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, 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.

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 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.

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, 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, 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, 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.

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.

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, 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.

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.

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.

Objectives: To study the differences between malignant hypermetabolic axillary lymphadenopathy (MHL) and COVID-19 vaccine-associated axillary hypermetabolic lymphadenopathy (VAHL) using clinical imaging. Methods: A total of 1,096 patients underwent Positron Emission Tomography-Computed Tomography (PET-CT) between June 1, 2021 and April 30, 2022, at Ehime University Hospital. In total, 188 patients with axillary lymphadenopathy after the COVID-19 vaccination were evaluated. The patients were classified into three groups such as VAHL (n=27), MHL (n=21), and equivocal hypermetabolic axillary lymphadenopathy (EqHL; n=140). Differences in lymph nodes (LNs) swellings were statistically analyzed using clinical imagings (echography, CT, and 18F-FDG PET) statistically. Results: MHL included a higher female population (90.5%) owing to a higher frequency of breast cancer frequency (80.9%). Axillary LNs of MHL did not show any LN fatty hilums (0%); however, those of VAHL and EqHL did (15.8 and 36%, respectively). After the logistic regression analysis of the patients who had axillary lymphadenopathy without any LN fatty hilums, the minor axis length and ellipticity (minor axis/major axis) in the largest axillary LN, SUVmax, and Tissue-to-Background Ratio (TBR) were useful in distinguishing malignant lymphadenopathies. Receiver-operating characteristic (ROC) analysis indicated that a cut-off value of ≥7.3 mm for the axillary LN minor axis (sensitivity: 0.714, specificity: 0.684) and of ≥0.671 for ellipticity (0.667 and 0.773, respectively) in the largest LN with the highest SUVmax and TBR were predictive of MHL. Conclusion: Axillary lymphadenopathy ≥7.3 mm of the minor axis and ≥0.671 of ellipticity in LN without fatty hilum suggests malignancy even in patients who have received COVID-19 vaccination. Further examinations such as 18F-FDG PET are recommended for such patients

A millimeter-wave (mmWave) gallium nitride (GaN) high-power amplifier (PA) monolithic microwave-integrated circuit (MMIC) was implemented, considering a source via effect. In this paper, we introduce guidelines for designing GaN high PA MMICs, from device sizing to meeting high-power specifications, power matching considering source via effects, schematic design of three-stage amplifier structures, and electromagnetic (EM) simulation. Based on the results of load pull simulation and small-signal maximum stable gain (MSG) simulation, the GaN high electron-mobility transistor (HEMT) size was selected to be 8×70 μm. However, since the source via model provided by the foundry was significantly different from the EM results, it was necessary to readjust the power matching considering this. Additionally, when selecting the source via size, the larger the size, the easier the matching, but since the layout of the peripheral bias circuit is not possible, a compromise was required considering the actual layout. To prevent in-band oscillation, an RC parallel circuit was added to the input matching circuit, and low-frequency oscillation was solved by adding a gate resistor on the PCB module. The proposed PA was fabricated with a commercial 0.1 μm GaN HEMT MMIC process. It exhibited 38.56 to 39.71 dBm output power (Pout), 14.2 to 16.7 dB linear gain, and 14.1% to 18.2% power-added efficiency (PAE) between 34 and 36 GHz. The fabricated GaN power amplifier MMIC shows competitive Pout in the Ka upper band above 33 GHz

Abstract: Cleft palate is a congenital condition result from incomplete fusion of palatine shelves. The current study aimed to assess the effects of vitamin B6 on the incidence of corticosteroid-induced cleft palate model. Eighteen pregnant mice were divided into three groups. Mice of control group were injected with sterile physiological saline from 11th - 14th days of gestation. Mice of group II were injected with 125 mg/kg hydrocortisone from 11th - 14th days of gestation. Mice of group III were injected with hydrocortisone as in group II and given drinking water containing 500 µg/ml of vitamin B6 from day zero of gestation until delivery. Two days after delivery, the offspring were counted, and their head circumferences were taken for statistical analysis. The heads of the offspring were fixed and processed for paraffin sectioning and stained with hematoxylin and eosin. Cleft palates were counted and statistically analyzed using ANOVA test to determine any significances (P

The advent of social commerce (SC) has transformed the landscape of online consumer behavior, emphasizing the significance of customer-to-customer relations in shaping sustainable relation-ships with customers. This research investigated the intricate relationships between social com-merce dimensions, particularly suggestions and recommendations, forums and communities, and ratings and reviews, and their influence on customer-to-customer value co-creation (C2CVCC) and sustainable customer relationships (SCRs). A questionnaire was designed and administered to 635 respondents. We examined the psychometric properties of the measurements and subse-quently applied Partial Least Squares as a Structural Equation Modeling method (PLS-SEM) for hypothesis testing. The findings reveal that the dimensions of SC significantly impact C2CVCC, with ratings and reviews playing a pivotal role. Furthermore, C2CVCC emerges as a substantial mediator in the path between SC and SCRs. The empirical analysis showcases strong support for the proposed model, with robust path coefficients (β) and p-values confirming direct and indirect effects. These findings offer valuable insights for businesses seeking to leverage SC and customer interactions to enhance SCRs in the digital era. Understanding the dynamics of C2CVCC within the context of SC has become essential for marketers and businesses aiming to thrive in today's competitive online marketplace.

The present study aims to evaluate the antibacterial activity of five commercially available essential oils (EOs): Lavender (LEO), Clove (CEO), Oregano (OEO), Eucalyptus (EEO), and Peppermint (PEO) against the most-known MDR Gram-positive and Gram-negative bacteria - Staphylococcus aureus (ATCC 25923), Escherichia coli (ATCC 25922) and Pseudomonas aeruginosa (ATCC 27853) - alone and in various combinations. Gas Chromatography-Mass Spectrometry (GC-MS) analysis established their complex composition. Then, the antibacterial activity was investigated in vitro by diffusimetric antibiogram method, using sterile cellulose discs with Ø 6 mm impregnated with 10 µl of sample and sterile borosilicate glass cylinders loaded with 100 µl of sample; MIC (µg/mL) for each EO was calculated from IZD values (mm) measured after 24 hours. The following EO combinations were evaluated: OEO+CEO, CEO+EEO, CEO+PEO, LEO+EEO, and EEO+PEO. Then, the influence of each dual combination on 3 conventional antibacterial drugs – Neomycin (NEO), Tetracycline (TET), and Bacitracin (BAC) - activity was investigated. The most active EOs against S. aureus and E. coli were LEO and OEO (IZD = 40 mm). They were followed by the CEO and EEO (IZD = 20-27 mm); PEO exhibited the lowest antibacterial activity (IZD = 15-20 mm). EEO alone showed the highest inhibitory activity on P. aeruginosa (IZD = 25-35 mm). It was followed by the CEO, LEO, and EEO (IZD = 7-11 mm), while PEO proved no antibacterial action against it (IZD = 0 mm). Only one synergic action was recorded (OEO+CEO against P. aeruginosa); EEO+PEO revealed partial synergism against S. aureus and CEO+PEO additive behavior against E. coli. Two triple associations with TET showed partial synergism against E. coli, and the other 2 ones (with NEO and TET) evidenced the same behavior against S. aureus; all contained EEO+PEO or CEO+PEO. Most combinations reported indifference. However, numerous cases were of antagonism between constituents included in double and triple combinations, and EOs with the strongest antibacterial activities belong to the highest antagonistic combinations. A consistent statistical analysis supports our results, showing that EOs with moderate antibacterial activities could generate combinations with higher inhibitory effects based on synergistic or additive interactions.

