In this essay, the new notion concerning longest path is introduced. Longest path has a close relation with the notion of diameter in graph. The classes of graph are studied in the terms of having the vertex with longest path. Valued number is the number of edges belong to the longest path in the matter of vertex. For every vertex, there’s a valued number and new notion of valued set is the generalization of valued number for the vertex when all vertices of the graphs are corresponded to a vertex which has the greater valued number. For any positive integer, there’s one graph in that, there’s vertex which its valued number is that. By deleting the vertices which don’t belong to valued set, new notion of new graph is up. It’s called valued graph. The comparison amid valued graph and initial graph is up, too.

The aim of this article is to introduce the new notion on a given graph. The notions of valued set, valued function, valued graph and valued quotient are introduced. The attributes of these new notions are studied. Valued set is about the set of vertices which have the maximum number of neighbors. The kind of partition of the vertex set to the vertices of the valued set is introduced and its attributes are studied. The behaviors of classes of graphs under these new notions are studied and the algebraic operations on these sets in the different situations get new result to understand the classes of graphs, these notions and the general graphs better and more.

In this article, we show the existence of fixed point for the derivative of interval-valued functions. Meanwhile, the fixed point inquiry will utilize the common fixed point methods under the condition of compatibility of the hybrid composite mappings in the sense of the Hausdorff metric. Some examples are given to support the usability of the result of this research .

In this study, we present the concept of interval-valued fuzzy soft point and then introduce the notions of neighborhood and quasi-neighbourhood of it in interval-valued fuzzy soft topological spaces. Separation axioms in interval-valued fuzzy soft topology, so-called $q$-$T_{i}$ for $ i=0,1,2,3,4 ,$ is introduced and some of its basic properties are also studied.

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.

In this paper, a positive answer to the open question of Fabino et al. is given, and the concept of I\c sik type set valued contractions is introduced and fixed point theorem for such contractions is established. Examples to support main theorems are given, and an application to integral inclusion is given.

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.

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.

The Pythagorean fuzzy set (PFS), which is characterized by a membership and a non-membership degree and the square sum of them is less or equal to one, can act as an effective tool to express decision makers’ fuzziness and uncertainty. Considering that the Heronian mean (HM) is a powerful aggregation operator which can take the interrelationship between any two arguments, we study the HM in Pythagorean fuzzy environment and propose new operators for aggregating interval-valued Pythagorean fuzzy information. First, we investigate the HM and geometric HM (GHM) under interval-valued intuitionistic fuzzy environment and develop a series of aggregation operators for interval-valued intuitionistic fuzzy numbers (IVIFNs) including interval-valued intuitionistic fuzzy Heronian mean (IVIFHM), interval-valued intuitionistic fuzzy geometric Heronian mean (IVIFGHM), interval-valued intuitionistic fuzzy weighted Heronian mean (IVIFWHM) and interval-valued intuitionistic fuzzy weighted geometric Heronian mean (IVIFWGHM). Second, some desirable and important properties of these aggregation operators are discussed. Third, based on these aggregation operators, a novel approach to multi-attribute decision making (MADM) is proposed. Finally, to demonstrate the validity of the approach, a numerical example is provided and discussed. Moreover, we discuss several real-world applications of these operators within policy-making contexts.

The objective of the paper is to introduce new similarity measure for single valued neutrosophic sets based on logarithm function. We define logarithm similarity measure and their weighted similarity measure for single valued neutrosophic sets. Then we define hybrid logarithm similarity measure and weighted hybrid logarithm similarity measure for single valued neutrosophic sets. We prove the basic properties of the proposed measures. We then define an entropy function using logarithm function to determine unknown attribute weights. We develop a novel multi attribute group decision making strategy for single valued neutrosophic sets based on the weighted hybrid logarithm similarity measure. We address an illustrative example to demonstrate the effectiveness and aptness of the proposed strategies. We conduct a sensitivity analysis of the developed strategy. We also make a comparison between the obtained results from proposed strategies and different existing strategies in the literature.

Soft set theory is a mathematical tool for dealing with uncertainty. This paper investigates limits of interval type of soft sets (for short, it-soft sets). The concept of it-soft sets is first introduced. Then, limits of it-soft sets are proposed and their properties are obtained. Next, point-wise continuity of it-soft sets and continuous it-soft sets are discussed. Finally, an application for rough sets is given.

This article describes an algorithm for generating fractals using polar coordinates. The classic Julie and Mandelbrot polynomial iteration applied to a complex number is replaced by a separate iteration for distance and angle. By varying the polynomial parameters of the iteration functions, a wide range of attractive images can be created. Distance and angle values ​​are used to colorize fractal images.

The kind of set which is based on edges, is introduced. The analysis on this set is done in the matter of operation which are the classes of graphs. The general notion which is related to this concept, is up. The set of edges is seen in the matter of common vertex, entitled neighbor edges and the set of edges which has specific condition on the vertices of graphs, entitled ghost set. The kind of viewpoint when the edges are up so the kind of efforts to assign some notions which get the sensible result of edges which make sense about these two types of notions. Notions of having some attributes about vertices concerning edges and edges' attributes to get result about edges in the matter of vertices.

In recent decades, power consumption has become an essential factor in attracting the attention of integrated circuit (IC) designers. Multiple-valued logic (MVL) and approximate computing are some techniques that could be applied to integrated circuits to make power-efficient systems. By utilizing MVL-based circuits instead of binary logic, the information conveyed by digital signals increases, and this reduces the required interconnections and power consumption. On the other hand, approximate computing is a class of arithmetic computing used in systems where the accuracy of the computation can be traded-off for lower energy consumption. In this paper, we propose novel designs for exact and inexact ternary multipliers based on carbon-nanotube field-effect transistors (CNFETs). The unique characteristics of CNFETs make them a desirable alternative to MOSFETs. The simulations are conducted using Synopsys HSPICE. The proposed design is compared against existing ternary multipliers. The results show that the proposed exact multiplier reduces energy consumption by up to 6X. At the same time, the best inexact design improves energy efficiency by up to 35X compared to the latest state-of-the-art methods. Using the imprecise multipliers for image processing provides evidence that these proposed designs are a low-power system with an acceptable error.

The hard-shelled seed industry plays an important role in the global agricultural economy. As a result of nut industrialization, considerable amounts of by-products and residues are produced year by year, burnt as fuel or discarded as non-valued waste, by-passing a potential source of valuable compounds or features. Over the last decade nutshells have received great interest due to their lignin concentration and their antioxidant, physical and mechanical features. It was found that these properties vary among cultivars, latitude and localities of plantation. On the other hand, there is inconsistences regarding to mechanical and some biochemical properties of both nutshells, which aimed to explore the status of potential hazelnut and walnut shells appli-cations into sustainable circular bio-economy chains. Hence, this review deals with the recent scientific literature on their chemical composition as well as their functional applications as an approach to sustain the utilization of the main by-product derived from the nut-industry.

A description is provided of a method -- the Set Equality Method (SEM) -- to determine the validity, or lack of validity, of each categorical syllogism. A justification is given for the presentation of a new method to solve a problem which has already been solved using different approaches. First, the SEM assigns an equality of certain sets (or two of those equalities in specific cases as will be indicated) to each of the categorical propositions composing each syllogism considered -- that is, to each of the two premises and to the conclusion. Each syllogism considered is valid if and only if a) it is possible to select one of those equalities corresponding to one of the premises such that one of its members is a certain set and the other of those equalities corresponding to the other premise such that one of its members is a subset of the set mentioned, and b) it is possible to deduce an equality corresponding to the conclusion of the two equalities corresponding to the premises. In some cases, as will be specified, it is possible to provide a second test for the validity of a syllogism whose validity was already proven, thus providing information about the logical form of categorical syllogisms.

