affect on other vertex but there’s no usage of edges. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New setting is introduced to study the global powerful alliance. Global powerful alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global powerful alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs excluding empty, path, star, and wheel and containing complete, cycle and r-regular-strong are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is used in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-powerful-alliance number and minimal-global-powerful-alliance-neutrosophic number. Two different types of sets namely global-powerful alliance and minimal-global-powerful alliance are defined. Global-powerful alliance identifies the sets in general vision but minimal-global-powerful alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-powerful-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-powerful alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs has an open avenue, in the way that, the family only contains same classes of neutrosophic graphs. The results are about minimal-global-powerful alliance, minimal-global-powerful-alliance number and its corresponded sets, minimal-global-powerful-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-powerful alliances, minimal-t-powerful alliance, minimal-t-powerful-alliance number and its corresponded sets, minimal-t-powerful-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-t-powerful alliances. The connections amid t-powerful-alliances are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications and closing remarks. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global powerful alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set and reversely for non-members of set with less members in the way that the set is simultaneously t-offensive and(t-2)-defensive. A set is global if t=0. It leads us to the notion of global powerful alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New setting is introduced to study the global offensive alliance. Global offensive alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global offensive alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, star, and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is defined in new way. It’s first time to define this type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-offensive-alliance number and minimal-global-offensive-alliance-neutrosophic number. Two different types of sets namely global-offensive alliance and minimal-global-offensive alliance are defined. Global-offensive alliance identifies the sets in general vision but minimal-global-offensive alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-offensive-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-offensive alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs is studied in the way that, the family only contains same classes of neutrosophic graphs. Three types of family of neutrosophic graphs including m-family of neutrosophic stars with common neutrosophic vertex set, m-family of odd complete graphs with common neutrosophic vertex set, and m-family of odd complete graphs with common neutrosophic vertex set are studied. The results are about minimal-global-offensive alliance, minimal-global-offensive-alliance number and its corresponded sets, minimal-global-offensive-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-offensive alliances. The connection of global-offensive-alliances with dominating set and chromatic number are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, path, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global offensive alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set. It leads us to the notion of global offensive alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification(neutrosofication) of twin vertices but using crisp concept of antipodal vertices are another approaches of this study. Thus defining two notions concerning vertices which one of them is fuzzy(neutrosophic) titled twin and another is crisp titled antipodal to study the behaviors of cycles which are partitioned into even and odd, are concluded. Classes of cycles according to antipodal vertices are divided into two classes as even and odd. Parity of the number of edges in cycle causes to have two subsections under the section is entitled to antipodal vertices. In this study, the term dimension is introduced on fuzzy(neutrosophic) graphs. The locations of objects by a set of some junctions which have distinct distance from any couple of objects out of the set, are determined. Thus it’s possible to have the locations of objects outside of this set by assigning partial number to any objects. The classes of these specific graphs are chosen to obtain some results based on dimension. The types of crisp notions and fuzzy(neutrosophic) notions are used to make sense about the material of this study and the outline of this study uses some new notions which are crisp and fuzzy(neutrosophic). Some questions and problems are posed concerning ways to do further studies on this topic. Basic familiarities with fuzzy(neutrosophic) graph theory and graph theory are proposed for this article.

This article presents a new method of segmenting images with gray levels. The method is based on determining several thresholds for separation of gray levels. The determination of these thresholds is done using the certainty of the neutrosophic information. The concept of this method can be stated simply: to choose the local maximums for the neutrosophic certainty.

In this paper, a geometric model is introduced for Neutrosophic data problem for the first time. This model is based on neutrosophic sets and neutrosophic relations. Neutrosophic control points are defined according to these points, resulting in neutrosophic Bézier curves.

New setting is introduced to study resolving number and chromatic number alongside dominating number. Different types of procedures including set, optimal set, and optimal number alongside study on the family of neutrosophic hypergraphs are proposed in this way, some results are obtained. General classes of neutrosophic hypergraphs are used to obtains these numbers and the representatives of the colors, dominating sets and resolving sets. Using colors to assign to the vertices of neutrosophic hypergraphs and characterizing resolving sets and dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on neutrosophic hypergraphs to get new results about numbers and sets in the way that some numbers get understandable perspective. Family of neutrosophic hypergraphs are studied to investigate about the notions, dimension and coloring alongside domination in neutrosophic hypergraphs. In this way, sets of representatives of colors, resolving sets and dominating sets have key role. Optimal sets and optimal numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal ones. Simultaneously, three notions are applied into neutrosophic hypergraphs to get sensible results about their structures. Basic familiarities with neutrosophic hypergraphs theory and hypergraph theory are proposed for this article.

This article presents a new method of segmenting grayscale images by minimizing Shannon's neutrosophic entropy. For the proposed segmentation method, the neutrosophic information components, i.e., the degree of truth, the degree of neutrality and the degree of falsity are defined taking into account the belonging to the segmented regions and at the same time to the separation threshold area. The principle of the method is simple and easy to understand and can lead to multiple thresholds. The efficacy of the method is illustrated using some test gray level images. The experimental results show that the proposed method has good performance for segmentation with optimal gray level thresholds.

New setting is introduced to study types of coloring numbers, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Different types of procedures including neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs are proposed in this way, some results are obtained. General classes of neutrosophic hypergraphs are used to obtain chromatic number, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Using colors to assign to the vertices of neutrosophic hypergraphs and characterizing representatives of the colors are applied in neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on neutrosophic hypergraphs to get new results about number, degree and co-degree in the way that some number, degree and co-degree get understandable perspective. Neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs are studied to investigate about the notions, coloring, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs. In this way, sets of representatives of colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal ones. Simultaneously, notions chromatic number, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges are applied into neutrosophic hypergraphs, especially, neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs to get sensible results about their structures. Basic familiarities with neutrosophic hypergraphs theory and hypergraph theory are proposed for this article.

Neutrosophic cubic set is the hybridization of the concept of neutrosophic set and interval neutrosophic set. Neutrosophic cubic set has the capacity to express the hybrid information of both the interval neutrosophic set and the single valued neutrosophic set simultaneously. As newly defined, little research on the operations and applications of neutrosophic cubic sets appear in the current literature. In the present paper we propose the score, accuracy functions for neutrosophic cubic sets and prove their basic properties. We firstly develop TODIM method to solve multi attribute group decision making in neutrosophic cubic set environment, which we call NC-TODIM. Also, we solve a MAGDM problem using the proposed NC-TODIM method to show the applicability and effectiveness of the developed method. We also conduct sensitivity analysis to show the impact of ranking order of the alternatives for different values of attenuation factor of losses for multi-attribute group decision making problem.

In this research, assume a SuperHyperGraph. Then a ``Failed SuperHyperClique'' $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperClique'' is a \underline{maximal} Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperClique'' is a \underline{maximal} neutrosophic Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Neutrosophic Failed SuperHyperClique theory, SuperHyperGraphs theory, and Neutrosophic SuperHyperGraphs theory are proposed.

Neutrosophic cubic set (NCS) is one of the important family members of neutrosophic hybrid sets. Neutrosophic cubic set has more strength than other family members of neutrosophic hybrid sets to express incomplete information due to the presence of interval valued neutrosophic set (IVNS) and single valued neutrosophic set (SVNS) in its structure. Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. In this paper we first define a new cross entropy measure under NCSs environment which we call NC- cross entropy measure. We investigate the basic properties of NC-cross entropy. We also propose weighted NC-cross entropy and investigate its basic properties. We develop a novel multi attribute decision making (MADM) strategy based on weighted NC-cross entropy. To show the feasibility and applicability, we solve a MADM problem using the proposed strategy.

New setting is introduced to study the alliances. Alliances are about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define these notions. Also, neighborhood is defined based on the edges, strong edges and some edges which are coming from connectedness. These three types of edges get a framework as neighborhood and after that, too close vertices have key role to define offensive alliance, defensive alliance, t-offensive alliance, and t-defensive alliance based on three types of edges, common edges, strong edges and some edges which are coming from connectedness. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, bipartite, t-partite, star and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study but it seems that analogous results are determined. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on different edges illustrate open way to get results. A set is alliance when two sets partitioning vertex set have uniform structure. All members of set have different amount of neighbors in the set and out of set. It leads us to the notion of offensive and defensive. New ideas, offensive alliance, defensive alliance, t-offensive alliance, t-defensive alliance, strong offensive alliance, strong defensive alliance, strong t-offensive alliance, strong t-defensive alliance, connected offensive alliance, connected defensive alliance, connected t-offensive alliance, and connected t-defensive alliance are introduced. Two numbers concerning cardinality and neutrosophic cardinality of alliances are introduced. A set is alliance when its complement make a relation in the terms of neighborhood. Different edges make different neighborhoods. Three types of edges are applied to define three styles of neighborhoods. General edges, strong edges and connected edges are used where connected edges are the edges arising from connectedness amid two endpoints of the edges. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for this notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

Single valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single valued neutrosophic cross entropy bears an asymmetrical behavior and produce an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under single valued neutrosophic set (SVNS) environment namely SN- cross entropy and prove its basic properties. Also we define weighted SN-cross entropy measure and investigate its basic properties. We develop a new multi attribute group decision making (MAGDM) strategy for ranking of the alternatives based on the proposed weighted SN-cross entropy measure between each alternative and the ideal alternative. Finally, a numerical example of MAGDM problem of investment potential is solved to show the validity and efficiency of proposed decision making strategy. We also present comparative anslysis of the obtained result with the results obtained form the existing solution strategies in the solution.