The rebound behaviors of rubber balls based on ethylene-propylene-diene monomer (EPDM) / chlorinated butyl rubber (CIIR) blends were investigated systematically. A novel method was proposed to characterize the damping capacity of the EPDM/CIIR blends. The damping capacity can be represented by the rebound height of rubber balls, and lower rebound height corresponds to better damping capacity. A mathematical model expressed by an equation obtained through theoretical derivation has been proposed to predict the rebound height of the rubber balls. The energy dissipation rate (EDR) defined by the ratio of the height loss to the rebound time was proposed to further characterize the damping capacity. The EDR value shows the highest for the pure CIIR and lowest for the pure EPDM, showing a decrease trend with the increase of EPDM content in the rubber blends. By comparison one can obtain that the damping capacity of the EPDM/CIIR blends decreases with the decrease of external excitation, the conclusion of which plays a key role in the formulation design of viscoelastic damping rubber materials.

First-line treatment for advanced large-cell neuroendocrine carcinoma of the lung (LCNEC) has limited efficacy. This study aimed to explore the efficacy and safety of everolimus combined with EP regimen chemotherapy (etoposide + cisplatin, EP) in the first-line treatment for LCNEC. The patients were randomly assigned to the experimental or control group, with 20 patients in each group. The experimental group received the mTOR inhibitor everolimus 5 mg once a day combined with EP ivgtt, d1-3, every 3 weeks for 4–6 cycles. The control group received EP only and the infusion method was the same as that of the experimental group. The safety in the experimental group was controllable and not inferior to that in the control group. Serious adverse effects were observed in approximately 10% of patients. Objective response rate (ORR) for the experimental and control groups were 15% vs. 0 (P=0.231), disease control rate (DCR) was 100% vs. 32% (P

A challenge in building large-scale superconducting quantum processors is the precise control and manipulation of the qubit state. However, the crosstalk between the microwave control lines impedes the parallel execution of high-fidelity digital and analog quantum operations. Here, we propose and demonstrate a universal compensation protocol for calibrating the microwave signal crosstalk. We also introduce amplified error sequences to optimize the accuracy. Furthermore, we show a definitive improvement in parallel gate operations with crosstalk cancellation, demonstrating the technique's effectiveness. This work paves the way for superconducting hardware that features automated calibration of microwave crosstalk, leading to enhanced fidelities in multiqubit circuits.

Introduction/Aim: Central sensitivity to thyroid hormones refers to the sensitivity of the hypothalamic-pituitary-thyroid (HPT) axis to changes in circulating free thyroxine (fT4). The relationship between fT4 levels and iodine intake is complex. The aim of the present study was to assess central sensitivity to thyroid hormones in pregnancy against iodine intake. Materials & Methods: One thousand one hundred two blood and urine samples were collected from pregnant women (with a mean age+SD of 30.4+4.6 years) during singleton pregnancies; women with known/diagnosed thyroid disease were excluded. Specifically, TSH & fT4 and 24-hour urinary iodine excretion (UI) were measured in each trimester and at two months postpartum. The Thyroid Feedback Quantile-based Index (TFQI) was calculated to assess central sensitivity to thyroid hormones. For the statistical analysis of TFQI by time period, analysis of variance (ANOVA) was used, while Pearson's correlation was used to assess TFQI versus UI. Results: The mean TFQI index ranged from -0.06 (first trimester) to -0.07 (two months postpartum), while the corresponding UI was 141 and 172 μg/L, respectively. The TFQI-UI correlation was negative (Pearson r: -0.325, p: 0.04 and r: -0.399, p: 0.023), for UI values over 250 μg/L, in the first and the third trimester of pregnancy, respectively. Discussion: TFQI is a new index reflecting central sensitivity to thyroid hormones. Lower TFQI indicates higher sensitivity to thyroid hormones. In our sample TFQI was inversely related to iodine intake, in the first trimester of pregnancy (the critical period of organogenesis) and the third trimester (the critical period of fetal growth). Thus, the observed changes in TFQI may reflect different ways of central action of thyroid hormones, according to the phase of pregnancy. The negative association between maternal TFQI (indicative of central sensitivity to thyroid hormone) and urine iodine levels during the third trimester of pregnancy may reflect the combined influence of maternal and fetal thyroid function. Our results are intriguing and have the potential to enhance our comprehension of the changes in the HPT axis’ function via variations in central sensitivity to thyroid hormones and its interplay with nutritional iodine status during pregnancy.

During the high-speed flight of a vehicle in the atmosphere, surface friction with the air generates aerodynamic heating. The aerodynamic heating phenomenon can create extremely high temperatures near the surface. These high temperatures impact material properties and the structure of the aircraft, so thermal deformation measurement is essential in aerospace engineering. This paper revisits high-temperature deformation measurement using the digital image correlation (DIC) technique under high-intensity blackbody radiation with a precise speckle pattern fabrication and a heat haze reduction method. The effect of speckle pattern on the DIC measurement has been thoroughly studied at room temperature, but high-temperature measurement studies have not reported such effects so far. We found that the commonly used methods to reduce the heat haze effect could produce incorrect results. Hence, we propose a new method to mitigate heat haze effects. An infrared radiation heater was employed to make an experimental setup that could heat a specimen up to 950 ℃. First, we mitigated image saturation using a short-wavelength bandpass filter with blue light illumination, a standard procedure for high-temperature DIC deformation measurement. Second, we studied how to determine the proper size of the speckle pattern under a high-temperature environment. Third, we devised a reduction method for the heat haze effect. As proof of the effectiveness of our developed experimental method, we successfully measured the deformation of stainless steel 304 specimens from 25 ℃ to 800 ℃. The results confirmed that this method can be applied to the research and development of thermal protection systems in the aerospace field.

This study presents an effective control algorithm to improve the robustness of fast steering mirror (FSM)-based laser beam steering systems against dynamic disturbances such as repetitive disturbances resulting from operating conditions. A stable control system must be able to maintain the required high-precision control even when dynamic disturbances affect the FSM system. In this study, an improved control method is proposed using an internal model principle (IMP)-based nonlinear controller with a disturbance observer (DOB) for the FSM system. This IMP-based controller with DOB can attenuate the residual control error signal under dynamic disturbance conditions.

The present study describes a comprehensive analysis of the Adverse Drug Reactions (ADRs) documented in the Database of the Spanish Pharmacovigilance System (FEDRA) concerning the use of biological medications used for severe refractory asthma, specifically omalizumab, mepolizumab, reslizumab, benralizumab, dupilumab, and tezepelumab. Emphasis was placed on ADRs not documented in the Technical Sheet (Summary of Product Characteristics, SmPC) of the respective specialties (Xolair®, Nucala®, Cinqaero®, Fasenra®, Dupixent®, and Tezspire®), which could potentially trigger a warning signal in Pharmacovigilance, indicating previously unidentified risks. The analysis encompassed data from the inception of each drug ́s marketing until January 22, 2024, including cases originating from various sources: direct submissions to the Spanish Pharmacovigilance System, communications from the Pharmaceutical Industry, and findings from literature review. Notifications were analyzed independently of their origin, so a complete review of all ADRs associated with these medications was ensured. In essence, this investigation highlights the critical role of post-marketing safety information, emphasizing the relevance of comprehensive reporting by healthcare professionals to facilitate a robust Pharmacovigilance system, ultimately advancing patient care and safety.