In this article, there's an effort to make sense about the new versions of matroid. I believe that there's new idea on the background of. matroid. Two styles of matroid is defined in the background of fixed graphs and after that the attributes of these new notion on the graph and its parameters have been studied. The focus of this article is on the version of matroid which has the basis on the cycles as if there's gentle discussion on the results which are based on the set of independent vertices as matroid-x. The relation amid fundamental parameters and specific set like independent set and minimal set in the terminology of graph theory have been considered. Matroid is the word to use in the study on the parameters of graph theory as if set theory and its terminology are also recorded. The terms of word in various terminology have been relatively used. There are open ways to use hypergraphs or some serious relations amid these two types.

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.

Based on the definition of double fuzzy relations, two types of new rough set models are constructed, which are multi-granulation double fuzzy rough sets called optimistic and pessimistic multi-granulation double fuzzy rough sets, and some of their properties were studied. In addition, we study the relationship between optimistic and pessimistic multi-granulation double fuzzy rough sets and double fuzzy rough sets.

In this paper, the author obtains an analytic exact form of Heaviside function, which is also known as Unit Step function and constitutes a fundamental concept of the Operational Calculus.In particulat, this function is explicitly expressed in a very simple manner by the aid of purely algebraic representations. The novelty of this work is that the proposed explicit formula is not performed in terms of non – elementary special functions, e.g. Dirac delta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with point wise or uniform convergence. Hence, it may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

This paper is devoted to the study of reproducing kernels on 2-inner product Hilbert spaces. We focus on a new structure to produce reproducing kernel Hilbert and Banach spaces. According to multi-variable computing, this structures can be useful in electrocardiographs, machine learning and economy

In this work, Further properties of bornological groups are studied to find the sufficient conditions to introduce a bornology on a group. In particular, we show that every left (right) translations in bornological groups are isomorphisms and therefore the bornological group's structures are homogeneous, and this property from the bornological group is not shared with bornological semigroups. Further, the boundedness of a bornological group can be deduced from its boundedness at the identity.

In this paper, we propose a method to find all efficient solutions of an interval multiple objective linear programming (IMOLP) problem with interval coefficients in the objective functions, the constraint matrix and the right-hand side vector. The set of all efficient solutions of an IMOLP problem can completely supply information to the decision makers in finding their most preferred solutions but, up to now, not all efficient solutions of an IMOLP problem can be found by known methods. A numerical example is given to illustrate the working of the proposed method.

Considerable amounts of agro-industrial by-products are discarded or burnt as fuel every year. However, they can be utilized as a valuable source of fiber, phenolics and other useful compounds such as antioxidants. The profile of beneficial compounds can be affected by genotype, locality, orchard management and productive season, adding or decreasing the bioactive potential of by-products. In this study, hazelnut (Corylus avellana L.) and walnut (Juglans regia L.) nutshells were investigated for their fiber content and antioxidant capacity as valorized by-products for the industry. Determinations (ORAC, TPC and color asses) were performed in hazelnut and walnut orchards located in Southern Chile during three consecutive seasons (2020/21; 2021/22 and 2022/23). Analyses of oxygen radical absorbance capacity (ORAC) in nutshells showed the highest ORAC from both species in the season 2020/21 (3217 µmol TE g1DW for hazelnut shells and 4663 µmol TE g DW1 for walnut shells), while variability in the consecutive seasons was lower for hazelnut than in walnut. Total phenolic content in hazelnut shells was positively correlated with L* (R: 0.883) and E (R: 0.924) during 2020/21 season, also with L* for 2022/23 (R: 0.907). While ORAC was negatively correlated with L* (R: 0.922) in 2021/22. In addition, morphological and structural features of both nutshells examined by Scavenging Electron Microscopy (VP-SEM) and Confocal Scavenging Laser Microscopy (CSLM) revealed differential tissue distribution and accumulation patterns of both cellulose and lignin. On the other hand, photo-colorimetric values were determined for both shells and corresponding seasons, and non-significative differences were found both shells and among seasons Finally, these results provide insight into the physicochemical characteristics of two shell types which should be considered together with antioxidant capacity in their valorization as a residual material.

In this paper, we shall introduce the interval-valued spatial error model. Based on the idea of least square method of single-valued case, we give the parameter estimator for interval-valued spatial error model. The theoretical properties of the proposed estimator are proved. Finally, we give the numerical analysis and a real example.

Marine oil spills seriously threaten the coastal environment, challenge the safety of marine eco-system, and cause huge economic losses to marine fishery, aquaculture, and tourism industries. Timely and accurate oil spill monitoring and early warning can not only make the oil spill acci-dent be handled timely and effectively but also provide key information for investigating the re-sponsibility of the polluters. Polarimetric synthetic aperture radar (SAR) has shown its great po-tential in oil spill classification for its capacity to distinguish mineral oil and biogenic look-alikes. Traditional oil spill classification approaches rely on the scattering matrix elements or pre-designed scattering mechanism-based polarimetric SAR features, which limits its robustness and generalization in large-scale marine surveillance tasks. The recent development of deep learning frameworks, especially the convolutional neural network (CNN) provides a powerful tool for remote sensing image classification. However, conventional CNN only accepts re-al-valued input, which cannot efficiently analyze the polarimetric information carried by com-plex-valued SAR data. In this study, a new framework that employs the complex-valued neural network was proposed for marine oil spill detection. Sophisticated studies were designed to evaluate the contribution of the physical scattering mechanism-based features, complex-valued framework, and convolutional feature extraction structures respectively. Comparative studies were conducted on four study cases using Radarsat-2 and SIR-C fully polarimetric SAR data. The outcome of the proposed study may shed light on the development of an end-to-end marine spill classification system and enlarge its application in practical marine surveillance operations.

This proposed research explores a novel approach to image classification by deploying a complex-valued neural network (CVNN) on a field-programmable gate array (FPGA), specifically for classifying 2D images transformed into polar form. The aim of this research is to address the limitations of existing neural network models in terms of energy and resource efficiency, by exploring the potential of FPGA-based hardware acceleration in conjunction with advanced neural network architectures like CVNNs. The methodological innovation of this research lies in the Cartesian to polar transformation of 2D images, effectively reducing the input data volume required for neural network processing. Subsequent efforts focused on constructing a CVNN model optimized for FPGA implementation, emphasizing the enhancement of computational efficiency and overall performance. The experimental findings provide empirical evidence supporting the efficacy of the image classification system developed in this study. One of the developed models, CVNN_128, achieves an accuracy of 88.3% with an inference time of just 1.6ms and a power consumption of 4.66mW for the classification of the MNIST test dataset consists of 10,000 frames. While there is a slight concession in accuracy compared to recent FPGA implementations that achieve 94.43%, our model significantly excels in classification speed and power efficiency—surpassing existing models by more than a factor of 100. In conclusion, the paper demonstrates the substantial advantages of FPGA-implementation of CVNNs for image classification tasks, particularly in scenarios where speed, resource, and power consumption are critical. The study’s reproducible results and corresponding code are available on GitHub at the following link: https://github.com/mahmad2005/CVNNonFPGA

In the era of sustainable development, green supplier selection has become a key component of supply chain management, as it considers criteria such as carbon footprint, water usage, energy usage and recycling capacity. Since the green supplier selection problem involves subjective criteria and uncertainty in preferences, it is well suited to using multi-criteria decision-making methods (MCDM). Although few researchers have investigated MCDM for green supplier selection under uncertainty using intuitionistic and Pythagorean fuzzy sets. Still, the newly developed fermatean fuzzy can handle greater data uncertainty than intuitionistic and Pythagorean fuzzy sets. Since interval extension of fuzzy theory provides more accurate modeling, in this paper, we propose an interval extension of fermatean fuzzy set and discuss its fundamental set operations, arithmetic operations and related properties. We propose the Hamming distance function and the score function of the interval-valued fermatean fuzzy numbers. The recently developed Multi-attribute Border Approximation Area Comparison (MABAC) method is also considered due to its stable and simple computation compared to other conventional MCDM methods. Therefore, an interval-valued fermatean fuzzy MABAC method is proposed and solved to select a green supplier based on multiple criteria. The proposed method's comparative analysis and sensitivity analysis validate the proposed method's effectiveness and robustness.