The concept of neutrosophic number is a significant mathematical tool to deal with real scientific problems because it can tackle indeterminate and incomplete information which exists generally in real problems. In this article, we use neutrosophic numbers (a + bI), where a and bI denote determinate component and indeterminate component respectively. We explore the situations in which the input information is needed to express in terms of neutrosophic numbers. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine unknown criteria weights. We define neutrosophic number harmonic mean operators and proved their basic properties. Then, we develop two novel MCGDM strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility and effectiveness of the proposed two strategies. Sensitivity analysis with variation of “I” on neutrosophic numbers is performed to demonstrate how the preference ranking order of alternatives is sensitive to the change of “I”. The efficiency of the developed strategies is ascertained by comparing the obtained results from the proposed strategies with the existing strategies in the literature.

The paper investigates some similarity measures in interval bipolar neutrosophic environment for multi-attribute decision making problems. At first, we define Hamming and Euclidean distances measures between interval bipolar neutrosophic sets and establish their basic properties. We also propose two similarity measures based on the Hamming and Euclidean distance functions. Using maximum and minimum operators, we define new similarity measures and prove their basic properties. Using the proposed similarity measures, we propose a novel multi attribute decision making strategy in interval bipolar neutrosophic set environment. Lastly, we solve an illustrative example of multi attribute decision making and present comparison analysis to show the feasibility, applicability and effectiveness of the proposed strategy.

New ideas on the framework of Neutrosophic SuperHyperGraph for different styles of Neutrosophic SuperHyper-Bipartite and Neutrosophic SuperHyper-Path are introduced. More instances and more clarifications alongside sufficient references.

In this research, assume a SuperHyperGraph. Then a ``Failed SuperHyperStable'' $\mathcal{I}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperStable'' is a \underline{maximal} Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperStable'' is a \underline{maximal} neutrosophic Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme Failed SuperHyperClique theory, Neutrosophic Failed SuperHyperClique theory, and (Neutrosophic) SuperHyperGraphs theory are proposed.

In this research, new setting is introduced for new notions, namely, SuperHyperDegree and Co-SuperHyperDegree. Two different types of definitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The cancer’s treatments are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called “SuperHyperVertex” but the relations amid them all officially called “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic SuperHyperGraph” are chosen and elected to research about “cancer’s treatments”. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and “cancer’s treatments”. Some avenues are posed to pursue this research. It’s also officially collected in the form of some questions and some problems. If there’s a SuperHyperEdge between two SuperHyperVertices, then these two SuperHyperVertices are called SuperHyperNeighbors. The number of SuperHyperNeighbors for a given SuperHyperVertex is called SuperHyperDegree. The number of common SuperHyperNeighbors for some SuperHyperVertices is called Co-SuperHyperDegree for them and used SuperHyperVertices are called Co-SuperHyperNeighbors. A graph is SuperHyperUniform if it’s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s only one SuperVertex as intersection amid all SuperHyperEdges; it’s SuperHyperBipartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The number of SuperHyperEdges for a given SuperHyperVertex is called SuperHyperDegree. The number of common SuperHyperEdges for some SuperHyperVertices is called Co-SuperHyperDegree for them. The number of SuperHyperVertices for a given SuperHyperEdge is called SuperHyperDegree. The number of common SuperHyperVertices for some SuperHyperEdges is called Co-SuperHyperDegree for them. The model proposes the specific designs. The model is officially called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this model, The “specific” cells and “specific group” of cells are modeled as “SuperHyperVertices” and the common and intended properties between “specific” cells and “specific group” of cells are modeled as “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise model which in this case the model is called “neutrosophic”. In the future research, the foundation will be based on the caner’s treatment and the results and the definitions will be introduced in redeemed ways. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, assume a SuperHyperGraph. Then an extreme SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperEdges such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge; a neutrosophic SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; an extreme SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the extreme SuperHyperPolynomial contains the coefficients defined as the number of the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperEdges such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge and the power is corresponded to its coefficient; a neutrosophic SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient; an extreme R-SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperVertices such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge; a neutrosophic R-SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; an extreme R-SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the extreme SuperHyperPolynomial contains the coefficients defined as the number of the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperVertices such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge and the power is corresponded to its coefficient; a neutrosophic R-SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient. Assume a SuperHyperGraph. Then $\delta-$SuperHyperMatching is a maximal of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a neutrosophic $\delta-$SuperHyperMatching is a maximal neutrosophic of SuperHyperVertices with maximum neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta;$ and $ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a neutrosophic $\delta-$SuperHyperDefensive It's useful to define a ``neutrosophic'' version of a SuperHyperMatching . Since there's more ways to get type-results to make a SuperHyperMatching more understandable. For the sake of having neutrosophic SuperHyperMatching, there's a need to ``redefine'' the notion of a ``SuperHyperMatching ''. A basic familiarity with Extreme SuperHyperMatching theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed.

New ideas on the framework of Neutrosophic SuperHyperGraph for different styles of Neutrosophic SuperHyper-Wheel and Neutrosophic SuperHyper-Star are introduced. More instances and more clarifications alongside sufficient references are featured with a specific type of independency of SuperHyperVertices.

Bipolar neutrosophic set is an important extension of bipolar fuzzy set. This set is a hybridization of bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent positive membership functions and three independent negative membership functions. In this paper, we develop cross entropy measures of bipolar neutrosophic sets and prove its properties. We also define cross entropy measures of interval bipolar neutrosophic sets and prove its properties. Thereafter, we develop two novel multi-attribute decision making methods based on the proposed cross entropy measures. In the decision making framework, we calculate the weighted cross entropy measures between each alternative and the ideal alternative to rank the alternatives and choose the best one. We solve two illustrative examples of multi-attribute decision making problems and compare the obtained result with the results of other existing methods to show the applicability and effectiveness of the developed method. In the end, the main conclusion and future scope of research are summarized.

Along with the economic growth, the companies must contribute to social progress and promote environmental sustainability in equal harmony. Sustainable human resource management (SHRM) strategies make it possible to attain the economic, social and environmental goals of a firm. In this regard, a survey method is discussed using the literature review and online questionnaire to identify the main factors/indicators during the SHRM evaluation of manufacturing firms in India. Uncertainty is commonly occurred in the assessment of SHRM factors. As a generalized version of fuzzy sets, single-valued neutrosophic set (SVNS) has been demonstrated as a valuable tool to illustrate the indeterminate, inconsistent and uncertain data of realistic decision-making problems. Considering the idea of SVNSs, this study develops a hybrid multi-criteria group decision-making (MCGDM) approach for assessing the SHRM of manufacturing firms under uncertainty settings. For this purpose, an SVN-alternative ranking order method accounting for two-step normalization (AROMAN) is proposed based on VIFI-score function-based decision experts’ (DEs’) weighting tool and integrated criteria weight-determining model to solve the MCGDM problems with fully unknown DEs and criteria weights. In this regard, we develop new SVN-distance measure to compute the degree of difference between SVNSs. Some examples are presented to demonstrate the efficacy of developed measure over the existing ones. In addition, new criteria weight-determination model is presented with the integration of objective weights through IVIF-distance measure-based model and subjective weights through ranking comparison (RANCOM) tool on SVNSs. The proposed ranking method is applied to an empirical study of SHRM assessment for manufacturing firms in India, which shows its applicability and feasibility. In this study, the evaluation criteria are characterized into social, environmental and economic aspects with DE’s opinions. Comparative and sensitivity analyses are made to show the strength and steadiness of presented approach. This study provides an innovative MCGDM analysis framework, which makes a significant contribution to the SHRM assessment problem under indeterminate, inconsistent and uncertain setting.

New setting is introduced to study “closing numbers” and “super-closing numbers” as optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. In this way, some approaches are applied to get some sets from (Neutrosophic)n-SuperHyperGraph and after that, some ideas are applied to get different types of super-closing numbers which are called by optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. The notion of dual is another new idea which is covered by these notions and results. In the setting of dual, the set of super-vertices is exchanged with the set of super-edges. Thus these results and definitions hold in the setting of dual. Setting of neutrosophic n-SuperHyperGraph is used to get some examples and solutions for two applications which are proposed. Both setting of SuperHyperGraph and neutrosophic n-SuperHyperGraph are simultaneously studied but the results are about the setting of n-SuperHyperGraphs. Setting of neutrosophic n-SuperHyperGraph get some examples where neutrosophic hypergraphs as special case of neutrosophic n-SuperHyperGraph are used. The clarifications use neutrosophic n-SuperHyperGraph and theoretical study is to use n-SuperHyperGraph but these results are also applicable into neutrosophic n-SuperHyperGraph. Special usage from different attributes of neutrosophic n-SuperHyperGraph are appropriate to have open ways to pursue this study. Different types of procedures including optimal-super-set, and optimal-super-number alongside study on the family of (neutrosophic)n-SuperHyperGraph are proposed in this way, some results are obtained. General classes of (neutrosophic)n-SuperHyperGraph are used to obtains these closing numbers and super-closing numbers and the representatives of the optimal-super-coloring sets, optimal-super-dominating sets and optimal-super-resolving sets. Using colors to assign to the super-vertices of n-SuperHyperGraph and characterizing optimal-super-resolving sets and optimal-super-dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on n-SuperHyperGraph to get new results about closing numbers and super-closing numbers alongside sets in the way that some closing numbers super-closing numbers get understandable perspective. Family of n-SuperHyperGraph are studied to investigate about the notions, super-resolving and super-coloring alongside super-dominating in n-SuperHyperGraph. In this way, sets of representatives of optimal-super-colors, optimal-super-resolving sets and optimal-super-dominating sets have key role. Optimal-super sets and optimal-super numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal-super ones. Simultaneously, three notions are applied into (neutrosophic)n-SuperHyperGraph to get sensible results about their structures. Basic familiarities with n-SuperHyperGraph theory and neutrosophic n-SuperHyperGraph theory are proposed for this article.

In this research, new setting is introduced for assuming a SuperHyperGraph. Then a ``SuperHyperClique'' $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$SuperHyperClique'' is a \underline{maximal} SuperHyperClique of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$SuperHyperClique'' is a \underline{maximal} neutrosophic SuperHyperClique of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme SuperHyperClique theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed.