LLMs are a compressed repository of a vast corpus of valuable information on which they are trained. Therefore, this work hypothesizes that LLMs such as Llama, Orca, Falcon, and Mistral can be used for misinformation detection by making them cross-check new information with the repository on which they are trained. Accordingly, this paper describes the findings from the investigation of the abilities of LLMs in detecting misinformation on multiple datasets. The results are interpreted using explainable AI techniques such as LIME, SHAP, and Integrated Gradients. The LLMs themselves are also asked to explain their classification. These complementary approaches aid in better understanding the inner workings of misinformation detection using LLMs and lead to conclusions about their effectiveness at the task.

The Simultaneous Localization And Mapping (SLAM) scanner is an easy and portable Light Detection And Ranging (LiDAR) data acquisition device. Its main output is a 3D point cloud covering the scanned scene. Regarding the importance of accuracy in the survey domain, this paper aims to assess the accuracy of two SLAM scanners: the NavVis VLX and the BLK2GO Scanner. This assessment is conducted for both outdoor and indoor environments. In this context, two types of reference data are used: the Total Station (TS) and the static scanner Z+F Imager 5016. To carry out the assessment, four comparisons are tested: cloud to cloud, cloud to mesh, mesh to mesh, and edge detection board assessment. However, the results of the assessments confirm that the accuracy of indoor SLAM scanner measurements (5 mm) is greater than that of outdoor ones (between 10 mm and 60 mm). Moreover, the comparison of cloud to cloud provides the best accuracy regarding direct accuracy measurement without manipulations. Finally, based on the high accuracy, scanning speed, flexibility, and the accuracy differences between tested cases, it is confirmed that SLAM scanners are effective tools for data acquisition.

The fourth industrial revolution (4IR) can offer significant benefits to the construction sector, improving productivity, efficiency, collaborative efforts, and product quality while promoting safety and sustainability. However, research on the application of 4IR technologies in construction is scarce in developing countries. It is crucial to understand the ability of construction companies to adopt new technologies and identify factors influencing the success of technology implementation. In this study, a questionnaire-based survey was conducted with construction professionals to evaluate the level of technological development of the construction market in an emerging economy, assess the potential for innovation implementation, and identify factors that might influence technological development. Although respondents recognized the importance of digital transformation, the results showed that most innovations are in the early stages of implementation in the construction sector, particularly technologies that are essential for the consolidation of the 4IR. Understanding the factors underlying this reality can support the development of strategies to foster innovation and harness the advantages of the 4IR in the construction industry in developing countries.

On the afternoon of January 31, 2022, the northwest and central part of the city of Quito (Ecuador) was hit by a mud-flow that originated in one of the ravines of the Pichincha volcanic complex. According to the official reports, there were 28 fatalities, one missing person, 52 injured, and 53 families affected. The mudflow was triggered by unusual and heavy rainfall in the upper part of the drainage. However, the analysis of the deposits allowed us to establish the existence of anthropogenic elements as crucial components of a local disaster that affected daily life in the city for more than a week. Based on the preliminary data, we were able to determine that the mud and water flowed through different streets of the city, reaching a maximum distance of 3.2 km from the overflow point (collector, construction works to dam the drainage under the city). The analysis of the multimedia material published on social networks and in the press also made it possible to detect the change in the behavior of the flow during its evolution, which went from a hyper-concentrated flow to muddy water. A similar event occurred in 1975, and although it was a larger event (52000 m3, seven times larger than in 2022), it caused two deaths and little damage in the same area. The main causes of the disaster included urban development that did not meet the needs of the area and a lack of awareness or ignorance about the management and intervention of drainage in Quito City.

Background: Hurricanes and other wind events are significant disturbances that affect coastal urban forests around the world. Past research has led to the creation of wind resistance ratings for different tree species which can be used in urban forest management efforts to mitigate the effects of these storms. While useful, these ratings have been limited to species common to one global region (Florida, USA).Methods: Drawing on past ratings and data from a global literature review on tropical storm research, we created a machine learning model to broaden both the geographic coverage and the variety of species currently assessed for their resistance to wind.Results: We were able to assign wind resistance ratings to 281 new species based on the available data and our modelling efforts. The model accuracy and agreement with the original ratings when applied to the testing data set was high with 91% accuracy.Conclusions: The resulting list of wind resistance ratings has been adapted into a spreadsheet-based decision aid for managers, allowing them to assess the overall susceptibility of their urban forest to wind events like hurricanes.

TAFRO syndrome (TS) is a rare variant of idiopathic multicentric Castleman's disease (iMCD) characterized by a confluence of symptoms: thrombocytopenia (T), anasarca (A), fever (F), reticulin myelofibrosis (R), and organomegaly (O). First described in Japan in 2010, the pathogenesis of the disease remains unclear. Due to its heterogeneous presentation and potential life-threatening delays in diagnosis, precise diagnosis is essential. According to the literature, no specific imaging modality has been recommended for the work-up of patients with suspected TS. Here, we report a case of TS and its management using 18F-FDG-PET/CT imaging as an attractive complementary diagnostic tool.

The growing demand in industrial and biotechnological settings for more efficient enzymes with enhanced biochemical features, particularly thermostability and thermotolerance, necessitates a timely response. Renowned for their versatility, thermostable enzymes, offer significant promise across a range of applications, including agricultural, medicinal, and biotechnological domains. This comprehensive review summarizes the structural attributes, catalytic mechanisms, and the relationships between structure and function of two major classes of thermostable enzymes: α-amylases and laccases. These enzymes serve as valuable models for understanding the structural basis of protein thermostability. Commercial significance of these enzymes and researchers' interest in further optimization and innovation, this article can greatly contribute to ongoing research on thermostable enzymes and aiding industries in optimizing production processes. It also give insights to the exploration of suitable strategies and factors for enhancing thermostability, resulting in heightened multipronged stability and notable enhancements in the enzymes’ industrial applicability.

Primary percutaneous coronary intervention (pPCI) has revolutionized the prognosis of ST-segment ele-vation myocardial infarction (STEMI) and is the gold standard treatment. As a result of its success, the number of pPCI centres has expanded worldwide. Despite decades of advancements, clinical outcomes in STEMI patients have plateaued. Out-of-hospital car-diac arrest and cardiogenic shock remain a major cause of high in-hospital mortality, whilst the growing burden of heart failure in long-term STEMI survivors presents a growing problem. Many elements aiming to optimize STEMI treatment are still subject to debate or lack sufficient evidence. This review provides an overview of the most contentious current issues in pPCI in STEMI patients, with an emphasis on unresolved questions and persistent challenges.