Extreme overvalued beliefs (EOB) are rigidly-held, shared beliefs that are the motive behind most acts of terrorism and mass shootings. EOBs are differentiated from delusions and obsessions. The concept of overvalued idea was first described by Wernicke and later applied to terrorism by McHugh. Our group of forensic psychiatrists (Rahman, Resnick, Harry) refined the definition as an aid in the differential diagnosis seen in acts of violence. The form and content of EOBs is discussed as well as group effects, conformity and obedience to authority. Religious cults such as: The People’s Temple, Heaven’s Gate, Aum Shinrikyo, Islamic State (ISIS) and conspiracy beliefs such as assassinations, moon-hoax and vaccine-induced autism beliefs are discussed using this construct. Finally, some concluding thoughts on countering violent extremism, including its online presence is discussed utilizing information learned from online eating disorder and consumer experience.

Fermatean fuzzy linguistic (FFL) set theory provides an efficient tool for modeling a higher level of uncertain and imprecise information, which cannot be represented using intuitionistic fuzzy linguistic (IFL)/Pythagorean fuzzy linguistic (PFL) sets. On the other hand, the linguistic scale function is the better way to consider the semantics of the linguistic terms during the evaluation process. In the present paper, we first define some new modified operational laws for Fermatean fuzzy linguistic numbers (FFLNs) based on linguistic scale function (LSF) to overcome the shortcomings of the existing operational laws and prove some important mathematical properties of them. Based on it, the work defines several new aggregation operators (AOs), namely, the FFL-weighted averaging (FFLWA) operator, the FFL-weighted geometric (FFLWG) operator, the FFL-ordered weighted averaging (FFLOWA) operator, the FFL-ordered weighted geometric (FFLOWG) operator, the FFL-hybrid averaging (FFLHA) operator and the FFL-hybrid geometric (FFLHG) operator under FFL environment. Several properties of these AOs are investigated in detail. Further, based on these operators, a multiple attribute group decision-making (MAGDM) approach with FFL information is developed. Finally, to illustrate the effectiveness of the present approach, a real-life supplier selection problem is presented where the evaluation information of the alternatives is given in terms of FFLNs.

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 the study of algebraic structures related to logical systems, Ideals and filters have different meanings and they are algebraic notions related to logical provable formulas. Unlike the classical Boolean lattice theory, ideals and filters are not dual notions in residuated lattices. An interesting subclass of residuated lattices is the class of triangle algebras, which is an equational representation of interval-valued residuated lattices that provides an algebraic framework for using closed intervals as truth values in fuzzy logic. The main aim of this article is to introduce and study the concept of ideals in triangle algebras and investigate the connection between ideals and filters. We first point out that the construction procedure for the filter generated by a subset of a triangle algebra established by Zahiri et al. is incorrect, and we proceed to give an alternative characterization.

In this article, we consider a class of nonsmooth interval-valued multiobjective semi-infinite programming problems with vanishing constraints (in short, NIMSIPVC). We introduce the VC-Abadie constraint qualification (in short, VC-ACQ) for NIMSIPVC and employ it to establish Karush-Kuhn-Tucker (in short, KKT)-type necessary optimality conditions. Related to NIMSIPVC, we formulate interval-valued vector Lagrange type dual and scalarized Lagrange type dual problems. Subsequently, we establish weak, strong, and converse duality results relating NIMSIPVC and corresponding dual problems. In addition, we introduce the notions of saddle points for interval-valued vector Lagrangian and scalarized Lagrangian of NIMSIPVC. Moreover, we establish the saddle point optimality criteria for NIMSIPVC. Various non-trivial examples are provided to demonstrate the validity of established results. To the best of our knowledge, optimality conditions, Lagrange type duality, and saddle point optimality criteria for NIMSIPVC have not been investigated yet via Clarke subdifferentials.

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.

Let $\mathbb{K}$ be a non-Archimedean (complete) valued field satisfying \begin{align*} \left|\sum_{j=1}^{n}\lambda_j^2\right|=\max_{1\leq j \leq n}|\lambda_j|^2, \quad \forall \lambda_j \in \mathbb{K}, 1\leq j \leq n, \forall n \in \mathbb{N}. \end{align*} For $d\in \mathbb{N}$, let $\mathbb{K}^d$ be the standard $d$-dimensional non-Archimedean Hilbert space. Let $m \in \mathbb{N}$ and $\text{Sym}^m(\mathbb{K}^d)$ be the non-Archimedean Hilbert space of symmetric m-tensors. We prove the following result. If $\{\tau_j\}_{j=1}^n$ is a collection in $\mathbb{K}^d$ satisfying $\langle \tau_j, \tau_j\rangle =1$ for all $1\leq j \leq n$ and the operator $\text{Sym}^m(\mathbb{K}^d)\ni x \mapsto \sum_{j=1}^n\langle x, \tau_j^{\otimes m}\rangle \tau_j^{\otimes m} \in \text{Sym}^m(\mathbb{K}^d)$ is diagonalizable, then \begin{align}\label{WELCHNONABSTRACT} \max_{1\leq j,k \leq n, j \neq k}\{|n|, |\langle \tau_j, \tau_k\rangle|^{2m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (\ref{WELCHNONABSTRACT}) as the non-Archimedean version of Welch bounds obtained by Welch [\textit{IEEE Transactions on Information Theory, 1974}]. We formulate non-Archimedean Zauner conjecture.

There are many problems based on solving non-autonomous differential equations of the form x¨(t)+ω2(t)x(t)=0, where x(t) represents the coordinate of a material point and ω is the angular frequency. The inverse problem involves finding the bounded coefficient ω. Continuity of the function ω(t) is not required. The trajectory x(t) is unknown, but the initial and final values of the phase variables are given. The variation principle of minimum time for the entire dynamic process allows for the determination of the optimal solution {x(t),ω(t)}. Thus, the inverse problem is an optimal control problem. No simplifying assumptions were made.

The development of autonomous vehicles is becoming increasingly popular and gathering real world data is considered a valuable task. Many datasets have been published recently in the autonomous vehicle sector, with synthetic datasets gaining particular interest due to availability and cost. For a real implementation and correct evaluation of vehicles at higher levels of autonomy it is also necessary to consider human interaction, which is precisely something that lacks in existing datasets. In this article the UPCT dataset is presented, a public dataset containing high quality, multimodal data obtained using state of the art sensors and equipment installed onboard the UPCT’s CICar autonomous vehicle. The dataset includes data from a variety of perception sensors including 3D LiDAR, cameras, IMU, GPS, encoders, as well as driver biometric data and driver behaviour questionnaires. In addition to the dataset, the software developed for data synchronisation and processing has been made available. The quality of the dataset was validated using an end-to-end neural network model with multiple inputs to obtain speed and steering wheel angle and obtained very promising results.

The growing need to use renewable sources and the current difficulty in spreading the electricity grid in a widespread manner raise the question of how to respond to the need for more electricity immediately. The idea behind this study is to power a horizontal axis wind turbine with the air flow generated for cooling a stationary internal combustion engine. The power extracted from this solution is significantly lower than that of the internal combustion engine (about 0.3%) and could be advantageous only in limited contexts. Installation costs are limited because many elements deriving from wind variability can be removed or simplified.

This paper explores multiple perspectives and proofs regarding the validity of what is considered to be one of the – if not THE - most controversial proofs in the field of mathematics, historical and contemporary applications alike. We consider the various explanations and equivalents of the axiom along with the more widely receptive alternatives. Furthermore, we review the resistance the axiom has encountered in various fields and its potential use in the research and expansion of said fields.

This paper analyzes the representation behaviors of a comparison measure between two compared fuzzy sets. Three types of restrictions on two fuzzy sets are considered in this paper: the two disjoint union fuzzy sets, the two disjoint fuzzy sets and the two general fuzzy sets. Differences exist among the numbers of possible representations of a comparison measure for the three types of fuzzy sets restrictions. The value of comparison measure is constant for the two disjoint union fuzzy sets. There are 42 candidate representations of a comparison measure for the two disjoint fuzzy sets. Of which 13 candidate representations with one or two terms can be used to easily calculate and compare a comparison measure.