In this research, assume a SuperHyperGraph. Then a ``Failed SuperHyperClique'' $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperClique'' is a \underline{maximal} Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperClique'' is a \underline{maximal} neutrosophic Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme Failed SuperHyperClique theory, Extreme SuperHyperGraphs theory, and Neutrosophic SuperHyperGraphs theory are proposed.

Integrating nanomaterials like carbon nanotubes (CNTs) and iron oxide (Fe₃O₄) into epoxy composites has significant interest due to their potential to enhance mechanical properties. This study evaluates the impact of dispersion quality on the mechanical performance of CNT/Fe₃O₄/Epoxy composites, comparing stirring and sonication methods at three different loadings: 0.1, 0.3, and 0.5 wt.%. Tensile testing revealed that sonicated composites consistently outperformed stirred composites, with a significant increase in elastic modulus and ultimate tensile strength (UTS). However, fracture strain decreased in both composite types compared to pure epoxy, with sonicated composites experiencing a more significant reduction than stirred composites. These results underscore the importance of high-quality dispersion for optimizing mechanical properties.

The Cobb angle is critical in assessing adolescent idiopathic scoliosis (AIS) patients. This study aimed to evaluate the error in selecting the cranial and caudal limit vertebrae on AIS digital X-rays of experienced and novice observers and its correlation with the error in measuring the Cobb angle and determining the length of the scoliotic curves. Using the TraumaMeter v.873 software, eight raters (four experienced and four novices) independently evaluated 68 scoliotic curves on 42 AIS X-rays across three sessions one month apart according to Hopkins’ criteria of absolute reliability. Two spine specialist experts using the Cobb method established the gold standard measurements. The percentage of error in the selection of the cranial vertebrae (the most-tilted vertebra above the apex) is higher than in the caudal vertebrae (the most-tilted vertebrae below the apex) (44.7%, CI95% 41.05-48.3 compared to 35%, CI95% 29.7-40.4). The error in the choice of the most tilted vertebrae, in number of vertebrae per scoliotic curve, was MBE (mean bias error) =0.45, CI95% 0.38-0.52 in the cranial and MBE=0.35, CI% 0.69-0.91 in the caudal. The percentage of errors in the choice of boundary vertebrae is lower for the experienced than for the novices, both in cranial and caudal. The experienced chose at least one boundary vertebrae incorrectly in 52% of the meas-urements and the novices in 65.1%. The error in the Cobb angle did not depend on the number of boundary vertebrae chosen incorrectly (r=0.198, p=0.111). Of the 50% of Cobb angle measurements closest to the actual value, 55.4% (454) were obtained by incorrectly selecting at least one boundary vertebra. There was a positive correlation (r=0.673, p=0.000) between the error in selecting the boundary vertebrae and the error in determining the length of the scoliotic curves. The error in quantifying the length of scoliotic curves was MBE=0.43, CI95% 0.35-0.51 vertebrae per curve. We can conclude that errors in selecting boundary vertebrae are common among experienced and novice observers, with a greater frequency of error in the cranial vertebrae. There is no correlation between the error in selecting the boundary vertebrae and the error in measuring the Cobb angle. Contrary to the consensus, the accuracy of determining the length of the scoliotic curve is limited by the Cobb method’s reliance on the correct selection of boundary vertebrae. Inappropriate choice of boundary vertebrae leads to an estimated error in determining the length of the scoliotic curves of 0.805 vertebrae for each boundary vertebra chosen incorrectly.

Globally, Type 2 diabetes (T2D) and Cancer are the major cause of morbidity and mortality worldwide and is considered to be one of the most significant public health concerns of the 21st century. Over the next two decades, the global burden is expected to increase by approximately 60%. Several observational studies as well as clinical trials have demonstrated the health benefits of consuming whole grains and lower the risk of several chronic non communicable diseases including T2D and cancer. Cereals grains are the primary source of energy in the human diet. The most widely consumed pseudo cereals include (quinoa, amaranth and buckwheat) and cereals (wheat, rice and corn). From a nutritional perspective, both pseudo cereals and cereals are recognized for their complete protein, essential amino acids, dietary fibres and phenolic acids. The bran layer of the seed contains the majority of these components. Greater intake of whole grains than refined grains has been consistently linked to a lower risk of T2D and cancer. Due to their superior nutritional compositions, whole grains make them a preferred choice over refined grains. The modulatory effects of whole grains on T2D and cancer are also likely to be influenced by several mechanisms, some of these effects may be direct; while others involve altering the composition of gut microbiota, increasing the abundance of beneficial bacteria, and lowering harmful bacteria, increasing insulin sensitivity, lowering solubility of free bile acids, protein broken down into peptides and amino acids, producing short-chain fatty acids (SCFAs) and other beneficial metabolites that promote the proliferation in the colon which modulate the anti-diabetic and anti-cancer pathway. Thus the present review are two folded; first summarizes the recent knowledge about the nutritional composition and bioactive acids in pseudo cereals (quinoa, amaranth and buckwheat) and cereals (wheat, rice and corn); the second section summarizes and discusses the progress in recent human studies, such as observational (cross-sectional studies, case-control studies and cohort studies) and intervention studies in understanding their role in T2D and cancer including the potential mechanism. Overall according to the scientific data, whole grain consumption may reduce the incidence of T2D and cancer. Future studies should carry out randomized controlled trials to validate observational results and establish causality; in addition the current manuscript encourages to investigate the specific mechanisms by which whole grains exert their beneficial effects on health by examining the effects of different types of specific protein, dietary fibres and phenolic acids that might help to prevent or treat T2D and cancer.

Cloud data centers play a vital role in modern computing infrastructure, offering scalable resources for diverse applications. However, managing costs and resources efficiently in these centers has become a crucial concern due to the exponential growth of cloud computing. User applications exhibit complex behavior, leading to fluctuations in system performance and increased power usage. To tackle these obstacles, we propose the consolidation of virtual machines (VMs) to optimize resource utilization and reduce operational costs. This paper introduces a novel algorithm, leveraging the Modified Artificial Feeding Birds Algorithm (ModAFBA), to manage cost optimally in cloud data centers by reducing power usage while meeting service level agreements (SLAs). The ModAFBA algorithm, inspired by bird foraging behavior, dynamically adjusts solutions based on environmental changes. Comprehensive experimental evaluation demonstrates the superiority of the proposed algorithm in terms of power usage, migration count, and SLA compliance. Through this research, we aim to advance cost management and resource optimization in cloud data centers, providing a valuable tool for cloud service providers to enhance infrastructure efficiency and achieve cost savings.

Tapioca, an abundant constituent of starch, is extensively grown and consumed, while a wet pathway is usually employed for starch extraction from it. The purpose of the study is to determine the functional properties like tensile properties, barrier properties such as oxygen, and water vapor transmission rate, as well as biodegradability of the standardized tapioca film, all in the context of its appropriateness for packaging purposes for a variety of food categories. Tapioca starch film was standardized with glycerol and citric acid by casting techniques in a film-making machine. The tensile strength of obtained films was measured as 0.71 MPa, with 11.5 percent elongation at break. The oxygen transmission rate was 750.52 cc/m²/day while the water vapor transmission rate ranged from 0.81 to 0.84 cm³/m²/24h/0.1MPa. This study revealed that tapioca starch films are appropriate for packing cereals, legumes, spices, condiments, extruded items, as well as sugar candies for prolonged periods hence even after 120th day, the total microbial count of the standardized film was 5.7 x 101 CFU/g which is below the permissible limit. In moist topsoil and vermicompost, it degrades completely within 24 days. The research findings highlight the tapioca starch films' potential as environmentally friendly and practical packaging solutions for a wide range of food items and a promising alternative for single-use plastics in the food sector.

This study investigates the pivotal role of leadership in driving sustainable supply chain initiatives (SSCI), highlighting the multifaceted ways through which leaders influence the successful integration and implementation of sustainability practices within supply chains. Using a qualitative approach, the research involved semi-structured interviews with leaders and managers from diverse industries, complemented by document analysis and thematic analysis to capture the complexities of leadership in SSCI. The findings reveal that visionary leadership, characterized by a clear and compelling sustainability vision, plays a crucial role in aligning organizational goals with sustainable practices, inspiring collective action, and fostering a shared commitment to long-term environmental and social objectives. Stakeholder engagement emerged as a critical factor, with leaders who prioritize open communication and collaboration successfully building trust, leveraging expertise, and co-creating innovative solutions to sustainability challenges. Additionally, the study highlights the importance of fostering a culture of innovation, where leaders support experimentation, risk-taking, and the adoption of new technologies and processes that enhance sustainability. Ethical leadership, emphasizing integrity, transparency, and accountability, is identified as essential for gaining stakeholder support and reinforcing the legitimacy of SSCI. Furthermore, the integration of sustainability into organizational culture, driven by leadership, is crucial for aligning individual and organizational behaviors with sustainability goals. The ability of leaders to navigate challenges, adapt to global supply chain complexities, and utilize robust sustainability metrics is also emphasized as key to sustaining SSCI. The study concludes that effective leadership is integral to the success of SSCI, offering valuable insights for organizations aiming to enhance their sustainability performance and contributing to the broader understanding of leadership’s role in sustainable supply chain management.