Traditional Medicine (TM) is a culturally-rooted healthcare practice, and its use, including for treating illnesses among children, has been reported in many countries. Despite the cultural significance of TM in managing children’s illnesses, evidence suggests that child mortality remains high in many settings. This indicates that the sole use of TM within families and communities might act as a barrier to using biomedical services, contributing to avoidable deaths. Globally, Indonesia is in the top 10 countries with the highest child mortality rates. In addition, Belu is a district in East Nusa Tenggara province, Indonesia that exhibits a high number of child deaths within the last three years. However, the use of TM for the treatment of illnesses among children in Indonesia has received minimal academic attention. This study aimed to understand parental beliefs, knowledge, views, and perceptions of TM and the impact on the use of TM and biomedical services in the treatment of illnesses among their children in Belu district, Indonesia. The participants (n=25) were parents with the real-life experiences of using TM for treating their children’s illnesses. They were recruited using the snowballing sampling technique. Data were collected using in-depth qualitative interviews. A thematic data analysis was performed and guided by a qualitative data analysis framework. The findings were grouped into four main themes: (i) parental beliefs, knowledge, views, and perceptions of TM, (ii) the influence of these factors on parental use of TM and biomedical services for the treatment of children’s illnesses, (iii) social and cultural influences on the use of TM and biomedical services among their children, and (iv) the impact of the sole use of TM or late medical diagnosis on the health condition and the death of children. The findings show that the use of TM is a common practice within families and communities in Belu, however evidence suggests that child mortality remains high in the setting, indicating less effectiveness of the sole use of TM. Thus, there is a need for the development of collaborative models of healthcare programs and service delivery fostering mutual respect and understanding between traditional healers and healthcare professionals, which could significantly contribute to improving parental use of biomedical services for the treatment of their children’s illnesses.

Accurate streamflow forecasting is crucial for effectively managing water resources, particularly in countries like Colombia, where hydroelectric power generation significantly contributes to the national energy grid. Although highly interpretable, traditional deterministic, physically-driven models often suffer from complexity and require extensive parameterization. Data-driven models like Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) networks offer simplicity and performance but cannot quantify uncertainty. This work introduces Sparse Variational Gaussian Processes (SVGPs) for forecasting streamflow contributions. The proposed SVGP model reduces computational complexity compared to traditional Gaussian Processes, making it highly scalable for large datasets. The methodology employs optimal hyperparameters and shared inducing points to capture short-term and long-term relationships among reservoirs. Training, validation, and analysis of the proposed approach consider the streamflow dataset from 23 geographically dispersed reservoirs recorded during twelve years in Colombia. Performance assessment reveals that the proposal outperforms baseline Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) models in three key aspects: adaptability to changing dynamics, provision of informative confidence intervals through Bayesian inference, and enhanced forecasting accuracy. Therefore, the SVGP-based forecasting methodology offers a scalable and interpretable solution for multi-output streamflow forecasting, thereby contributing to more effective water resource management and hydroelectric planning.

Malaria parasites increase their host erythrocyte’s permeability to obtain essential nutrients from plasma and facilitate intracellular growth. In the human P. falciparum pathogen, this increase is mediated by the plasmodial surface anion channel (PSAC) and has been linked to CLAG3, as encoded by one member of the conserved clag multigene family. Whether paralogs encoded by other clag genes also contribute to PSAC formation or serve unrelated roles remains unknown. Here, we generated transfectant lines carrying epitope-tagged versions of each CLAG. Each paralog colocalized with CLAG3, with concordant trafficking via merozoite rhoptries to the host erythrocyte membrane of newly-invaded erythrocytes. Each also exists within infected cells in at least two forms: an alkaline-extractable soluble form and a form integral to the host membrane. Like CLAG3, CLAG2 has a variant region cleaved by extracellular protease but CLAG8 and CLAG9 are protease-resistant. Paralog knockout lines, generated through CRISPR/Cas9 transfection, exhibited uncompromised growth in PGIM, a modified medium with more physiological nutrient levels; this finding is in marked contrast to a recently reported CLAG3 knockout parasite. CLAG2 and CLAG8 knockout lines exhibited compensatory increases in transcription of remaining clags and associated rhoph genes, yielding increased PSAC-mediated uptake to specific solutes. We also report distinct transport properties of these knockout lines, suggesting partially overlapping roles of CLAG paralogs in PSAC activity. We propose that the nutrient channel pore is formed by a higher order assembly of CLAG proteins at the host membrane.

This article uses machine learning analysis of wearable sensor data to explore the topic of driver differentiation. The study focuses on using detailed analyzes of data collected from wearable sensors to identify patterns that differentiate skilled drivers from inexperienced ones. On a predetermined driving route, participants experienced a variety of driving conditions, including parking, navigating cities, driving on highways and driving through residential neighborhoods. The gathered data was analyzed using machine learning techniques, yielding a classification accuracy of 94% overall. The results highlight important differences in sensor data between inexperienced and experienced drivers, providing insight into possible uses for improving safety protocols, driver education, and personalized feedback systems. The article fosters improvements in traffic safety and driver education by offering insightful information on the link between driver behavior analysis and machine learning.

Rural areas are not only faced with the problems of rural depopulation but also with the problem of water supply and water quality which is a basic necessity of life. In light of this, this paper assesses the rural water supply situation and the bacteriological quality of different water sources in the Obokun Local Government Area of Osun State, Nigeria. The safety of the water sources for human consumption and possible occurrence of the water borne diseases in the study area were determined. The study employed descriptive and analytical methods of data analysis to achieve the objectives of the inquiry. Findings showed that the study area suffered from inadequate water supply and poor locations of the sources of water: The study also revealed that the microbiological quality of the water sources used was unsafe, poor and not acceptable for human consumption. In addition, many man- days-hours were wasted in search of water. It is therefore recommended that the government should make the rural water supply and the maintenance of water quality a priority in its policy formulation.

Human papillomavirus (HPV) uses the cellular trafficking machinery to reach the cell nucleus and initiate a successful infection. The HPV capsid consists of two proteins: L1 (the major capsid protein) and L2 (minor capsid protein), and L2 is known to be responsible for trafficking the viral genome to the nucleus. From previous studies, we know that many cellular proteins interact with L2 and are involved in the trafficking process at different stages of the infectious entry process. To further investigate how HPV-16 achieves successful viral entry, we have performed a mass spectrometry analysis to identify novel interacting proteins that associate with incoming HPV-16 virions. We show that HPV-16 pseudovirions interact with a group of cellular cargo proteins (COPI), and here we confirm that this is mediated by the direct binding of L2, but not L1, to the COPB1 subunit. We also show that the ability of L2 to interact with COPB1 is conserved in both low- and high-risk HPV types. Furthermore, we also show that the interaction is essential for successful infection entry of multiple HPV types, thereby identifying a novel constituent of the infectious entry pathway of the HPV.

This research aims to explore factors that influence sustainable music education from a psychological perspective, and innovatively constructs a combination of qualitative and quantitative approaches. For first time, combines stochastic nonlinear system of control theory and identifies relevant factors affecting sustainable music learning by establishing a data system for questionnaire answering and a quantitative model for actual academic performance. Existing research mainly looks at several factors that affect fragmented music education from perspective of teachers' teaching rules, emphasizing phased teaching state and learning goals of teachers as main body, thus ignoring sustainable music education and students, who are a large group of music learning objects. The research fills gap in this type of research object, focusing on sustainable music education from an emotional perspective and students who occupy a dominant position in music learning, so as to more accurately explore impact of their emotional influencing factors on sustainable music learning. The most prominent innovation of this study lies in construction of stochastic nonlinear system for psychological influencing factors of sustainable student music learning and a quantitative model for actual learning effect. Through analysis of nonlinear system, weight values of several negative emotions on sustainable music learning are obtained.