Among the various generalizations of persistent topology, the one based on rank functions and leading to indexing-aware functions appears to be particularly suited to catch graph-theoretical properties without the need for a simplicial construction and a homology computation. This paper defines and studies "simple" and "single-vertex" features in directed and undirected graphs, by which several indexing-aware persistence functions are produced, within the scheme of steady and ranging sets. The implementation of the "sink" feature and its application to trust networks provide an example of the ease of use and meaningfulness of the method.

In this paper, we classify the function space of all real-valued functions on R denoted as F(R,R) into 28 distinct blocks. Each block contains elements that share common features in terms of the cardinality of their sets of continuity and differentiability. Alongside this classification, we introduce the concept of the Connection, which reveals a special relationship structure between four well-known real-valued functions in real analysis: the Cantor function, Dirichlet function, the Thomae function, and the Weierstrass function. Despite the significance of this field, several perspectives remain unexplored.

Traditional silicon binary circuits continue to face challenges such as high leakage power dissipation and large area of interconnections. Multiple-Valued Logic (MVL) and nano-devices are two feasible solutions to overcome these problems. In this paper, we present a novel method to design ternary logic circuits based on Carbon Nanotube Field Effect Transistors (CNFETs). The proposed designs use the unique properties of CNFETs, e.g., adjusting the Carbon Nanotube (CNT) diameters to have the desired threshold voltage and have the same mobility of P-FET and N-FET transistors. Each of our designed logic circuits implements a logic function and its complementary via a control signal. Also, these circuits have a high impedance state which saves power while the circuits are not in use. We show a more detailed application of our approach by designing a two-digit adder-subtractor circuit. We simulate the proposed ternary circuits using HSPICE via standard 32nm CNFET technology. The simulation results indicate the correct operation of the designs under different process, voltage and temperature (PVT) variations. Moreover, we designed a two-digit adder/subtractor and a power efficient ternary logic ALU based on the proposed gates. Simulation results show that the two-digit adder/subtractor using our proposed gates has 12X and 5X lower power consumption and PDP (power delay product) respectively, compared to previous designs.

The amide group (R-C(=O)-NH-R') is crucial in the functionality of biologically relevant compounds, such as peptides, proteins, and active pharmaceutical ingredients. Its significance in drug design and development is underlined by its presence in several top-selling drugs, where it contributes to the formation of hydrogen bonds. This research examines how heteroatoms in a six- or five-membered pyridine, thiophene or furan ring spacer between two carboxamide groups influence the hydrogen-bonding for advancements in supramolecular chemistry and drug development. The solvent-free crystal structures of 3,5-pyridinedicarboxamide (PDC), 2,5-thiophenedicarboxamide (TDC) and 2,5-furandicarboxamide (FDC-subl, crystallized by sublimation) and the monohydrate structure of FDC-solv (crystallized from methanol) were described by the Etter graph-set notation in level 1 units with the shortest rings and chains as calculated by Mercury. The nearly planar dicarboxamide molecules all have an angular or V-shaped orientation of the two amide groups. The carbon atoms of the amide groups form an angle of 124° in PDC, 129° in TDC and 117° in FDC with the ring centroid. The orientations of the two amide groups with respect to each other are C=O anti NH2 in PDC, syn-CO and syn-NH2 in TDC and FDC. In TDC the CO groups are on the side of the sulfur heteroatom. In FDC the NH2 groups lie on the side of the furan O atom which enables a chelating-type R21(10) ring H-bonding interaction with with the O=C group of a nearby symmetry-related molecule. Only in the structure of PDC the heteroatom acts as an H-bond acceptor as part of a C11(6) chain. In TDC and FDC the heteroatoms do not interact with the amide -NH2 groups. In all structures except for FDC-subl complementary head-to-tail R22(8) rings are formed together with C11(6) and C11(8) chains in PDC, with three different C11(4) chains in TDC with two of them straight and one 21-helical, and with C11(8), C22(10) and C22(16) chains, two finite D11(2) patterns and R21(10) rings in FDC-solv. From sublimation the FDC-subl crystals contain two symmetry independent molecules in the asymmetric unit combining through two C11(4), two C11(8) chains, four different finite D11(2) patterns and two R21(10) rings.

Honey bee colonies rapidly decline when confined to greenhouses, increasing pollination rental costs as they need to be replaced frequently. We tested a hive system with entrances that can be manipulated to direct bees to inside or outside greenhouses containing a zucchini crop. In one greenhouse, the bees could only forage inside for 15 days; in another, bees were directed to the inside from 5 to 9 AM, after which they foraged outside. This procedure was repeated two more times in each greenhouse with new hives. Data was collected on how the number of bee flower visits affected fruit production, the frequency of flower visits, and the amount of bee brood and food in the hives. Flowers visited by bees four times or more set more and larger fruit. The frequency of flower visits by bees from the hives confined to the greenhouse was reduced after eight days; it was not reduced in the greenhouse with bees that could forage outside. Bee brood area was reduced in the colonies that were confined to the greenhouse, while it was maintained in the semiconfined hives. The hive system with controllable entrances proved effective for pollination, while causing less damage to the bees.

In this paper we exploit concepts from Information Theory to improve the classical Chvatal’s greedy algorithm for the Set Covering Problem. In particular, we develop a new greedy procedure, called Surprisal-Based Greedy Heuristic (SBH), incorporating the computation of a “surprisal” measure when selecting the solution columns. Computational experiments, performed on instances from the OR-Library, show that SBH yields a 2.5% improvement in terms of the objective function value over the Chvatal’s algorithm while retaining similar execution times, making it suitable for real-time applications. The new heuristic was also compared with Kordalewski’s greedy algorithm, obtaining similar solutions with much lower times on large instances, and Grossmann and Wool’s algorithm for unicost instances, where SBH obtained better solutions.

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.

Hash tables are widely used. They rely on good quality hash functions. Popular data structure libraries either provide no hash functions or weak hash functions for sets or maps, making it impossible or impractical to use them as keys in other tables. This article presents three algorithms for hashing a set, two of which are simple to implement, practically fast, and can be combined. The quality evaluations follow the method of [1, chapter 2]. The insight that we are looking for commutative semigroups suggests that even better methods than symmetric polynomials may be found.

In modern mathematics, many concepts and ideas are described in terms of category theory. From this viewpoint, it is desirable to analyze what can be determined if, instead of the basic category of sets, we consider a similar category of fuzzy sets. In this paper, we describe a natural fuzzy analog of the category of sets and functions, and we show that, in this category, fuzzy relations (a natural fuzzy analogue of functions) can be determined in category terms -- of course, modulo 1-1 mapping of the corresponding universe of discourse and 1-1 re-scaling of fuzzy degrees.

To understand the possibility of interaction between scientific experimenting and artistic drawing in the form of drawings made in notebooks, assumed is a common element, a spiritual property, and transference as a mechanism for causality. Scientists, scientific experiments and artistic drawings all have different merits. Here the concept ‘speaking out’ in its meaning of expressiveness is proposed to bridge these differences. Scientific action and artistic action cannot be compared directly. However, a common spiritual element will make the investigated object, experimental set-up and notebook drawings comparable in the sense of translations authorized by the physicist. They all then speak out from the same source. In this paper considered are recent drawings made by physicists during experimentation, in notebooks and diaries. Discussed is transferal causality between the physicist, the artistic drawing and all the relevant objects belonging to the experiment. Spiritual properties are introduced for the physicist being a person, and for the investigated object, the experimental set-up and the drawings as objects.