NMR spectroscopy, which is based on the phenomenon of nuclear magnetic resonance, has been widely popularized by its application in medical imaging under the name of MRI. In the organic laboratory, the 13C NMR spectrum of a newly synthetized compound remains an essential step in elucidating its structure. For the chemist, the interpretation of such a spectrum, which is a set of chemical shift values, is made easier if he has a tool capable of predicting with sufficient accuracy the carbon shift values from the structure he intends to prepare. As there are few open source methods for accurately estimating this property, we applied our graph machine approach to build models capable of predicting the chemical shifts of carbons. For this study, we have focused on benzene compounds building an optimized model derived from training a database of 10577 chemical shifts originating from 2026 structures which contain up to ten types of atoms other than carbon, namely H, O, N, S, P, Si and halogens. It provides a training root mean squared relative error (RMSRE) of 0.5 %, i.e. a root mean squared error (RMSE) of 0.6 ppm, and a mean absolute error (MAE) of 0.4 ppm for estimating the chemical shifts of the 10k carbons. The predictive capability of the graph machine model is also compared with that of three commercial software on a data set of 171 original benzenic structures (1012 chemical shifts). The graph machine model proves very efficient in predicting chemical shifts with an RMSE of 0.9 ppm, and compares favorably with the RMSEs of 3.4, 1.8 and 1.9 ppm computed with ChemDraw, ACD and MestReNova softwares respectively. Finally, a Docker-based tool is proposed to predict the carbon chemical shifts of benzenic compounds solely from their SMILES codes.

Genetic engineering has become an essential element in developing climate-resilient crops and environmental sustainable solutions to respond to the increasing need for global food security. Genome editing using CRISPR/Cas [Clustered regulatory interspaced short palindromic repeat (CRISPR)-associated protein (Cas)] technology is being applied to a variety of organisms, including plants. This technique has become popular because of its high specificity, effectiveness, and low production cost. Therefore, this technology has the potential to revolutionize agriculture and contribute to global food security. Over the past few years, increasing efforts have been seen in its application in developing higher-yielding, nutrition rich, disease resistant, stress-tolerant “crops” fruits and vegetables. Cas proteins such as Cas9, Cas12, Cas13, and Cas14, among others, have distinct architectures and have been used to create new genetic tools that improve features that are important for agriculture. The versatility of Cas has accelerated genomic analysis and facilitated the use of CRISPR/Cas to manipulate and alter nucleic acid sequences in cells of different organisms. This review provides the evolution of CRISPR technology exploring its mechanisms and contrasting it with traditional breeding and transgenic approaches to improve different stress tolerance. We have also discussed the CRISPR/Cas system and explored three Cas proteins that are currently known to exist: Cas12, Cas13, and Cas14 and their potential to generate foreign DNA free or non-transgenic crops that could be easily regulated for commercialization in most countries.

Aim: This study aimed to evaluate the effectiveness of a plyometric training program designed to enhance agility, speed, and social interaction among boys with mild intellectual disability (ID) aged 10-12, within the Special Olympics framework. Participants: Thirty-two boys (mean age = 10.69 ± 0.8 years; mean IQ = 61 ± 7) from three inclusive education centers participated in the study. Methods: The intervention consisted of a 10-week plyometric training program, conducted twice a week. Pre- and post-intervention assessments included the Reaction Time Test, 4-Corner Agility Test, 10-Meter Speed Run, 4x5 Meter Relay Test, and the Friendship Activity Scale (FAS). Results: The study found significant improvements across all measures. Reaction time decreased by 0.83 seconds (t = 7.44, p < 0.001), 4-corner agility improved by 0.77 seconds (t = 11.93, p < 0.001), 4x5 meter speed improved by 0.61 m/s (t = 17.37, p < 0.001), and 10-meter run speed improved by 1.55 m/s (t = -12.76, p < 0.001). Additionally, the FAS score increased by 0.81 points (t = 9.59, p < 0.001), indicating enhanced social interactions. Conclusion: The plyometric training program significantly improved agility, speed, and social interaction in children with mild ID, demonstrating the effectiveness of inclusive, adaptive physical education strategies within the Special Olympics framework.

Human epidermal growth factor receptor 2 (HER2), a targetable transmembrane glycoprotein receptor of the epidermal growth factor receptor (EGFR) family, plays a crucial role in cell proliferation, survival, and differentiation. Aberrant HER2 signaling is implicated in various cancers, particularly breast and Gastric cancer, where HER2 overexpression or amplification correlates with aggressive tumor behavior and poor prognosis. Her2 activating mutations contribute to accelerated tumorigenesis and metastasis. This review provides an overview of HER2 biology, signaling pathways, mechanisms of dysregulation, diagnostic approaches, and therapeutic strategies targeting HER2 in cancer. Understanding the intricate details of HER2 regulation is essential for developing effective targeted therapies and improving patient outcomes.

Volumetric models are a crucial tool for forest management. The study aimed to adjust the mixed model by Schumacher and Hall for estimating commercial volume in a dense ombrophilous forest situated in Ferreira Gomes, Amapá, Brazil. Cubage data from 100 sample trees of 5 species were used to adjust the Schumacher and Hall model in fixed and mixed non-linear forms with the diameter class as a random effect. In addition, the same model was also adjusted for each class to verify whether good equations will be generated by stratifying by diameter class. After analysis, it was found that most of the equations by diameter class do not present all significant parameters. On the other hand, the mixed models using class as a random effect showed good results. Finally, it can be seen that mixed models are a much better alternative than stratification by diameter class for volume estimation.

Early childhood may be a stressful period for families with a significant impact on parents’ mental health and the child’s healthy development. The goal of the SKKIPPI cohort study was to assess the occurrence and determinants of psychosocial stress and mental health disorders in parents as well as in their offspring in early childhood in three German regions. Based on random samples from three residents' registration offices, parents with infants up to 12 months of age at the time of sampling, were invited to participate in the study. A screening online questionnaire was newly developed, available in four languages, to assess common psy-chosocial stressors and mental health problems of parents with small children. The study enrolled 4,984 mothers and 962 fathers. The most common potential psychosocial stressors at baseline were professional problems (mothers 22%, fathers 33%), lack of social sup-port (20%, 14%), and severe, negative experiences in childhood (22%, 16%). Obses-sive-compulsive thoughts (21%, 16%), depressive (9%, 9%) and anxiety symptoms (11%, 7%) were the most frequently reported mental health problems by both parents. Regulatory prob-lems of the child were reported by between 1.5% and 5.1% of parents. The SKKIPPI study showed that a substantial proportion of parents are burdened by psychoso-cial problems and suffer from mental health problems in the first years after birth. Early pre-ventive and low-threshold support measures should be available in the health and social care system. The newly developed questionnaire can be used to screen in the relevant populations in order to avoid disturbances in the mother-child attachment.

Airborne distributed position and orientation system (ADPOS), which integrates multi-inertia measurement units(IMUs), data-processing computer and Global Navigation Satellite System (GNSS), serves as a key sensor in new higher-resolution airborne remote sensing, such as array SAR, multinode imaging loads and so on. ADPOS can provide multinode high accuracy spatio-temporal reference information to realize multinode motion compensation with the various state estimation methods such as Central Difference Kalman Filtering (CDKF), modifed CDKF. However, these methods focus on noise optimization based on known nonlinear models and its linear minimum variance estimation criterion, which cannot gain better estimation performance for high-dimensional nonlinear systems. For this reason, the variational optimization process based on conjugate gradient algorithm is proposed for the estimation of filtering update step, which is more efficient than linear minimum variance estimation criterion. Therefore, aiming at ADPOS with high-dimensional and nonlinearity, Central Difference Variational Filtering (CDVF) using variational optimization based on conjugate gradient algorithm for mean correction in the filtering update stage is devoted to advancing the estimation accuracy of multinode motion parameters. A real ADPOS flight test has been conducted, the experimental results show that the accuracy of the slave motion parameters has a distinct progress than the up to date CDKF, and the compensation performance is distinct.

When profit-driven renewal is difficult to implement, many historic districts are “frozen protected” in China. In the social context of “building cities for the people” in recent years, the public value-oriented renewal of urban historic areas plays an important role in the transformation of cities. This study investigates the strategies of historic district regeneration in China by integrating spatial form, urban governance, and public value. We propose a novel framework to analyze the regeneration of historic districts, using Taiyuan Bell Tower Street as a case study. The framework distinguishes between two dimensions: spatial and economic-social. In the spatial dimension, we focus on the transformation of spatial form to regenerate public value, emphasizing the attribute of "publicness" as central to urban regeneration efforts. This involves a tiered approach of excavating and upgrading historic districts at macro, meso, and micro levels. In the economic-social dimension, we explore urban governance to strengthen public value, involving government, market, and societal actors in a collaborative renewal process. The analysis highlights that a public value-oriented approach to heritage regeneration offers greater sustainability and could serve as a model for other cities seeking similar outcomes.

Three types of double perovskite La1-xPrxBa0.5Sr0.5Co1.5Fe0.5O5+δ(x=1,0.3,0) are prepared using the EDTA-citrate method and identified as solid oxide fuel cell (SOFC) cathodes. The microstructures, as well as electrochemical performances of La1-xPrxBa0.5Sr0.5Co1.5Fe0.5O5+δ (LPBSCF) and La2NiO4-impregnated LPBSCF (LN-LPBSCF) cathodes, are investigated in detail. An optimum impregnation amount of LN-LPBSCF (LN loading of 0.64 mg/cm2) electrode exhibits relatively lower electrode polarization resistance (Rp) and better stable performance as compared to that of pure LPBSCF electrode in symmetrical SOFCs. The maximum power density of LN-LPBSCF single cells is 800 mW/cm2 at 800 °C and demonstrates good stability for 100 h in short-term testing.