Fraudulent transactions pose a significant threat to financial institutions and e-commerce platforms.Machine learning models, trained on historical labeled data (fraudulent vs. legitimate transactions), are often employed to identify and prevent fraud. However, real-world datasets frequently exhibit class imbalance, where fraudulent transactions (minority class) are significantly outnumbered by legitimate transactions (majority class). Machine learning models may perform poorly as a result of this imbalance, underestimating fraud and favouring the majority class. This paper proposes a novel approach to address class imbalance and improve fraud detection accuracy. We explore the implementation of FROST (Feature space RObust Synthetic saTuration) oversampling, a technique specifically designed to generate synthetic samples for the minority class. The FROST function leverages the k-nearest neighbors (KNN) algorithm and a user-defined amplification factor (m) to create synthetic data points that closely resemble existing minority class instances. We integrate the FROST-enhanced oversampling technique into the machine learning pipeline for fraud detection. The paper evaluates the effectiveness of this approach compared to traditional oversampling methods and analyzes its impact on classification accuracy metrics.

Public transportation scheduling aims to optimize the allocation of transportation resources, enhance transportation efficiency, and increase passenger satisfaction, which is crucial for building a sustainable urban transportation system. As a complement to public transportation, shared bikes provide users with a solution for the last mile of travel, compensating for the lack of flexibility in public transportation and helping to improve its utilization rate. Due to the characteristics of shared bikes, such as peak usage periods in the morning and evening and significant fluctuations in demand across different areas, the optimization of shared bike dispatch can better meet user needs, thereby reducing vehicle vacancy rates and increasing operating revenue. Addressing this issue, this paper designs a comprehensive decision-making approach for spatio-temporal demand prediction and bike dispatch optimization. For demand prediction, we designed a T-GCN based bike demand prediction model. In terms of dispatch optimization, we considered factors such as dispatch capacity, distance restrictions, and dispatch costs, and designed an optimization solution based on genetic algorithms. Finally, this paper validates the approach using shared bike operating data, shows that T-GCN can effectively predict short-term demand for shared bikes. Meanwhile, the optimization model based on genetic algorithms provides a complete dispatch solution verifying the model’s effectiveness. The shared bike dispatch approach proposed in this paper, which combines demand prediction with resource scheduling. This scheme can also be extended to other transportation scheduling problems with uncertain demand, such as store replenishment delivery and intercity inventory dispatch.

This article reports the results of an ecological study of cancer incidence rates by state in the US for the period 2016-2020. The goals of this study were to determine the extent to which solar UVB doses still reduced cancer risk compared to findings reported in 2006 for cancer mortality rates for the periods 1950–1969 and 1970-1794 as well as cancer incidence rates for the period 1998–2002 and to determine which factors were recently associated with cancer risk. The cancer data were obtained from the Centers for Disease Control and Prevention. Indices were obtained for solar UVB at the surface for July 1992, and alcohol consumption, and diabetes and obesity prevalence near the 2016–2020 period. Lung cancer incidence rates were also used in the analyses. The cancers for which solar UVB is significantly associated with reduced incidence are bladder, brain (males), breast, corpus uteri, esophageal, gastric, non-Hodgkin’s lymphoma, pancreatic, and renal cancer. Lung cancer was significantly associated with colorectal, laryngeal, and renal cancer. Diabetes was also significantly associated with breast, liver, and lung cancer. Obesity prevalence was significantly associated with breast, colorectal and renal cancer. Alcohol consumption was associated with bladder and esophageal cancer. Thus diet has become a very important driver of cancer incidence rates. The dietary approach that would reduce the risk of diabetes, obesity, lung cancer, and, therefore cancer, would be one based mostly on whole-plants and restrictions on red and processed meats and ultraprocessed foods.

Objective: The goal of this review is to provide a succinct, yet comprehensive, guide to the an-tepartum management of multiple gestations. Methods: This narrative review on twins and multiple gestation provides a concise guide for providers with this ever-growing patient population. PubMED was utilized for literature search. Each reference was evaluated and graded for quality of evidence by US Preventative Services Task Force and Cochrane Review guidelines. Screening, surveillance, and management strategies are delineated succinctly and organized by type of multiple gestation being managed from the lowest risk dichorionic twin pair to the increasingly escalating risks of twins and higher order multiples sharing a placenta and/or amniotic sac. Results: The incidence of twin pregnancies has grown over the past several years, due in large part to delayed reproductive timing and surge in assisted reproductive technologies. Twin pregnancies are associated with higher morbidity for both gravidas and offspring, warranting evidence-based approach in counseling and management. Conclusions: We note the important differences among multiples in chorionicity and amnionicity, in the importance of close surveillance and early delivery. Graded clinical pearls and evi-dence-based recommendations are presented to guide obstetric providers.

We introduce a novel microscopic image dataset augmented with segmentation and detection labels specifically designed for microplastic analysis in sewage environments. Recognizing the increasing concern over microplastics — particles of synthetic polymers smaller than 5mm — and their detrimental effects on marine ecosystems and human health, our research focuses on enhancing detection and analytical methodologies through advanced computer vision and deep learning techniques. The dataset comprises high-resolution microscopic images of microplastics collected from sewage, meticulously labeled for both segmentation and detection tasks, aiming to facilitate accurate and efficient identification and quantification of microplastic pollution. In addition to dataset development, we present example deep learning models optimized for segmentation and detection of microplastics within complex sewage samples. The models demonstrate significant potential in automating the analysis of microplastic contamination, offering a scalable solution to environmental monitoring challenges. Furthermore, we ensure the accessibility and reproducibility of our research by making the dataset and model codes publicly available, accompanied by detailed documentation on GitHub and LabelBox. The dataset and example deep learning models are publicly available at the following GitHub link. https://anonymous.4open.science/r/Microplastics-in-Sewage-1BEF

The use of endophytic microbes is increasing in commercial agriculture. This review will describe the endophyte-plant relationship and the fungi and bacteria involved. Their abilities to alleviate biotic (diseases and pests) and abiotic stresses (drought, salt and flooding), remediate pollution and increase photosynthetic capabilities will be described. Their mechanisms of action will be elucidated. These frequently result in increased plant yields. Finally, methods and practices for formulation and commercial use will be described.

We report the case of a 44-year-old woman who suffered gastric perforation after receiving bag-valve-mask (BVM) ventilation in the setting of alcohol intoxication. She had a markedly distended abdomen and cold, dusky lower extremities upon arrival to the emergency department. Imaging revealed a large volume intraabdominal accumulation of air with compression of the aorta. Needle decompression relieved symptoms of lower extremity arterial insufficiency. However, the patient quickly decompensated and subsequent exploratory laparotomy confirmed gastric rupture. A subtotal gastrectomy was performed but the patient ultimately passed on post-operative day two due to multi-organ dysfunction. Although BVM ventilation is commonplace in both the hospital and field, there is a lack of awareness of the serious complications of abdominal air accumulation due to their rareness in the adult population. Checking for abdominal distention during resuscitation ought to be routine in all patients. Signs of arterial insufficiency accompanying abdominal distention, once confirmed by diagnostic imaging that shows extensive pneumoperitoneum, are indicators of having reached a life-threatening level of air accumulation, calling for immediate needle decompression and exploratory laparotomy.