SET protein carries out multiple functions including those for protein phosphatase 2A (PP2A) inhibition, histone modification, DNA repair and gene regulation. SET overexpression has been detected in brain neurons of Alzheimer's disease patients, follicle theca cells of Polycystic Ovary Syndrome (PCOS) patients, and ovarian cancer cells, indicating that SET may play a pathological role for these disorders. SET transcript 2, produced by a specific promoter, represents a major transcript variant in different cell types. In this study, we characterized the transcriptional activation of human SET transcript 2 promoter in HeLa cells. Promoter deletion experiments and co-transfection assays indicated that ZFX, the Zinc finger and X-linked transcription factor, was able to transactivate the SET promoter. A proximal promoter region containing four ZFX-binding sites was found to be critical for the ZFX-mediated transactivation. Mutagenesis study indicated that the site located closest to the transcription start site accounted for most of the ZFX-mediated transactivity. Manipulation of ZFX levels by overexpression or siRNA knockdown confirmed the significance and specificity of the ZFX-mediated SET promoter activation. Chromatin immunoprecipitation results verified the binding of ZFX to its cognate site in the SET promoter. These findings have led to identification of ZFX as an upstream factor regulating SET gene expression. More studies are required to define the in vivo significance of this mechanism, and specifically, its implication for several benign and malignant diseases related to SET dysregulation.

The literature on substance use usually extracts conclusions from data with correlational methods. Our study shows the usefulness of complementing ordered logistic regression (OLR) and fuzzy set qualitative comparative analysis (fsQCA) to assess factors inducing cannabis consumption in a sample of 1,935 teenagers. OLR showed a significant influence of gender (odd ratio (OR) =0.383, p<0.0001), parental monitoring (OR=0.587, p=0.0201); religiousness (OR=0.476, p=0.006); parental tolerance to substance use (OR=42.01, p<0.0001) and having close peers that consume substances (OR=5.60, p<0.0001). FsQCA has allowed fitting linkages between factors from a complementary perspective. (1) Coverage (cov) and consistency (cons) attained by solutions explaining use (cons=0.808, cov=0.357) are clearly lower than by recipes of non-use (cons=0.952, cov=0.869) (2) The interaction of gender, a tolerant family to use and the attitude toward substances by peers is very consistent to explain cannabis use. (3) The most important recipe explaining resistance to cannabis is simply parental disagreement with substance consumption (cons=0.956, cov=0.861) (4) Factors as gender, religiosity, parental monitoring and age show also a relevant impact on attitude toward cannabis use. However, whereas some of them impact symmetrically on use and non-use this does not follow in factors such as parental monitoring or age.

This paper presents an unsupervised feature selection method for multi-dimensional histogram-valued data. We define a multi-role measure, called the compactness, based on the concept size of given objects and/or clusters described by a fixed number of equal probability bin-rectangles. In each step of clustering, we agglomerate objects and/or clusters so as to minimize the compactness for the generated cluster. This means that the compactness plays the role of a similarity measure between objects and/or clusters to be merged. To minimize the compactness is equivalent to maximize the dis-similarity of the generated cluster, i.e., concept, against the whole concept in each step. In this sense, the compactness plays the role of cluster quality. We also show that the average compactness of each feature with respect to objects and/or clusters in several clustering steps is useful as feature effectiveness criterion. Features having small average compactness are mutually covariate, and are able to detect geometrically thin structure embedded in the given multi-dimensional histogram-valued data. We obtain thorough understandings of the given data by the visualization using dendrograms and scatter diagrams with respect to the selected informative features. We illustrate the effectiveness of the proposed method by using an artificial data set and real histogram-valued data sets.

The independent set, IS, on a graph $G=(V,E)$ is $V^{*}\subseteq V$ such that no two vertices in $V^{*}$ have an edge between them. The MIS problem on G seeks to identify an IS with maximum cardinality, i.e. MIS. $V^{*}\subseteq V$ is a vertex cover, i.e. VC of $G=(V,E)$ if every $e\in E$ is incident upon at least one vertex in $V^{*}$ . $V^{*}\subseteq V$ is dominating set, DS, of $G=(V,E)$ if $\forall v\in V$ either $v\in V^{*}$ or $\exists u\in V^{*}$ and $(u,v)\in E$ . The MVC problem on G seeks to identify a vertex cover with minimum cardinality, i.e. MVC. Likewise, MCV seeks a connected vertex cover, i.e. VC which forms one component in G, with minimum cardinality, i.e. MCV. A connected DS, CDS, is a DS that forms a connected component in G. The problems MDS and MCD seek to identify a DS and a connected DS i.e. CDS respectively with minimum cardinalities. MIS, MVC, MDS, MCV and MCD on a general graph are known to be NP-complete. Polynomial time algorithms are known for bipartite graphs, chordal graphs, cycle graphs, comparability graphs, claw-free graphs, interval graphs and circular arc graphs for some of these problems. We introduce a novel graph class, layered graph, where each layer refers to a subgraph containing at most some k vertices. Inter layer edges are restricted to the vertices in adjacent layers. We show that if $k=\Theta (log\mid V\mid )$ then MIS, MVC and MDS can be computed in polynomial time and if $k=O\left({(log\mid V\mid )}^{\alpha }\right)$ , where $\alpha <1$ , then MCV and MCD can be computed in polynomial time. If $k=\Theta \left({(log\mid V\mid )}^{1+ϵ}\right)$ , for $ϵ>0$ , then MIS, MVC and MDS require quasi-polynomial time. If $k=\Theta (log\mid V\mid )$ then MCV, MCD require quasi-polynomial time. Layered graphs do have constraints such as bipartiteness, planarity and acyclicity.

Abstract—Traditional automatic modulation classificationmethods operate under the closed-set assumption, which provesto be impractical in real-world scenarios due to the diversenature of wireless technologies and the dynamic characteristicsof wireless propagation environments. Open-set environments introduce substantial technical challenges, particularly in terms ofdetection effectiveness and computational complexity. To addressthe limitations of modulation classification and recognition inopen-set scenarios, this paper proposes a semi-supervised openset recognition approach, termed SOAMC (Semi-SupervisedOpen-Set Automatic Modulation Classification). The primaryobjective of SOAMC is to accurately classify unknown modulation types, even when only a limited subset of samples ismanually labeled. The proposed method consists of three keystages: (1) A signal recognition pre-training model is constructedusing data augmentation and adaptive techniques to enhancerobustness. (2) Feature extraction and embedding are performedvia a specialized extraction network. (3) Label propagation isexecuted using a graph convolutional neural network (GCN) toefficiently annotate the unlabeled signal samples. Experimentalresults demonstrate that SOAMC significantly improves classification accuracy, particularly in challenging scenarios with limitedlabeled data and high signal similarity. These findings are criticalfor the practical identification of complex and diverse modulationsignals in real-world wireless communication systems.

In this article, we first introduced new types of higher separation axioms called (r,s)-GFS-regular and (r,s)-GFS-normal spaces with the help of (r,s)-generalized fuzzy semi-closed sets (briefly, (r,s)-gfsc sets) and discussed some topological properties of them. Thereafter, we defined a stronger form of (r,s)-gfsc sets called (r,s)-g*fsc sets and investigated some of its features. Moreover, we showed that (r,s)-fsc set → (r,s)-g*fsc set → (r,s)-gfsc set, but the converse may not be true. In addition, we explored new types of fuzzy generalized mappings between double fuzzy topological spaces (U, τ, τ*) and (V, η, η*), and the relationships between these classes of mappings were examined with the help of some illustrative examples. Finally, some new types of compactness via (r,s)-gfso sets were defined and the relationships between them were introduced.

This communication explores the transition from Cognitive Behavioural Therapy (CBT) to a more holistic model, named Complex Therapy, developed by Tullio Scrimali for explaining and treating mental disorders. The Author delves into the limitations of traditional CBT and introduces an innovative framework that integrates multiple therapeutic modalities. While CBT is based on the study and modification of behaviour and cognition, Complex Therapy includes, in its focus, the theory of human relationships, the attachment theory, neuroscience, applied neuroscience, complex systems theory and ecology.Complex Therapy addresses the multifaceted nature of mental health issues by combining evidence-based techniques with personalized care strategies. The goal is to enhance patient outcomes through a tailored, comprehensive treatment plan that adapts to the evolving needs of individuals facing mental health challenges.Two innovative and original items which Scrimali has developed, which are a device for Applied Neuroscience MindLAB Set and a new botanical drug, NegEnt, are presented and discussed.The topic also describes, an original and integrated protocol, named Negative Entropy, the author has developed for treating a challenging disorder, such as schizophrenia, he renamed Entropy of Mind.