Pygeum africanum bark has been shown to inhibit the production of pro-inflammatory prostaglandins in the prostate and reduce the production of leukotrienes and other 5-lipoxygenase (5-LO) metabolites. It has been suggested that inflammation plays an important role in the pathophysiology of benign prostatic hyperplasia (BPH). In clinical trials, P. africanum improved the symptoms and objective measures of BPH. This in vitro study aimed to assess the anti-inflammatory potential of a proprietary Pygeum bark standardized extract (Prunera®) on cytokine release by lipopolysaccharide-simulated human peripheral blood mononuclear cells (PBMCs). PBMCs were obtained from four donors and a bead-based assay (ProcartaPlex™ panel) was used for the detection and quantitation of cytokines. Pygeum africanum bark standardized extract (PABE) showed the following effects: IL-2 was lowered in all donors in absence of a clear dose–response relationship; IL-4, IL-5, IL-6, IL-9, and IL-13 levels were decreased in most donors; IL-22 levels seemed to be suppressed only for donor 4 at lower and medium concentrations; and IL-27 and levels of TNF-α decreased at all PABE concentrations in all donors. The anti-inflammatory effect of PABE supports the potential use of this natural compound in the management of BPH and other conditions in which pro-inflammatory cytokines are involved in their underlying pathophysiological mechanisms.

In this study, the biodegradation properties of leather treated with various finishing chemicals were evaluated in order to enhance the sustainability of leather processing. We applied advanced analytical techniques including FT-IR, thermogravimetric analysis (TGA), and solid-state NMR spectroscopy. Leather samples treated with different polymers, resins, bio-based materials, and traditional finishing agents were subjected to a composting process under controlled conditions to measure their biodegradability. The findings revealed that bio-based polyurethane finishes and acrylic wax exhibited biodegradability, while traditional chemical finishes like isocyanate and nitrocellulose lacquer showed moderate biodegradation levels. The results indicated significant differences in the biodegradation rates and the impact on plant germination and growth. Some materials, such as black pigment, nitrocellulose lacquer and wax, were beneficial for plant growth, while others, such as polyurethane materials, had adverse effects. These results support the use of eco-friendly finishes to reduce the environmental footprint of leather production. Overall, this study underscores the importance of selecting sustainable finishing chemicals to promote eco-friendly leather manufacturing practices.

This study explores the barriers and opportunities faced by women in supply chain leadership, a field traditionally dominated by men. Through in-depth interviews and thematic analysis, it uncovers the pervasive cultural and societal biases that undermine women's perceived competence and suitability for leadership roles. These biases, often rooted in deep-seated stereotypes, influence hiring and promotion decisions, creating significant obstacles for women. Structural and organizational barriers, such as the lack of formal diversity policies, flexible working arrangements, and adequate mentorship, further hinder women's career progression. The dual burden of professional and domestic responsibilities also disproportionately affects women, limiting their availability for work-related travel and extended hours, which are often required in supply chain roles. Despite these challenges, the study identifies several pathways to promote gender diversity in supply chain leadership. Organizational commitment to diversity and inclusion, flexible working policies, and comprehensive mentorship programs are crucial in supporting women's advancement. Education and professional development opportunities are essential in equipping women with the necessary skills for leadership roles. Additionally, fostering an inclusive corporate culture that values diverse perspectives and addresses discrimination is vital for creating a supportive environment. Broader societal and policy-level changes, such as government and industry initiatives promoting gender diversity, are also necessary. The integration of emerging areas like sustainability, entrepreneurship, emotional intelligence, marketing, and supplier relationship management offers new opportunities for women to contribute to the industry's evolution. By addressing these barriers and leveraging the identified opportunities, it is possible to create a more inclusive and equitable supply chain industry, benefiting both the industry and society.

The taxonomy of the Fabeae (Vicieae) has long been problematic, but an analysis by Schaefer et al in 2012 gave an exceptionally clear view of the tribe and noted the possibility that some nomenclatural adjustments may be required at some future date. These authors suggested several options, expressing some preferences. However, there has been a recent change to formally accepted names implementing one of these possibilities, but without any additional relevant information. This change seems unjustified and unhelpful. We therefore present an argument for the retention, or re-instatement, of the genera Pisum, Vavilovia and Lens until such time as new data supports this requirement and there is no nomenclatural solution that is both accurate and convenient.

Recently concluded, large-scale cancer genomics studies involving multiregion sequencing of primary tumors and paired metastases appear to indicate that many or most cancer patients have one or more “clonal" mutations in their tumors. Clonal mutations are those that are present in all of a patient’s cancer cells. Achilles Therapeutics is currently the only company specifically targeting clonal mutations. However, they are doing so with tumor-derived T cells. To address the potential limitations of immunotherapy, I have devised another approach for exploiting clonal mutations, which I call “Oncolytic Vector Efficient Replication Contingent on Omnipresent Mutation Engagement” (OVERCOME). The ideal version of OVERCOME would likely employ a bioengineered facultative intracellular bacterium. The bacterium would initially be attenuated, but (transiently) reverse its attenuation upon clonal mutation detection.

Abstract: To obtain bovine oocytes in high quality, effects of vitamin C (VC) on in vitro maturation (IVM) of bovine oocytes and early embryo development were investigated. The results showed that: 1) The IVM medium containing 50 µg/mL VC improved the oocyte maturation rate, while no effects on the development of parthenogenetic embryos; 2) The in vitro culture (IVC) medium containing 20 µg/mL VC increased the cleavage rate of the in vitro fertilized (IVF) embryos, enhanced the mRNA levels of pluripotency gene Oct4, Sox2, Cdx2 and Nanog in the blastocysts, but no effect on the blastocyst rate; 3) Combing supplemention of 50 µg/mL in IVM medium + 20 µg/ml VC in IVC medium (VC 50/20) increased the cleavage rate of IVF embryos and enhanced the mRNA levels of Oct4, Sox2, Cdx2 and Nanog in the blastocysts; 4) Combination of VC 0/20 and VC 50/20 enhanced the expression of anti-apoptotic gene Bcl-2 and VC 50/0 weakened the expression of pro-apoptotic gene Bax, while VC 0/40 and VC 0/60 increased Bax expression and decreased the Bcl-2/Bax ratio in blastocysts. Together, VC supplementation at tuned concentration as well its combination in IVM and IVC media improves the developmental rates of bovine oocytes and embryos.

Background: In response to inflammation, the absorption of nutritional iron is restricted. Multiple inflammation-related signaling pathways can lead to ferroptosis, an iron-dependent mechanism of programmed cell death. Since the pathophysiological significance of the presence and uptake of iron in chronic inflammation is still unknown, we tested the effect of a low iron diet on the clinical course of arthritis in the mouse model of collagen-induced arthritis (CIA). Methods: Six- to eight-week-old male DBA/1 mice were fed either a normal or a low iron diet starting three weeks before arthritis induction. From day four after the collagen-booster made on day 25, the development of arthritis was regularly monitored until the end of the experiment (day 34), using a standard clinical arthritis score. The complete blood count was determined as well as Fe2+, Fe3+, oxidized and reduced glutathione (GSH and GSSG) and malondialdehyde (MDA) in whole paw tissue by ELISA. Quantitative PCR was performed from whole paw tissue for glutathione peroxidase 4 and other key regulator genes of iron metabolism and ferroptosis. We used nonparametric tests to com-pare markers of iron metabolism and ferroptosis as well as nonlinear regression models for longitu-dinal data for signs of arthritis. Results: Mice fed a low iron diet showed a significantly less severe course of arthritis compared to mice fed a normal iron diet (p

Concurrent Optical and Magnetic Stimulation (COMS) combines extremely low frequency electromagnetic and light stimulation modalities for enhanced wound healing. In this report, we investigated the potential mechanistic synergism between magnetic and light components by comparing their individual and combined cellular responses. Although each individual stimulation mode was capable of stimulating cell proliferation, magnetic fields exposure alone produced greater proliferation enhancement than light alone, yet their combined effects of were supra-additive of the individual responses. Reactive oxygen species were incrementally reduced by exposure to light, magnetics fields and their combination, where statistical significance was ultimately achieved. On the other hand, ATP production was significantly enhanced in response to magnetic exposure alone or in combination with light. These results suggest that mitochondrial respiratory efficiency was preferentially improved by the combination of the two stimuli. Protein expression related to cell proliferation was preferentially enhanced by the combinatory COMS modality as were the protein levels of the TRPC1 cation channel previously implicated as part of a calcium-mitochondrial signaling axis invoked by electromagnetic exposure and involved in proliferation. These results corroborate that light facilitates functional synergism with magnetic fields that ultimately impinge on mitochondria-dependent developmental responses. The aminoglycoside antibiotics (AGAs) have been previously shown to antagonize TRPC1-mediated magnetotransduction. Streptomycin applied during the exposure to any of the stimulation modes reduced proliferation enhancement, whereas streptomycin added after the exposure did not. Notably, the COMS modality and magnetic field exposure were capable of partially overcoming streptomycin antagonism of proliferation, whereas light alone was not. Transductional antagonism of combinatorial photon-electromagnetic effects by streptomycin thus aligns with previous studies showing that the AGAs block TRPC1-mediated magnetotransduction when applied during exposure. The prophylactic usage of the AGAs (neomycin) should be avoided during COMS therapy to maintain clinical efficacy and would be a common concern with most other electromagnetic regenerative paradigms.

This study introduces an innovative approach to designing membranes capable of separating CO2 from industrial gas streams at higher temperatures. The novel membrane design seeks to leverage the well-researched high-temperature CO2 adsorbent, hydrotalcite, by transforming it into a membrane. This is achieved by combining it with an amorphous organo-silica-based matrix, extending the polymer-based Mixed Matrix Membrane concept to inorganic compounds. Following the membrane material preparation and investigation of the individual membrane in Part 1 of this study, we examine its permeation and selectivity here. The pure 200 nm thick hydrotalcite membrane exhibits Knudsen behavior due to large intercrystalline pores. In contrast, the organo-silica membrane demonstrates a permselectivity of 13.5 and permeance for CO2 of 1.3 107 mol m2 s1 Pa1 at 25°C, at 150°C the good separation behavior is reduced. Combining both components results in a hybrid microstructure, featuring selective surface diffusion in the microporous regions and unselective Knudsen diffusion in the mesoporous regions. Further attempts to bridge both components to form a purely microporous microstructure are outlined.