The flourishing landscape of agritourism in Albania has witnessed a steady increase in destinations over the years. Recognizing their pivotal role in driving economic development in rural areas, considerable attention is directed towards the promotion and expansion of these agricultural tourism spots. To enhance interactivity with visitors, these agritourism destinations actively leverage social networks and various digital platforms. However, the wealth of information pertaining to these destinations is currently scattered across different platforms, posing a challenge to accessibility. To address this issue, these points are strategically placed on Google Maps, along with essential details collected from users, such as websites, contact numbers, visitor ratings, and comments. Nevertheless, other valuable data remains dispersed on various social networks. In response to this fragmentation, this study proposes the development of algorithms and scripts to systematically collect and analyze this dispersed information. By doing so, the goal is to centralize and streamline the data, enabling a comprehensive understanding of the agritourism landscape in Albania. This approach not only facilitates efficient access to information for potential visitors but also provides valuable insights for stakeholders involved in the development and management of these agritourism destinations. The study aims to contribute to the sustainable growth of agritourism in Albania by harnessing the power of digital platforms to create a unified and organized database. Through this integration, the research seeks to unveil patterns, trends, and opportunities that can further guide policy-making, marketing strategies, and overall decision-making processes in the realm of agritourism development.

This article explores the geothermal resources of Kazakhstan's Zharkent Basin, with a specific focus on the high-temperature geothermal sources in the Almaty region of Southern Kazakhstan. The research aims to analyze the energy characteristics of the Organic Rankine Cycle (ORC) for harnessing low-enthalpy geothermal energy for small-scale electricity generation. A detailed thermodynamic model was developed, employing R134a as the working fluid. An in-depth analysis of the Zharkunak field (Zharkent, Almaty region) revealed that well 5539, with its notably high temperatures, offers the highest potential for geothermal electricity production, achieving an annual output of approximately 10,371 MWh. The total electric power output from the studied wells in the region is estimated at 20,111 MWh annually, representing a significant contribution towards sustainable energy production and reducing reliance on traditional coal-fired power plants. The study concludes that the Organic Rankine Cycle is not only a viable and efficient technology for utilizing low-enthalpy geothermal resources to generate electricity on a small scale, but also a key player in enhancing energy independence. By leveraging local geothermal energy, the Almaty region can significantly reduce its reliance on external energy sources, thereby fostering sustainable development and reducing environmental impacts.

Western countries are experiencing an increasing aging population, resulting in heightened disability and mobility issues. This trend is expected to escalate in the coming decades. Therefore, ensuring adequate accessibility in collective residential housing –where individuals spend much of their daily lives– is of paramount importance. This paper presents a case study focused on the accessibility of building entrances in collective residential housing in Southeast Spain, specifically in the Region of Murcia. In this region, 9.8% of the population has disabilities, and 15.75% were over 64 years old in 2020. The study began by compiling the relevant national and regional accessibility regulations for existing buildings. Subsequently, extensive fieldwork was conducted, analyzing 150 collective residential housing buildings. Based on this analysis, a set of recommendations to enhance accessibility was formulated for buildings not complying with the regulations. The results are presented and discussed in detail. The most frequent recommendation was the construction of accessible ramps, identified as the primary solution in over 40% of cases, either alone or in conjunction with other measures. In 54% of the cases, multiple interventions were necessary to achieve effective accessibility adaptation. The findings of this study could inform the development of public policies aimed at improving accessibility conditions in urban areas.

Inverse gas chromatography at infinite dilution was used to determine the surface thermodynamic properties of silica particles and PMMA adsorbed on silica, and more particularly, to quantify the London dispersive energy γsd, the Lewis acid γs+ and base γs- polar surface energies of PMMA/silica composites as a function of the temperature and the recovery fraction θ of PMMA. The polar acid–base surface energy γsAB and the total surface energy of the different composites were then deduced as a function of the temperature. In this paper, the Hamieh thermal model was used to quantify the surface thermodynamic energy of poly methyl methacrylate (PMMA) adsorbed on silica particles at different recovery fractions. A comparison of the new results was carried out with those obtained by applying other molecular models of the surface areas of organic molecules adsorbed on the different solid substrates. An important deviation of these molecular models from the thermal model was proved. The determination of γsd, γs+, γs-, and γsAB of PMMA in both bulk and adsorbed phases showed an important non-linearity variation of these surface parameters as a function of the temperature. The presence of maxima in the curves of γsd(T) highlighted the second order transition temperatures in PMMA showing beta-relaxation, glass transition and liquid-liquid temperatures. These three transition temperatures depended on the adsorption rate of PMMA on silica. The proposed method gave a new relation between the recovery fraction of PMMA and its London dispersive energy showing an important effect of the temperature on the surface energy parameters of adsorption of PMMA on silica. A universal equation relating γsd(T,θ) of the systems PMMA/silica to the recovery fraction and the temperature was proposed.

Kisspeptin (KISS1) and its cognate receptor (KISS1R) are implicated in the progression of various cancers. However, a theranostic radiopharmaceutical targeting the KISS1 receptor (KISS1R) has yet to be explored. A gallium-68 labelled kisspeptin-10 (KP10) has potential as a pan-tumor radiopharmaceutical for the detection of cancers. Furthermore, a lutetium-177 labelled KP10 could find therapeutic application in treating oncological diseases. We attached DOTA to the NH2-terminus of KP10 as we posited that this modification would not impair biological activity and showed that receptor stimulation of inositol phosphate accumulation in HEK293 transfected with the KISS1R gene was similar for KP10 and DOTA-KP10. We describe optimization of radiolabeling with gallium-68 and lutetium-177 and stability in serum, plasma, and whole blood. Pharmacokinetics was established with µPET/CT and ex vivo measurements. Dynamic studies with µPET/CT demonstrated that background clearance for the radiopharmaceutical was rapid with a blood half-life of 18 ± 3 minutes. DOTA-KP10 demonstrated preserved functionality at KISS1R and good blood clearance. These promising results advocate the further development of KP10 structures which have high binding affinity along with proteolytic resistance.

As a result of increased energy consumption, global trade has surged, and serious environmental problems have arisen. The problem is made more complicated by the fact that either environmental damage or economic advancement cannot be compromised. The elements contributing to environmental contamination must be identified and dealt with accordingly if we are to have a healthier future. In this study, what causes CO₂ emissions in Malaysia are examined using the Autoregressive distributed lag (ARDL) model using time series data from 1995 to 2020. The paper also examines the impact of energy use and economic complexity on CO2 emissions. Firstly, it is noted that the Environmental Kuznets Curve (EKC) theory holds in Malaysia. Furthermore, energy consumption has a detrimental impact on reducing CO2 emissions. Furthermore, it has been noted that a greater degree of economic complexity leads to an elevated amount of CO2 emissions over an extended period. The findings suggest significant environmental policy implications for reducing CO2 emissions in Malaysia.