As the problem of air pollution becomes more urgent, the precise determination of the characteristics of air pollution and the associated mechanisms of transport of pollutants becomes an increasingly urgent task. The simulation results of the Copernicus Atmospheric Monitoring Service (CAMS) [18] were used as initial data sets. The area of the Crimean Peninsula (within coordinates 44.50 latitude, 33.50 longitude) in 23 - 26 January, 2019 was chosen for the study. That time concentrations of pollutants (aerosol particles with a diameter of 2.5 (PM2.5) and 10 micrometers (PM10)) steadily increased and reached the maximum value. Four kinds of meteorological data sets were used in the work. The first and second data sets were the global NCEP/NCAR and (ERA-5) re-analyses. The third and fourth meteorological data sets were obtained using the Weather tracking and Forecasting model (WRF) as domains on high-resolution grids: 9 km and 2 km. The analysis of meteorological data sets was carried out to analyze the nature of the air masses movement in the studied region. Using the HYSPLIT model simulation was carried out to determine area of the sources of negative impact. The emissions transfer from the supposed sources of negative impact on the Crimea region is analyzed. The sensitivity of simulation the inverse and direct trajectories of air masses transfer was studied based a set of simulation results. On the basis of HYSPLIT model the simulation was carried out separately using meteorological data sets having different spatial and temporal resolutions. In general, the simulation results allowed us to conclude that the HYSPLIT model in combination with high-resolution meteorological input data of the WRF model are good to identify the sources of possible negative effects on atmospheric air located at long distances from the study site.

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.

In this article, some kinds of triple belongs to metric dimensions are defined. Some classes of graphs in the matter of these kinds, are studied and the relation amid these kinds are considered. The kind of having equivalency amid these notions and some classes of graphs, is obtained. The kind of locating some vertices by some vertices when the number of locating vertices is increased, has the key role to analyze the classes of graphs, general graphs, and graph's parameters.

In this article, some notions about set, weight of set, number, number's position, special vertex are introduced. Some classes of graph under these new notions have been opted as if the study on the special attributes of these new notion when they've acted amid each other is considered. Internal and external relations amid these new notions have been obtained as if some classes of graphs in the matter of these notions are been pointed out.

In this article, some notions about set, weight of set, number, number's position, special vertex are introduced. Some classes of graph under these new notions have been opted as if the study on the special attributes of these new notion when they've acted amid each other is considered. Internal and external relations amid these new notions have been obtained as if some classes of graphs in the matter of these notions are been pointed out.

We introduce the notion of p-adic magic contraction on p-adic Hilbert space. We derive p-adic Halmos dilation, p-adic Egervary N-dilation, p-adic von Neumann inequality and p-adic Sz.-Nagy dilation for p-adic magic contraction.

Alzheimer’s is a degenerative brain condition brought on by intricate brain changes after cell injury. The prevalence of Alzheimer’s disease is highest in those over 65. Presently, AD is detected by manual examination of a patient’s Magnetic Resonance Imaging (MRI) scan and neuropsychological assessments. Due to its subpar accuracy and performance, solutions based on artificial intelligence (AI) have not been made more widely available. This paper proposes a deep Convolutional Neural Network (CNN) with the pre-trained MobileNet-V2 architecture as the model’s base for feature extraction and reducing the parameter size and training time. The proposed model accurately classifies various early stages of AD. The proposed approach visualizes the class activation maps in the form of a heat map on brain MRI scans via the Grad-CAM algorithm that lifts the black-box nature of the deep model. To handle the imbalance problem of the AD data set acquired from Kaggle, the oversampling algorithm SMOTE interpolates new images to even the class samples. The proposed multi-class classification deep model is named Bio-AD and evaluated using different quality metrics. The Bio-AD model has the following values for evaluation metrics: 97.92%, 99.87%, 97.87%, 98%, 98%, and 0.0646 for accuracy, Area Under the Curve (AUC), F1-score, Precision, Recall, and loss respectively. The proposed Bio-AD model is compared with DenseNet-169, VGG-19, and InceptionResNet-V2 using different quality metrics and outperformed in comparison with all other models using the AD data set.

In this article, we first defined a stronger form of (r,s)-generalized fuzzy semi-closed sets (briefly, (r,s)-gfsc sets) called (r,s)-g*fsc sets and investigated some of its features. Moreover, we showed that (r,s)-fsc set → (r,s)-g*fsc set → (r,s)-gfsc set, but the converse may not be true. In addition, we explored novel types of fuzzy generalized mappings between double fuzzy topological spaces (U, τ, τ*) and (V, η, η*), and the relationships between these classes of mappings were examined with the help of some illustrative examples. Thereafter, we introduced novel types of higher separation axioms called (r,s)-GFS-regular and (r,s)-GFS-normal spaces with the help of (r,s)-gfsc sets and discussed some topological properties of them. Finally, some novel types of compactness via (r,s)-gfso sets were defined and the relationships between them were introduced.

Prescribed fire is increasingly utilized for conservation and restoration goals, yet there is limited empirical evidence supporting its effectiveness in reducing wildfire-induced damages to valued resources of significant worth—whether natural, cultural, or economic. This study evaluates the efficacy of prescribed fire in reducing wildfire severity to LANDFIRE-defined vegetation classes and valued resources impacted by the 2017 West Mims event. Wildfire severity, measured using the differenced normalized burn ratio (dNBR) index, was highly heterogeneous both within and between vegetation classes; however, profound differences between treated and untreated areas were evident. The beneficial effects of prescribed fire were most pronounced within ca. two-years post-treatment but remained evident beyond three-years relative to untreated areas. For example, actively managed areas that were treated with prescribed fire just one month prior to the West Mims event exhibited an 88% reduction in mean wildfire severity relative to unmanaged areas. When post-treatment duration reached 38 months, mean wildfire severity remained 17% lower than untreated areas. Findings from this study reveal significant reductions in both average and peak wildfire severities in areas treated with frequent fire, supporting burn rotations of one to two years to balance fuel reduction and ecological conservation.

In this study, we first discover some new concept coordinated UD-convex mappings with fuzzy-number values. After that, we look into Hermite-Hadamard type inequalities via fuzzy-number-valued coordinated UD-convex fuzzy-number-valued mapping (coordinated UD-convex FNVM). In the case of coordinated UD-convex FNVM, novel conclusions are derived by making particular decisions in recently proven inequalities. Additionally, it is demonstrated that the recently discovered inequalities are expansions of comparable findings in the literature. It is important to note that the main outcomes are validated by nontrivial examples.

Interval-valued functions have been widely used to accommodate data inexactness in optimization and decision theory. In this paper, we study interval-valued vector optimization problems, and derive their relationships to interval variational inequality problems, of both Stampacchia and Minty types. Using the concept of interval approximate convexity, we establish necessary and sufficient optimality conditions for local strong quasi and approximate $LU$-efficient solutions to nonsmooth optimization problems with interval-valued multiobjective functions.

As a method of lightweight design, multi-material design aims to make targeted use of materials in order to reduce CO2 emissions. In this context, it can be described as one of the product development methods used to meet the challenges of climate change. However, since the design of structures in multi-material design is complex, topology optimization can be used to support the product developer. In this article, a multi-material topology optimization method is developed that combines the Velocity Field Level Set method with the Reconciled Level Set method. Furthermore, the current design is explicitly resolved in each iteration by means of multi-material remeshing. The edge collapse phase in the remeshing process is achieved by applying the producer consumer pattern. The developed method is then validated using known examples from the state of research and the influence of parameters of the method on the result is analyzed by means of studies.