Accurately assessing forest structure and maintaining up-to-date information about forest structure is crucial for various forest planning efforts, including the development of reliable forest plans and assessments of the sustainable management of natural resources. Field measurements traditionally applied to acquire forest inventory information (e.g., basal area, tree volume, and aboveground biomass) are labor-intensive and time-consuming. To address this limitation, remote sensing tech-nology has been widely applied in modeling efforts to help estimate forest inventory information. Among various remotely sensed data, LiDAR can potentially help describe forest structure. This study was conducted to estimate and map forest inventory information across the Talladega Na-tional Forest by employing ALS-derived data and aerial photography. The quality of predictive models was evaluated to determine whether additional remotely sensed data can help improve forest structure estimates. Additionally, the quality of general predictive models was compared to that of species-group models. This study confirms that quality level 2 LiDAR data was sufficient for developing adequate predictive models (R2adj. ranging between 0.71 and 0.82) when compared to the predictive models based on LiDAR and aerial imagery. Additionally, this study suggests that species-group predictive models were of higher quality than general predictive models. Lastly, landscape-level maps were created from the predictive models, and these may be helpful to plan-ners, forest managers, and landowners in their management efforts.

Although mask-wearing is now widespread, knowledge of how to quantify or improve its performance remains surprisingly limited and largely based on empirical evidence. The objective of this study was to visualize the expiratory airflows from facemasks and evaluate aerosol transmission between two persons. Different visualization methods were explored, including the Schlieren optical system, laser/LED-particle imaging system, thermal camera, and vapor-SarGel system. The leakage flows and escaped aerosols were quantified using a hotwire anemometer and a particle counter, respectively. The results show that mask-wearing reduces the exhaled flow velocity from 2~4 m/s (with no facemask) to around 0.1 m/s, thus decreasing droplet transmission speeds. Cloth, surgical, and KN95 masks showed varying leakage flows at the nose top, sides, and chin. The leakage rate also differed between inhalation and exhalation. The neck gaiter has low filtration efficiency and high leakage fractions, providing low protection efficiency. There was considerable deposition in the mouth-nose area, as well as the neck, chin, and jaw, which heightened the risk of self-inoculation through spontaneous face-touching. A face shield plus surgical mask greatly reduced droplets on the head, neck, and face, indicating that double face coverings can be highly effective when a single mask is insufficient. The vapor-SarGel system provided a practical approach to study interpersonal transmission under varying close contact scenarios or with different face coverings.

Lane detection is a foundational technology for autonomous driving systems. It involves identifying the boundaries of lanes on the road and ensuring the vehicle stays within these boundaries. Accurate lane detection is crucial for safety, navigation and traffic management. This paper presents an artificial intelligent based autonomous road lane detection and navigation system for vehicles. The system can detect and analyze road lanes accurately and efficiently in real-time, with frame rates of up to 17 FPS. By utilizing image processing techniques, the system can identify the location and boundaries of road lanes and obstacles on the road and provide accurate and reliable navigation guidance to the driver. The system is integrated with sensors and actuators to provide comprehensive autonomous navigation. The efficiency of the proposed system is demonstrated using accuracy of lane detection on straight and curve lanes covering frames per second and motor of the speed as parameters for assessment. Results show that the proposed system detects lane as entire lane detection, partial lane detection and no detection status on different settings.

The aim of the study is to obtain a more complete picture of the blood plasma melatonin concentration in the donkey species. To this purpose sampling and statistical processing were carried out in such a way that allowed to establish the annual and daily rhythm. Based on human observations, according to the hypothesis of the authors, the blood plasma melatonin concentration of pregnant individuals rises during late gestational period, before parturition. To confirm this, the melatonin concentration of pregnant and non-pregnant mares was monitored and compared. In regard to the circannual rhythm, the significantly lowest midnight melatonin value (27.67 pg/ml) is typical for the summer solstice. Under consideration of circadian changes, a significantly strongest melatonin production (45.16 pg/ml) can be observed on the night of the winter solstice (p &lt; 0.001). Considering the gestational age, the blood plasma melatonin concentration (around 38 pg/ml) does not change as pregnancy progresses (p = 0.136). The results obtained in the study population of the domestic ass usefully expand the little knowledge previously gathered about the development of blood plasma melatonin concentration of this species.

The aim of this article is to present the course of the COVID-19 pandemic in Poland in 2020-2022, the formation of ad hoc health and anti-crisis policies, an assessment of crisis management and the perceived impact of the pandemic and anti-crisis measures.The paper draws on literature, official reports on the pandemic, data from Eurostat and other information from state institutions and public organisations.Particular attention was paid to the analysis and evaluation of the objectives, instruments and effects of the policies pursued by the state in a coordinated manner, i.e. the anti-pandemic policy and the anti-crisis policy. The anti-pandemic policy in Poland has failed to protect the country from significant personal losses and negative impacts on the health of the population and demographic processes.The anti-crisis policy of the state carried out with the mobilisation of businesses and disciplined society, in the form of anti-crisis shields supplemented and adjusted on an ongoing basis, allowed Poland to avoid a deep crisis and economic recession. Attention was drawn to the need to coordinate the management of health and economic crises nationally and internationally, and to the need to have a medium-term anti-crisis state strategy and a system for the early detection of crisis symptoms.

A dynamic impact test was performed on as-rolled AZ31 alloy with gradient microstructure under various strains. The microstructural evolution and mechanical properties were systematically investigated. As the strain rate gradually increases, an increasing number of twins are formed, facilitating dynamic recrystallization (DRX), and the mechanical properties are also gradually improved as well. The microstructure becomes heterogeneous at higher strain rates, but the peak stress decreases. The impact process results in significantly higher performance due to microstructural refinement, work hardening by dislocations and precipitates. In addition, both the adiabatic shear band and the adjacent crack experience a temperature rise that exceeds the recrystallization temperature of the alloy. This observation also explains the presence of ultrafine recrystallized grains within the adiabatic shear band and the appearance of molten metal around the crack.

A processual texture lies at the core of phenomena that undergo change. Philosophers have observed the incessant becoming of our world from antiquity to the present day, but an explanation must still be found in terms of contemporary metaphysics. This article strives to bring the focus on the domain of possibles, an under-theorised philosophical issue that dwells in the ontological realm between the possibility and its actual realization. Sketching a more comprehensive concept of the possible unravelling the thread of its main meanings, the process of change will be not simply clarified from inside, but also understood as an activator of reality. Finally, the discussion will argue for a principle of prudence and responsibility derived from an ontological basis.

Colorectal cancer (CRC) is a weighty cause of mortality worldwide, with growing incidence in the Middle East. Understanding the level of awareness about CRC screening among the Syrian pop-ulation is crucial public health interventions. A cross-sectional study was conducted from Sep-tember 22, 2023, to October 15, 2023, involving 928 participants from six major governorates in Syria. An online questionnaire containing socio-demographic, knowledge, and attitude sections was used to collect data. Descriptive statistics and chi-square tests were employed for data analysis using (SPSS) v28.0. The survey revealed a lack of awareness regarding CRC screening among the Syrian population, with only 499(53%) of the proportion demonstrating adequate knowledge about the disease and its screening methods. Significant associations were observed between the level of knowledge and socio-demographic factors including gender, work status, and economic status (p < 0.05). The findings emphasize the need for public health initiatives to enhance awareness and knowledge about CRC and its early screening methods in Syria. Education is essential for improving early detection and reducing the burden of colorectal cancer in the region. Efforts to increase public understanding of CRC screening are critical for reducing the incidence and mortality.

The cooling of server components has been continuously developed over the past few years in order to meet the increasing cooling requirements of server component manufacturers such as for the processor chips. The growth in performance and power density increases the cooling demand. These requirements directly influence the energy consumption and performance of the hardware. To gain a better understanding of the historical evolution and possible future technology development paths in the field of data center cooling, a patent analysis method was used. The focus is on previous and current development priorities and possible research gaps within the server and computer room levels. The European patent database was selected as data source. To determine relevant patents, the search terms for various cooling technologies were developed iteratively. After the patent extraction for the period 2000 - 2023 (earliest priority year), the search results were classified and analysed. Most of the patents deal with air or liquid cooling. In the area of liquid cooling, the focus was on direct liquid cooling, followed by total liquid cooling. Since 2015 a technological shift from air to liquid cooling can be identified on the level of patent activities. In this context, the patent groups with focus on “constructional details for different types of electric apparatus” and “electrical digital data processing” have the largest share of patents. In addition, the technology focus of the TOP 10 patent applicants was in the field of liquid cooling. In conclusion from the patent analysis, it can be derived that liquid cooling will continue to gain in importance in the future and could also be combined with other approaches in the form of hybrid cooling. However air cooling may still be relevant, even if the main cooling load is handled by liquid-based approaches. At the same time, the optimisation potential for air cooling seems to have been largely exploited in comparison to liquid cooling, as can be seen from the falling number of the patent applications.

Emerging molecular and computational techniques may allow construction and computational treatment of dynamic digital twins on the scale of populations to individuals. This approach may pave the way for predictive, preventive, and personalized treatment. Because digital twins are independent of geographical location, this may also contribute to global equitable health.

We introduce a full binary directed tree structure to represent the set of natural numbers, further categorizing them into three distinct subsets: pure odd numbers, pure even numbers, and mixed numbers. We adopt a binary string representation for natural numbers and elaborate on the composite methodology encompassing odd- and even-number functions. Our analysis focuses on examining the iteration sequence (or composition) of the Collatz function and its reduced variant, which serves as an analog to the inverse function, to scrutinize the validity of the Collatz conjecture. To substantiate this conjecture, we incorporate binary strings into an algebraic formula that captures the essence of the Collatz sequence. By this means, we transform discrete powers of 2 into continuous counterparts, ultimately culminating in the smallest natural number, 1. Consequently, the sequence generated through infinite iterations of the Collatz function emerges as an eventually periodic sequence, thereby validating an enduring 87-year-old conjecture.