The refractive index of a liquid serves as a fundamental parameter reflecting its composition, thereby enabling the determination of component concentrations in various fields such as chemical research, food industry, and environmental monitoring. Traditional methods for refractive index (RI) measurement rely on light deflection angles at interfaces between the liquid and a material of known refractive index. In this paper, the authors present a new differential refractometer for highly sensitive measurement of RI differences between two liquid samples. Using a configuration with two cells equipped with flat parallel plates as measuring elements, the instrument facilitates accurate analysis. Namely, the sensor signals from both the solution and the solvent cuvette are generated simultaneously with one laser pulse, reducing the possible fluctuations of the laser radiation intensity. Our evaluation shows the high sensitivity of RI measurements (< 7 · 106), so this differential refractometer can be proposed not only as a high-sensitivity sensing tool that can be used for mobile detection of nanoparticles in solution samples, but also to determine the level of environmental nano-pollution using water (including rain, snow) samples from various natural as well as industrial sources, thus helping to solve some important environmental problems.

Coronary heart disease (CHD) has become a prevalent issue in Indonesia, resulting in a majority of fatalities and illnesses. The most recent guidelines in the United States for managing patients with chronic coronary syndrome (CCS) have undergone significant changes, with the recommendation for conducting percutaneous coronary intervention (PCI) strictly limited to patients who continue to experience symptoms despite receiving optimal medical treatment (OMT). However, adopting this approach may lead to increased morbidity and mortality due to the presence of vulnerable plaque. Vulnerable plaque is characterized by minimal obstruction during coronary angiography (40-70%) and may not produce ischemia during physiological studies. Identifying vulnerable plaques can be accomplished through several methods, among which computed tomography coronary angiography (CTCA) is the most cost-effective approach. Recently, experts have employed different techniques, either with stents or drug-coated balloons, to manage vulnerable plaques, showing the methods to be safe and effective. The other challenge faced by patients with CCS is the possibility of achieving complete revascularization (CR) to reduce the likelihood of future major adverse cardiac events (MACE) and mortality. Both approaches, identifying and intervening in the vulnerable plaque, are difficult to perform in developing countries due to the limited budget. Studies have shown that plant-based diets (PBD) can reverse atherosclerotic plaque and stabilize vulnerable plaque, possibly leading to CR. PBD is an affordable and effective approach, but it requires healthcare providers skilled in educating and implementing this dietary approach with their patients. Large-scale randomized controlled trials in PBD, specifically aimed at addressing the vulnerable plaque and achieving CR, are necessary before implementing the PBD intervention.

Developing a dependable gas and condensate value chain is vital for the ongoing prosperity of the oil and gas industries. To achieve this, NNPC is enhancing its production facilities by employing process modeling and simulation with the assistance of Symmetry iCON®. As a part of this initiative, a simulation model was created using the Symmetry iCON® pipe plexus solver to simulate the dynamic environment of the gas and condensate pipeline network in the Nigerian Southern region. To validate the model, data from a single month, specifically December 2022, was utilized. Furthermore, the algorithm was utilized to generate projections for the month of January 2023, providing valuable insights into its effectiveness. The study also highlighted the significance of accurately estimating the characteristics and properties of a pseudo component of C6+ in relation to thermodynamics and material properties, which was a particularly insightful finding. he assessment of this property has transitioned from being relatively unimportant to becoming critically important, primarily due to the lack of condensate data monitoring at specific terminals. However, it's worth noting that the model currently has an error margin of 4-6% when predicting the data. As more information becomes available in the future, the model can be easily fine-tuned to better align with the actual conditions, allowing for more accurate predictions.

Multiple sequence alignments and phylogenetic trees are rich in biological information and are fundamental to research in biology. PhyKIT is a tool for processing and analyzing the information content of multiple sequence alignments and phylogenetic trees. Here, we describe how to use PhyKIT for diverse analyses, including (i) constructing a phylogenomic supermatrix, (ii) detecting errors in orthology inference, (iii) quantifying biases in phylogenomic data sets, (iv) identifying radiation events or lack of resolution using gene support frequencies, and (v) conducting evolution-based screens to facilitate gene function prediction. Several PhyKIT functions that streamline multiple sequence alignment and phylogenetic processing—such as renaming FASTA entries or tree tips—are also discussed. These protocols demonstrate how simple command-line operations in the unified framework of PhyKIT facilitate diverse phylogenomic data analysis and processing, from supermatrix construction and diagnosis to gene function prediction.

Clinical trials, by contributing to the development of diagnostics and to the search for modern, more effective, and safer therapies, have become one of the most important elements of the healthcare system. The aim of this study was to assess Poles' knowledge and beliefs about clinical trials. Methods: The survey was conducted among Poles aged 18 and over with the help of external company, Ariadna, which is an independent research panel. The questionnaire contained 22 questions, of which 13 questions concerned beliefs and attitudes towards clinical trials. Results: One thousand and seventy-nine participants took part in the study (N = 1079). The mean age of respondents was 44.96 years (SD = 16.30). Slightly more women (N = 568, 52.6%) than men (N = 511, 47.4%) took part in the study. Among the respondents, 86.5% (N = 933) were aware of clinical trials. The main sources of information about clinical trials were the media (53.8%) including the Internet (N= 355, 32.9%), TV (N = 175, 16.2%), press (N = 30, 2.8%) and radio (N = 21, 1.9%). 43.2% (N = 466) of respondents reported little knowledge of clinical trials, while more than three quarters (N = 805, 75.2%) said they would like to learn more about clinical trials. Most respondents (N = 879, 81.4%) agreed with the statement that participation in a clinical trial is completely voluntary, and more than half (N = 580, 53.7%) agreed with the statement that hospitals participating in clinical trials provide better healthcare. The statement that the results of clinical trials are made available to the public was disagreed with by 37.2% (N = 402) of participants. Only 30.3% (N = 327) of participants agreed that clinical trials should be conducted with children. Conclusions: Poles rate their knowledge of clinical trials as low and would like to learn more. To reach the largest possible group of Polish patients, parallel educational activities on multiple levels may have the best effect. Poles' knowledge of clinical trials is mainly based on commercial sources. Further studies in different groups, i.e., clinical trial patients and investigators, are needed.

The human gastrointestinal gut contains about 100 trillion of microorganisms including up to 5000 different types of bacteria called the "gut microbiome". Alterations in the composition of gut microorganisms (dysbiosis) can cause threatening for life diseases. This present seeks to evaluate if finally diet and more specifically functional foods affect the intestinal microbiome, and if obesity and the metabolic syndrome (Mets) are associated with the intestinal microbiome. This systematic review was accomplished according to PRISMA guidelines mostly using the key words functional foods, microbiome, obesity, Mets, Mediterranean diet. The search was carried out of recent scien-tific articles from the databases Pubmed, Scopus, and Google Scholar. The most studies discussed in this review showed a potential therapeutic effect of the Mediterranean diet rich in beneficial nutrients, on body weight, fat deposition, in correlation with modulation of the synthesis of gut microbiome. This literature review demonstrates a possible relationship between the metabolites of the microflora, the endotoxemia, obesity and Mets. The role of probiotics, prebiotics, and polyphe-nols in the prevention of obesity and Mets is of high importance in promoting healthy aging. The future challenge is to understand how different dietary patterns can regulate the composition of the gut microflora and whether these changes could be long-term.