Nitrogen is the most commonly managed mineral nutrient in olive groves because it is essential for plant growth. The precise management of N fertilization in olive cultivation is still not fully clarified, but it is now essential for providing sustainable production. A nitrogen fertilizer ex-periment with olive trees (cv. Kalinioti) was carried out over a six-year period. Seven levels of nitrogen fertilizer given as ammonium nitrate (control, 1, 2, 3, 4, 5, and 6 kg/tree) were annually applied in order to determine the effect of nitrogen on vegetative growth, fruit set, fruit weight, yield, maturation index and leaf N,P, and K concentrations. The results indicate that, under these conditions, application of up to 4 kg NH4NO3/tree significantly increased yield to 62.5 kg/tree compared to the control. The positive effect was attributed to the initial and final fruit set increases (7.63 and 3.73%, respectively). However, the weight of 100 olives (337 g) at the same fertilizer rate was considerably lower compared to the control. Higher nitrogen rates decreased yield while increasing overall shoot growth. Nitrogen fertilization did not significantly influence the oil content of olive fruit. Fruit weight, maturation index and concentration of oil reached maximum levels in the beginning of December, indicating a suitable start to olive harvesting with reduced yield losses due to unfavorable weather conditions. With increasing fertilizer levels from 0 to 6 kg NH4NO3,/tree concentration of N in olive leaves also increased from 1.23% to 2.38%. Maximum yield was achieved at a level of 6 kg NH4NO3/tree, which corresponded to 2.01% N in leaves. The results suggest that application of 3 kg NH4NO3/tree can be recommended for table olive pro-duction due to the fact that fruit weight was not decreased, while fertilization with 4 kg NH4NO3/tree was suitable for oil olives.

Reliable and accurate flood prediction is a challenging task in poorly gauged basins due to data scarcity. Data is an essential component of any AI/ML model today, and the performance of such models hugely depends on the availability of sufficient amount of trusted, representative data. However, unlike a few well-studied rivers, most of the rivers in developing countries are still insufficiently monitored, which significantly hinges the design and development of advanced flood prediction models and early warning systems. This paper presents a multi-modal, sensor-based and near-real time river monitoring system to produce a multi-feature data set for the Kikuletwa river in Northern Tanzania, an area that heavily suffers from frequent floods. Our deployed system, which gather information about river depth levels and weather at several locations, aims at widening the ground truth of the river characteristics and eventually improve the accuracy of flood predictions. We provide details on the monitoring system used to gather the data as well as report on the methodology and the nature of the data. Finally, we present the relevance of the data set in the context of flood prediction, discussing the most suitable AI/ML-based forecasting approaches, while also highlighting some applications of the data set beyond flood warning systems.

I want to find an extension of the Hausdorff Measure and Fractal Measure which allows me to compute a unique, satisfying average for functions defined on non-fractal, measurable sets in the sense of Carathedory which has no gauge function.

The global financial crisis of 2008, triggered by the collapse of Lehman Brothers, highlighted a banking system that was widely exposed to systemic risk. The minimization of the systemic risk via a close and detailed monitoring of the entire banking network became a priority. This is a complex and demanding task considering the size of the banking systems: in the US and the EU they include more than 10000 institutions. In this paper, we introduce a methodology which identifies a subset of banks that can: a) efficiently represent the behavior of the whole banking system and b) provide, in the case of a failure, a plausible range of the crisis dispersion. The proposed methodology can be used by the regulators as an auxiliary monitoring tool, to identify groups of banks that are potentially in distress and try to swiftly remedy their problems and minimize the propagation of the crisis by restricting contagion. This methodology is based on Graph Theory and more specifically Complex Networks. We termed this setting a “multivariate Threshold – Minimum Dominating Set” (mT–MDS) and it is an extension of the Threshold – Minimum Dominating Set methodology (Gogas e.a., 2016). The method was tested on a dataset of 570 U.S. banks: 429 solvent and 141 failed ones. The variables used to create the networks are: the total interest expense, the total interest income, the tier 1 (core) risk-based capital and the total assets. The empirical results reveal that the proposed methodology can be successfully employed as an auxiliary tool for the efficient supervision of a large banking network.

The meta hybrid M06-2X functional combined with the 6-311++G(d,p) basis set are used to investigate the antioxidant activity of five benzoic acid derivatives naturally occurring in several plant food: gallic acid, para-hydroxybenzoic acid, protocatechuic acid, syringic acid and vanillic acid. To assess the antioxidant properties of these compounds, three mechanisms of free radicals scavenging are considered, namely the hydrogen atom transfer (HAT), stepwise electron transfer proton transfer (SET-PT) and sequential proton loss electron transfer (SPLET) models. The effect of polar environments on the antioxidant power of these compounds is mimicked in water and methanol using the IEF-PCM solvation method. Our findings suggest that HAT is the preferred mechanistic pathway in gas phase, while SPLET is favoured in polar mediums. Protocatechuic and gallic acids are the most active in gas and polar solutions respectively, whereas PHBA is the least active in all the environments considered. The O-H group in para position of the carboxylic group (O3-H for GA and O2-H for the rest) is confirmed to be the most reactive site in gas phase, while in solution it is either of the O1-H site (for PHBA, PCA, SA and VA) or O4-H groups (for GA). The “HOMO-rule” of free radical scavenging ability does not seem to account properly for the antioxidant properties of this set of chemicals.

In perennial fruit crops, bearing can be influenced by various factors, including environmental conditions, germplasm, rootstocks, and cultivation methods. Cherries, one of the most important and popular fruit species from the temperate climate zone, achieve high prices on the market. New agricultural technologies and environmental factors force a change in the approach to cherry cultivation. Old-type cherry orchards with their high demand for water, nutrients and manual work are replaced by orchards of self-pollinating cherry cultivars grown on dwarf rootstocks. These changes make it necessary to search for ways to regulate fruiting, in particular to thin buds, flower and fruit. In view of environmental regulations and consumer pressure, thinning methods are being sought that either do not involve the use of chemicals or that use eco-friendly chemical agents. This review examines recent progress in understanding the effect of thinning methods on the physiology, tree growth and fruit quality of cherries, discusses horticultural practices aimed to ensure regular cropping and their influence on fruit quality, and provides suggestions for future research.

n our previous paper, we showed that the so-called quantum entanglement also exists in classical mechanics. The inability to measure this classical entanglement was rationalized with the definition of a classical observer which collapses all entanglement into distinguishable states. It was shown that evidence for this primary coherence is Newton’s third law. However, in reformulating a "classical entanglement theory" we assumed the existence of Newton’s second law as an operator form where a force operator was introduced through a Hilbert space of force states. In this paper, we derive all related physical quantities and laws from basic quantum principles. We not only define a force operator but also derive the classical mechanic's laws and prove the necessity of entanglement to obtain Newton’s third law.

With the revolution of computing and biology technology, data sets containing information could be huge and complex that sometimes are difficult to handle. Dynamic computing is an efficient approach to solve some of the problems. Since neighborhood multigranulation rough sets(NMGRS) were proposed, few papers focused on how to calculate approximations in NMGRS and how to update them dynamically. Here we propose approaches for computing approximations in NMGRS and updating them dynamically. First, static approaches for computing approximations in NMGRS are proposed. Second, search region in data set for updating approximations in NMGRS is shrunk. Third, matrix-based approaches for updating approximations in NMGRS while decreasing or increasing neighborhood classes are proposed. Fourth, incremental algorithms for updating approximations in NMGRS while decreasing or increasing neighborhood classes are designed. Finally, the efficiency and validity of the designed algorithms are verified by experiments.

The aim of this work is to broaden the theory of computation by making use of fuzzy sets and multisets, which are generalization of ordinary sets. We study fuzzy multiset finite automata (FMFA), which are characterized by the incorporation of vagueness when it comes to the choice of the next state and multiple occurrences of the same input symbol. The resulting automaton is a genaralization of both classical automata and fuzzy automata. We discuss the algebraic characteristics of FMFA sub-automata—separatedness, strongly connectedness, cyclic, directable, and triangular FMFA in terms of equivalence classes induced by an equivalence relation defined on state set of FMFA. Intrestingly, for a given FMFA, a new FMFA can be constructed that is a homomorphic image of the original FMFA. We define different posets structures that can be associated with a given FMFA and show that some of them are upper semilattices and discuss the inter-relationship of a given poset, a finite upper semilattice (FUSL), a FMFA and a posets/FUSL associated with a given FMFA. Finally, we introduce the concept of decomposition of a FMFA in two different ways and characterize the strongly connected, triangular and directable FMFA.