The objectives of this study was to assess the impact of a reproductive approach in high-yielding nulliparous and parous Holstein cows on the interestrus interval, estrus detection rates, conception rates, and pregnancy rates. The strategy involved giving GnRH on day 5 following artificial insemination (AI). For nulliparous cows, there appears to be no noticeable effect of GnRH therapy on the interestrus interval. In both groups, nearly all of the cows exhibited an 18–25-day cycle interval (P < 0.05). In the 18–25 day cycle period, the untreated multiparous cows exhibited the highest proportion (P < 0.05), while the treated group demonstrated the highest proportion (P < 0.05) in the 26–35 day cycle interval. The study found that the conception rate was higher in repeat breeder nulliparous and 3+ lactation treated Holstein cows compared with untreated ones. However, the cumulative heat detection rate, pregnancy rate and conception rates were similar in both groups (P > 0.05). Also, this study found that in the hottest months of the year, this therapeutic approach can't counteract the negative effect of heat stress in high-yielding dairy cows. Thus, it is not advised of using the hormonal method to create supplementary corpus luteum across the herd.

Carpels are a reproductive feature restricted to angiosperms, therefore they are a focus of many botanical studies. However, there are controversies over the nature of carpels. A reason underly-ing these controversies is mixing implications given by conflicting interpretations on fossil carpels in early fossil angiosperms from the Cretaceous. These controversies hinder a clear understanding of angiosperm evolution and systematics. A key to these questions is older fossil fruits bearing concerned information. Here we report a new fossil fruit, Xenofructus dabuensis gen. et sp. nov, from the Middle Jurassic of Liaoning, China. Unlike previously reported fruits of early angio-sperms that were interpreted as bearing seeds either on adaxial or abaxial margin by various au-thors, our fossil demonstrates clearly that the seeds in Xenofructus are neither borne on the adaxial nor abaxial margin of the fruit, instead the seeds of Xenofructus are borne on an axis positioned between two margins. This new feature implies that a placenta in carpels is an ovule/seed-bearing axis, a carpel is a composite organ comprising an enclosing leaf (fruit wall) and an axis (placenta). The adaxial or abaxial position of ovules/seeds frequently seen in fossil and extant angiosperms is a consequence derived through long time evolution (coalescence of placenta with either margin of fruits). Carpels can be taken as foliar structures enclosing their associated ovulate branches.

The endeavor to decode the brain's intricate architecture and its multifaceted functions has propelled scientists into the domain of complex differential equations, aiming to construct a computational framework capable of representing its uncountable intricacies. This article delves into the sophisticated and daunting task of modeling the brain, a system of seemingly uncountable coupled differential equations, each symbolizing the vast array of interconnected neural pathways and processes. We discuss the current limitations of computational resources and the significant challenges faced in accurately capturing the non-linear, high-dimensional, and plastic nature of neural dynamics. Despite these challenges, we explore the progressive strides in computational neuroscience that lay the groundwork for partial models, offering insights into the brain's localized circuits and broader network interactions. These models serve as pivotal stepping stones towards a more comprehensive understanding, which is incrementally built upon by interdisciplinary approaches, leveraging advancements in neuroimaging, data analysis, and theoretical biology. Looking ahead, the article speculates on the potential paradigm shifts that could arise from breakthroughs in computational technology, such as quantum computing, that may one day enable the simulation of the brain in its entirety. The article ultimately paints a picture of cautious optimism, where each incremental discovery is a valuable piece of the grand puzzle, bringing us closer to the epochal goal of comprehensively modeling the human brain.

Background and Objectives: Renal cell carcinomas and upper tract urothelial carcinomas are types of malignancies that originate in the kidneys. Each of these examples shows an increasing trend in the frequency and the mortality rate. This study aims to comprehensively define carcinomas by analysing clinical, paraclinical, and histological aspects to predict aggressiveness and mortality. Materials and Methods: We conducted a retrospective investigation on a group of patients suspected with kidney cancers. Results: We identified 188 cases. We observed a higher mortality rate and older age in individuals with urothelial carcinomas. Anemia, acute kidney injury, hematuria and perineural invasion were the main risk factors that predicted their mortality. Tumour size in renal cell carcinomas correlates with the presence of necrosis and sarcomatoid areas. Factors that indicate a higher rate of death are older age, exceeding of the renal capsule, the lesion that includes the entire kidney, lymphovascular invasion, acute kidney injury, and anemia. Conclusions: Even if they originate at the renal level, and the clinical-paraclinical picture is similar, the histopathological characteristics make the difference. In addition, to these are added the previously mentioned common parameters that can represent important prognostic factors. In conclusion, the characteristics commonly identified in one type of cancer may act as risk factors for the other tumor. The detected data include threshold values and risk factors, making a significant contribution to the existing literature.

Device to Device (D2D) is a pivotal technology in the next generation of communication, allowing for direct task offloading between mobile devices (MDs) to improve the efficient utilization of idle resources. This paper proposes a novel algorithm for dynamic task offloading between active MDs and idle MDs in the D2D-MEC (Mobile Edge Computing) system by deploying multi-agent deep reinforcement learning (DRL) to minimize the long-term average delay of delay-sensitive tasks under deadline constraints. Our core innovation is a dynamic partitioning scheme for idle and active devices in the D2D-MEC system, accounting for stochastic task arrivals and multi-time-slot task execution, which has been insufficiently addressed in existing literature. We adopt a queue-based system to formulate a dynamic task offloading optimization problem. To address the challenges of large action space and coupling of actions across time slots, we model the problem as a Markov Decision Process (MDP) and perform the multi-agent DRL through Multi-Agent Proximal Policy Optimization (MAPPO). We employ a centralized training with decentralized execution (CTDE) framework to enable each MD to make offloading decisions solely based on its local system state. Extensive simulations demonstrate the efficiency and fast convergence of our algorithm. In comparison with the existing sub-optimal results deploying single-agent DRL, our algorithm reduces the average task completion delay by 11.0% and the ratio of dropped tasks by 17.0%.

1,2-Dihydroisoquinolines are important compounds due to their biological and medicinal activities, and numerous approaches to their synthesis have been reported. In this study, a palladium-catalyzed cascade cyclization-coupling of trisubstituted allenamides containing a bromoaryl moiety with arylboronic acids is described. The reaction proceeds via intramolecular cyclization, followed by transmetallation with the arylboronic acid of the resulting allylpalladium intermediate. A variety of substituted 1,2-dihydroisoquinolines were concisely obtained using this methodology because the allenamides, as reaction substrates, were prepared from readily available propargylamines in one step.

With the introduction of policies to promote intangible cultural heritage into schools, intangible cultural heritage plays an increasingly important role in primary education. However, the implementation of the intangible cultural heritage policy in primary schools is mostly formalized, which leads to many problems in the introduction of intangible cultural heritage, such as mainly staying at the level of visual display and public opinion publicity, carrying out a small number of intangible cultural experience activities, and insufficient materialization and scenization of intangible cultural heritage, so that students cannot feel the inherent charm of intangible cultural heritage. In order to promote the development of intangible cultural heritage education, this paper uses the AGIL model of Parsons, literature analysis, case analysis and interview methods to study the promotion path of intangible cultural heritage in primary schools, and proposes solutions such as setting educational goals for school segments, setting up intangible cultural experience activities in schools, combining intangible cultural heritage with subject courses, and establishing a good maintenance mode. After the program is applied into practice, it is found that the use of storytelling by teachers to popularize the relevant knowledge of intangible cultural heritage is conducive to stimulating students' interest and prompting students to think. In addition, teaching and life practice should be combined, and students' five education should be emphasized at the same time to avoid teaching uniformity.

Background and Objectives: The existing recommendations for female pelvic magnetic susceptibility weighted imaging MRI (FP-SWI) have not been optimized to capture the disease characteristics of the female pelvis. Therefore, it is imperative to explore acquisition parameters before conducting larger-scale studies. To establish optimized flip angle (FA) for acquiring FP-SWI to improve the image quality of female pelvic lesion sites. Materials and Methods: To evaluate signal quality and lesion conspicuity, regions of interest (ROIs) were manually drawn within the lesion on SWI sequences. Signal intensity was measured within the ROIs. Additionally, signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) were calculated for SWI sequences acquired at three FA: 10°, 15°, and 20°. Finally, a qualitative assessment of anatomical detail visualization, geometric distortion extent, artifacts, and lesion clarity was performed using a four-point scale. The Wilcoxon rank sum test was employed to compare the qualitative evaluation parameters. The intra-class correlation coefficient (ICC) was calculated to determine the consistency of subjective ratings between two observers. Results: FA=10° showed significantly higher SNR than FA=15° and 20° in most anatomical regions (P&lt;0.05), while the CNR was significantly higher than FA=15° and 20° (P&lt;0.05). Compared with FA=15° and 20°, the image quality of FA=10° was significantly higher, with less distortion and ghosting, and better image contrast (P&lt;0.05). Lesions with FA=10° exhibited higher clarity compared to FA=15° and 20° (P&lt;0.05). Conclusions: The image quality of FP-SWI images at FA=10° exceeds that at FA=15° and 20°. We recommend that when conducting SWI examination of the female pelvic cavity, the FA value should be set at 10° to stabilize the SWI sequence and improve image quality.