Objectives: This study assessed the performance of a novel fluoride dentifrice containing micro- fibrillated cellulose (MFC) and 7% silica (Protegera™) versus common fluoride dentifrices. Methods: Removal of extrinsic stains was assessed using the pellicle cleaning ratio (PCR) method, and radioactive dentin abrasivity (RDA) was measured, to calculate a cleaning efficiency index (CEI). Fluoride efficacy was evaluated using widely used remineralization and fluoride uptake methods. Results: The MFC dentifrice removed stained pellicle significantly more effectively than the ADA reference material, Crest Cavity Protection™ and Sensodyne Pronamel™, and had equal performance to three known marketed stain-removing dentifrices (Arm & Hammer™ Advanced Whitening, Crest ProHealth™, and Colgate Optic White™). The MFC dentifrice vehicle had a low RDA (88), which was significantly less than Crest ProHealth (166) and Crest 3D-White™ (183). Based on PCR and RDA data, the CEI was 31% greater for the MFC product than for Crest ProHealth. In a 10-day pH cycling study, the fluoride efficacy of the MFC product was superior to a non-fluoridated control and was not significantly different from Sensodyne Pronamel and Crest Cavity Protection. The MFC dentifrice was superior for promoting fluoride uptake into incipient enamel lesions than the USP reference dentifrice. Conclusion: The low dentin abrasivity MFC dentifrice is highly effective in removing stained pellicle, and is an efficacious fluoride source when compared to other relevant commercially available fluoride dentifrices with high dentin abrasivity. Clinical Significance: Including micro-fibrillated cellulose into a fluoride dentifrice may enhance cleaning performance for the removal of external stain, while lowering abrasivity, and providing an effective fluoride source. This combination of benefits seems well suited to enamel protection and caries prevention.

The influence of the secondary process of evaporation of the reaction product on the kinetics of interaction of gases (O₂, Cl₂, NH₃, H₂O and N₂H₄ vapors) with the surface of some metals (Cr, Pb, Si, Ge) and compounds (BN, SiO₂, SiC) is discussed. Also is considered the case when the growth of the scale is preceded by the process of gas etching of the metal surface. A general equation is given that describes the scale growth-evaporation kinetic (sample mass change - time) curves during the interaction of gases with the surface of metals and compounds. Special cases of parabolic, cubic and fourth degree processes are discussed.

The Cauto River Basin (CRB), the heartland of Cuban agriculture, has been hit hard by drought and water shortage. In response to this pressing issue, this study provides a comprehensive as-sessment of water supply, demand and balance within the Cauto River Basin, considering the baseline and projected socio-economic and climatic conditions by coupling of SWAT and WEAP models. The obtained results reveal that the annual flow in the CRB is projected to slightly de-crease (2.5%) in which the reduction in the rainy season (3.1%) is higher than that in the dry sea-son (1.3%). Total water demand in the baseline scenario is around 1.194 billion m3, dominated by agriculture (96%), with rice crop requiring nearly half. For the future scenario of 2050, the study shows a 16.6% surge in demand to 1.394 billion m3, driven by climate change and agricultural expansion. However, domestic use decreases by 10% due to population reduction. Water deficit in the future is projected to increase by 52% from 172.4 to 262.7 million m3 due to rising water demand and declining water supply. This study shows that integrating a hydrological model into a water allocation model is a promising approach to estimate the water supply, demand and balance, which is a crucial component of water resources management.

Turbidity stands as a crucial indicator for assessing water quality, and while turbidity sensors exist their high cost prohibit their extensive use. In this paper, we introduce an innovative turbidity sensor, and it is the first low-cost turbidity sensor which is designed specifically for long-term stormwater in-field monitoring. Its low cost ($23.50 USD), enables the implementation of high spatial resolution monitoring schemes. The sensor design is available under open hardware and open-source licences, and the 3D-printed sensor housing is free to modify based on different monitoring purposes and ambient conditions. The sensor was tested both in the laboratory and in the field. The laboratory results show a strong linear relationship (R2 > 0.99) between the sensor readings and the commercial hand-held turbidimeter (Thermo Scientific AQ4500) results of the solution. In the field, the low-cost sensor measurements were statistically significantly correlated (p < 0.01) to a standard high-cost commercial turbidity sensor (GreenSpan TS-1000). Biofouling and drifting issues were also analysed after the sensors were deployed in the field for more than 6 months, showing both biofouling and drift occur during monitoring. Nonetheless, in terms of maintenance requirements, the low-cost sensor exhibited similar needs compared to the Green-Span sensor.

The literature study delves into novel therapeutic strategies in transplantation medicine, highlighting unique approaches that could revolutionize current practices. It emphasizes novel patterns that have the potential to transform the current landscape. Commencing with a thorough examination of the historical environment, it traces crucial advances and changes in transplantation. The focus is on traditional techniques, emphasizing their limitations and challenges. An extensive examination of contemporary transplantation therapies offers valuable insights into the most recent progress in organ, cellular, and tissue transplantation. This analysis examines the immunological obstacles and outlines the current advancements and constraints. The exploration further navigates into novel models and concepts such as immunomodulation, developments in organ preservation techniques, gene editing, biomaterials, scaffold-based solutions, and the integration of precision medicine, artificial intelligence, and machine learning applications. Each section analyzes the potential for change and current progress in various areas, backed by relevant scientific sources up to 2023. The subsequent sections delve into innovative cellular therapies, biotechnological progress, current clinical trials, and case studies demonstrating effective applications. This examination delves into the ethical and regulatory considerations of innovative therapeutic procedures, emphasizing ethical implications, regulatory frameworks, and the importance of balancing innovation with patient welfare. The literature review concludes by offering a forward-looking perspective, emphasizing potential progress, anticipated challenges, and advocating for collaboration and interdisciplinary approaches to overcome limitations in the field of transplantation medicine.

p-Toluenesulfonic acid is commercially available, non-toxic, cheap organic compound with robust stability. p-Toluenesulfonic acid is solid, non-corrosive and a strong organic acid that can be handled easily. Due to this p-toluenesulfonic acid could be the better replacement of other conventional acids like nitric acid, sulfuric acid, perchloric acid and AlCl3 in organic transformations. Moreover, p-toluenesulfonic acid could be used synergistically with other mode of catalysis like transition metal catalysis and photocatalysis. In recent years, the use of this solid organic acid in organic and polymer synthesis has grown tremendously. In this review, we present an overview of p-toluenesulfonic acid promoted various organic reactions with particular emphasis to the more recently reported methods. In some cases, we also detailed the understanding of the reactions by providing the reaction mechanism. Despite these advances, there are still many opportunities for the development of new reactions using PTSA. Industry and academia have become more conscious to adopt sustainable chemical processes using safer reagents and solvents and the use of PTSA in this context is highly significant. This review will inspire researchers for further reaction development employing p-toluenesulfonic acid.

This work presents preliminary experimental results advancing non-destructive testing methods for detecting steel bars in concrete structures via contactless investigation in the X-band spectrum. The study reveals the field’s penetration into concrete, extracting insights into embedded bars through scattered data. Applying a quasi-quadratic inverse scattering technique to numerically simulated data yields promising results, confirming the effectiveness and reliability of the proposed approach. In this realm, using a higher frequency allows the use of lighter equipment and smaller antennas. Identified areas for improvement include accounting for antenna behavior and establishing undeformed target morphology and precise orientation. Transitioning from powder-based and sand specimens to real solid reinforced concrete structures is expected to alleviate laboratory challenges. Although accurately determining concrete properties such as relative permittivity and conductivity is essential, it remains beyond the scope of this study. Finally, overcoming these challenges could significantly enhance non-invasive testing, improving structural health monitoring and disaster prevention.