Background: The role of preoperative serum carcinoembryonic antigen (sCEA) and postopeative tissue CEA (tCEA ) were widely elaborated separately for colorectal cancer (CRC). But the role of the combined sCEA and tCEA was scarcely described by now. Methods: 1757 cases of 0~ⅣCRC from January 2006 to January 2016 in our institution were involved. Clinicopathological features and follow up data were collected. 0 stage was combined into 0&Ⅰ stages. SCEA was classified to normal and high(>10ng/ml) and tCEA were classified into three grades (+,++,+++). So combined groups were six (2ⅹ3). ANOVA and Crosstab were used to analyze continuous and counting data, Univariate and multivariate were analyzed by Cox regression. All data were analyzed by SPSS27 and survival curves with number at risk were visualized by R 4.3.1. Results: Gender, age, tumor location, tumor size, blood loss, T stage, differentiation, harvested lymph nodes, positive lymph nodes, chemotherapy, TNM stage and complication have difference between the combined CEA test (all P

This study describes the synthesis and characterization of mixed hydrotalcite–organosilica membrane for gas separation. Hydrotalcite exhibits the capability to adsorb carbon dioxide at elevated temperatures. High surface area and favorable coating properties are essential to harness its potential for practical applications. Stable alcohol-based dispersions are needed for thin film applications of mixed membranes containing hydrotalcite. Currently, producing such dispersions without the need for delamination and dispersion agents is a challenging task. This work introduces for the first time a manufacturing approach to overcoming the drawbacks mentioned above. It includes a synthesis of hydrotalcite nanoparticles, followed by agent-free delamination of their layers and final dispersion into alcohol without dispersion agents. Further, the hydrotalcite-derived sorption agent is dispersed in a matrix based on organo-silica gels derived from 1,2-bis(triethoxysilyl)ethane (BTESE). The analytical results indicate that the interconnection between hydrotalcite and BTESE-derived gel occurs via forming a strong hydrogen bonding system between the interlayer species (OH groups, CO32-) of hydrotalcite and oxygen and silanol active gel centers. These findings lay the foundation for applications involving incorporating hydrotalcite-like compounds into silica matrices, ultimately enabling the development of materials with exceptional mass transfer properties. In part 2 of this study, gas separation performance of the organo-silica and the hydrotalcite-like materials and their combined form will be investigated

This qualitative research explores the adoption of blockchain technology in supply chain management, aiming to understand the drivers, barriers, and implications associated with its integration. Through in-depth interviews and thematic analysis, insights are gathered from key stakeholders in the supply chain ecosystem. The findings reveal a complex landscape, with stakeholders recognizing blockchain's potential to enhance transparency, efficiency, and trust while acknowledging challenges related to technical complexities, regulatory uncertainties, and organizational barriers. Despite these challenges, participants express optimism about blockchain's transformative potential, citing opportunities for improved traceability, supply chain resilience, and sustainability. Collaboration, governance, and ecosystem development emerge as critical factors for driving blockchain adoption within supply chains, alongside the need for continuous education and capacity-building initiatives. Overall, the study underscores the importance of addressing challenges and fostering a culture of innovation and collaboration to unlock the full potential of blockchain-enabled supply chains.

The rapid urban expansion requires an effective management of water resources in small basins, where data are often limited. This article addresses a combination of an empirical hydrological model and Steven Method, a flow extrapolation method that considers the morphological char-acteristics of the cross-section. It also proposes an approach for overcoming the challenges asso-ciated with the lack of information on small water basins in rural to urban transition. A rain-fall event occurred in Pau de Caixeta stream basin (33,7 km²), in the Federal District (DF), in De-cember 2022, was evaluated. The simulation was carried out on the decision support system, Analysis of Complex Basins (ABC), using the rainfall registred by the rain gauge instaled within the monitered area with 3 hours duration and 38 mm of total rainfall, in addiction to the mor-phological and hydraulics characteristics of the study section. The basin presented in this study, has a classification regarding land use: i) urban area: horizontal and vertical residential neigh-borhoods (in the study phase) and rapidly expanding urban infrastructure, ii) rural areas and iii) environmental preservation areas. The results were within the acceptable range of flow extrap-olation errors (16%), indicating the integration of the proposed approaches can guide the devel-opment of impact mitigation strategies and promote sustainable practices in sub-basins.

Abstract: Herbicide flashback is an undesirable response that results in damage or mortality of non-target plants near chemically treated plants. In severe instances, crop trees can be injured resulting in financial loss or inability to capture management objectives. Land managers need to know the potential limitations of using triclopyr acid (50% solution in water) and what quantity can cause damage to non-target trees (trees not aimed to control via herbicide). Three naturally regenerated (previous clearcut) bottomland hardwood sites, ranging from 14–20 years of age, received partial overstory deadening using Trycera® herbicide. Residual “leave” trees experienced indirect herbicide uptake resulting in some trees either experiencing mortality or partial mortality with top die-back/epicormic branching. An increased probability of damage occurred as tree diameter decreased and the number of treated stems around non-target stems increased. American sycamore, green ash, and sweetgum were most susceptible to flashback. This study examines the unanticipated chemical effect of deadening adjacent stems surrounding residual leave trees in poorly drained soils.

Terpenes and terpenoids content in cannabis plant was already studied in the past with three used methods. Since these works did not compare the content of these substances under the same conditions, we tried to make this comparison exactly. Three different gas chromatography/mass spectrometry (GS/MS) methods - hexane based liquid extraction (Liq), static head-space extraction (HS), and head-space solid phase microextraction (SPME) – were compared to identify volatile compounds in four different cannabis chemotypes - Green fields, Titan chemotype, Black Domina chemotype, and Neptune chemotype. The main compounds focused on were monoterpenes/monoterpenoids and sesquiterpenes/sesquiterpenoids. Extraction with hexane gave comparable results, however the other two methods allowed for the identification of more substances. For the final evaluation of the comparison of the three methods of analysis, extraction with hexane gives comparable results (which is advantageous for quantitative analysis), although the other two methods allowed for the identification of more substances. This means that the same method should be used everywhere for the quantitative evaluation of constituents in cannabis.

This study proposes the first extracellular domain (residues 1-34) of the CCR1 protein as the Gc protein-derived Macrophage Activating Factor (GcMAF) receptor. The CCR1 gene, expressed in monocytes and 168 other cell types or tissues, encodes this transmembrane protein. Electrostatic and hydrophobic interactions, along with hydrogen bonds mediate the molecular interactions between the TPT^420-GalNAcELAK (or TPK⁴²⁰ELAK) sequences of GcMAF (or Gc2 protein variant) and the TTEDYDTTT sequence of its receptor.

This study explores the impact of regular physical exercise on the quality of life and body image among Para-athletes, emphasizing the necessity of such activities for physical, social, and psychological health. This qualitative study employs content analysis and ethnomethodology to evaluate seven Para-athletes from the Navy's Paralympic Project, using focus group interviews to assess their perceptions. The findings reveal that participation in structured sports programs positively influences body image and quality of life, leading to improved performance in training, social interactions, and competitive events. The analysis suggests that motivation and self-esteem are fundamental to the sporting success of Paralympic athletes. Both external and internal motivations are crucial for sustaining athletic careers and overcoming challenges. Self-esteem enables athletes to remain confident in their abilities, even after setbacks.

Africa, home to the world's second-largest population of approximately 1.3 billion, grapples with significant challenges in meeting its medical needs, particularly in accessing quality healthcare services and products. The continent faces a continuous onslaught of emerging infectious diseases, exacerbating the strain on its already fragile public health infrastructure. The emergence of SARS-Cov2 has further exposed the deficiencies in Africa's public health response, ranging from limited diagnostic capabilities to difficulties in vaccine distribution. Compounding these challenges is vaccine hesitancy, which is prevalent in many regions due to varying levels of understanding and trust regarding vaccines. The disparities in vaccine literacy across the continent stem from a complex interplay of factors, including low literacy rates and a history of medical exploitation and misinformation campaigns. These factors have led to a pervasive distrust in medical institutions and healthcare providers among certain African communities. Despite concerted efforts by national governments, private entities, and international partners to address these challenges and improve vaccine literacy, significant hurdles persist. This manuscript examines the current state of education in vaccinology and related sciences in Africa, as well as the continent's efforts to address educational needs in vaccine development and manufacturing. It evaluates initiatives aimed at strengthening vaccine education and literacy, highlighting successful approaches and ongoing challenges. By assessing the progress made and identifying remaining obstacles, this review offers insights into how Africa can enhance its capacity in vaccinology and accelerate its contributions to global health security.

This ethnographic study investigates the cross-cultural challenges encountered in global supply chains, focusing on communication barriers, diverse business practices, trust-building, ethical and legal standards, and cultural competence. By embedding within the day-to-day operations of multinational corporations and conducting in-depth interviews with supply chain professionals, the research provides a nuanced understanding of the cultural dynamics that impact global supply chain management. The findings highlight that effective communication goes beyond language proficiency, requiring an understanding of varying communication styles and contextual nuances. Business practices shaped by cultural values such as power distance and uncertainty avoidance necessitate adaptive management strategies that balance local norms with global standards. Trust and relationship-building are critical, particularly in cultures where personal relationships underpin business transactions, demanding long-term investment in relationship-building activities. Ethical and legal standards vary significantly across regions, presenting challenges that require a nuanced approach to global governance. The study underscores the importance of cultural competence as a critical skill for supply chain professionals, enabling them to bridge cultural gaps and foster productive collaborations. Sustainability efforts, entrepreneurship, and innovation are also influenced by cultural factors, highlighting the need for culturally sensitive strategies. Emotional intelligence is identified as essential for managing cross-cultural interactions, with participants demonstrating high emotional intelligence more effectively navigating the emotional and social complexities of cross-cultural communication. The use of technology in managing cross-cultural challenges is acknowledged, but the findings suggest that it must be complemented by cultural competence. Overall, the study provides valuable insights for companies seeking to enhance their cross-cultural effectiveness, emphasizing the importance of cultural competence, communication, and relationship-building in achieving sustainable success in global supply chains.