Today, mobile phones are at the center of many consumers' lives and a part of people's lives. Although this tool was considered a luxury initially, it has gradually become a necessary tool with the reduction of the price and the increase of its functions. Consumers choose specific models of mobile phones according to their needs. Mobile phones have quality features that are expressed in the form of quality dimensions. These dimensions are mostly expressed by word of mouth (WOM). In this research, first; we collected the opinions of 350 students about 4 brands of mobile phones based on Garvin's quality of dimensions, finally; the students’ opinions about mobile phones were evaluated with integrated TOPSIS with interval-valued intuitionistic fuzzy numbers technique, and the priority of 4 phone brands was determined based on students' opinions.

Many people, including Horadam, have studied the numbers $W_n$, satisfying the recurrence relation $W_n=u W_{n-1}+v W_{n-2}$ ($n\ge 2$) with $W_0=0$ and $W_1=1$. In this paper, we study the $p$-numerical semigroups of the triple $(W_i,W_{i+2},W_{i+k})$ for integers $i,k(\ge 3)$. For a nonnegative integer $p$, the $p$-numerical semigroup $S_p$ is defined as the set of integers whose nonnegative integral linear combinations of given positive integers $a_1,a_2,\dots,a_\kappa$ with $\gcd(a_1,a_2,\dots,a_\kappa)=1$ are expressed in more than $p$ ways. When $p=0$, $S=S_0$ is the original numerical semigroup. The largest element and the cardinality of $\mathbb N_0\backslash S_p$ are called the $p$-Frobenius number and the $p$-genus, respectively.

This study investigates the implementation and performance benefits of using a MongoDB replica set compared to a single node setup. The primary objective was to evaluate the efficiency and reliability improvements provided by replication in a NoSQL database cluster. The research involved configuring a single node and a three-node replica set, followed by conducting performance tests using CRUD operations on both setups. The results indicated that while the single node exhibited faster write operations, the replica set significantly improved read performance and provided high availability and fault tolerance. The findings highlight the advantages of using a replica set for applications requiring robust data access and consistent performance under varying workloads.

Optimal control is a critical tool for mechanical robotic systems, facilitating precise manipulation of dynamic processes. These processes are described through differential equations governed by a control function, addressing a time-optimal problem with bilinear characteristics. Our study utilizes the classical approach complemented by Pontryagin's Maximum Principle (PMP) to explore this inverse optimal problem. The objective is to develop an exact piecewise control function that effectively manages trajectory control while considering the effects of viscous friction. Our simulations demonstrate that the proposed control law markedly diminishes oscillations induced by boundary conditions. This research not only aims to delineate the reachability set but also strives to determine the minimal time required for the process. The findings include an exact analytical solution for the stated control problem.

Study of differential equation theory has come a long way with applications in the various fields. In 1961, Zygmund and Calderón introduced the notion of derivatives on metric Lr which proved to be better in applications than approximate derivatives. But most of the studies involved are on fuzzy set theory, so it seems likely that intuitionistic fuzzy Lr - norm - based derivatives deserve study. In the study, the fuzzy derivative is extended to intuitionistic fuzzy derivatives with respect.to Lr - norm - based derivatives using intuitionistic fuzzy number valued functions. The efficacy of the proposed method is established by proving the associated theorems along with numerical examples. Further, the Cauchy problem is also studied with respect to intuitionistic fuzzy setting.

Humans are a vision-dominated species, and what we see depends on where we look. Therefore, eye movements (EM) are essential to our interactions with the environment, and experimental findings show EM is affected in neurodegenerative disorders (ND). It could be a reason for some cognitive and movement disorders in ND. Therefore, we aim to determine if changes in EM-evoked responses can tell us about ND, such as Alzheimer’s (AD) and Parkinson’s Disease (PD) progression in different stages. In the present review, we have analyzed the results of neurological, psychological, and EM (saccades, antisaccades, pursuit) tests to predict disease progression with Machine Learning (ML) methods. Described predictive algorithms are using various approaches, including Granular Computing, Naive Bayes, Decision Trees/Tables, Logistic Regression, C-/LinearSVC, KNC, and Random Forest. We demonstrated that EM is a robust biomarker for assessing symptom progression in PD and AD. There are also navigation problems in 3D space in both diseases. Consequently, we investigated EM experiments in the virtual space and how they may help find neurodegeneration-related brain changes. In conclusion: EM parameters with clinical symptoms are powerful precision instruments that, in addition to predictions of ND progression with the help of ML, could be used to indicate the different preclinical stages of both diseases.

Consider a robot that is navigating in a space modeled by a graph, and that wants to know its current location. It can send a signal to determine how far it is from each landmark among a set of fixed landmarks. We study the problem of computing the minimum required number of landmarks, and where they should be placed so that the robot can always determine its location. Since the problem is an NP-complete problem, the robot's responses to the actions are slow. To accelerate this response, we can use the parallel version of this problem. In this work, we introduce a new parallel implementation for determining the metric dimension of a given graph. We run the proposed algorithm on a symmetric multi-processing (SMP) cluster using C programming language and the Message Passing Interface (MPI) library. Finally, we run our implementation on four categories of graphs (the tracks in which the robot moves): a cycle graph Cn, a path graph Pn, a triangular snake graph and a ladder graph Ln. Preliminary computational results indicate that the metric dimension problem is an NP-complete problem and prove the ability of the proposed algorithm to achieve a speedup of 6 for 8 processors.

Polarimetric Synthetic Aperture Radar (PolSAR) images encompass valuable information that can facilitate extensive land cover interpretation and generate diverse output products. Extracting meaningful features from PolSAR data poses challenges distinct from those encountered in optical imagery. Deep Learning (DL) methods offer effective solutions for overcoming these challenges in PolSAR feature extraction. Convolutional Neural Networks (CNNs) play a crucial role in capturing PolSAR image characteristics by leveraging kernel capabilities to consider local information and the complex-valued nature of PolSAR data. In this study, a novel three-branch fusion of complex-valued CNN named Shallow to Deep Feature Fusion Network (SDF2Net) is proposed for PolSAR image classification. To validate the performance of the proposed method, classification results are compared against multiple state-of-the-art approaches using the Airborne Synthetic Aperture Radar (AIRSAR) datasets of Flevoland, San Francisco, and ESAR Oberpfaffenhofen dataset. The results indicate that the proposed approach demonstrates improvements in OA, with 1.3% and 0.8% enhancement for the AIRSAR datasets and 0.5% improvement for the ESAR dataset. The analyses conducted on the Flevoland data underscore the effectiveness of the SDF2Net model, revealing a promising OA of 96.01% even with only 1% sampling ratio.

This study investigates the factors influencing consumers' intentions to purchase overseas travel packages via social media in Thailand, with a focus on consumer trust and perceived risks. A mixed-methods approach was employed, combining qualitative and quantitative research techniques. In the qualitative phase, the Fuzzy Set Delphi Method was applied to gather expert consensus from 19 participants. For the quantitative phase, a survey was conducted among 600 individuals who had experience purchasing overseas travel packages on social media in Thailand. First-order and second-order confirmatory factor analyses were used to examine the relationships between eight identified factors: social media influencer, e-WOM, trust, perceived risk, brand image, rating review, personal attitude, and destination image. The results indicate that trust and perceived risk are the most significant factors affecting purchase intention. Trust plays a crucial role in customers' decision-making processes, while perceived risk influences their tendency to avoid purchasing packages if the risk is perceived as high. The insights gained from this study contribute to the understanding of factors influencing purchase intentions for overseas travel packages through social media in Thailand, providing valuable information for travel agencies to develop effective marketing strategies.

Private Set Intersection Cardinality(PSI-CA) is a cryptographic method in secure multi-party computation that allows entities to identify cardinality of the intersection without revealing their private data.Traditional approaches assume similar-sized datasets and equal computational power, overlooking practical imbalances.In real-world applications, dataset sizes and computational capacities often vary, particularly in the Internet of Things and mobile scenarios where device limitations restrict computational types. Traditional PSI-CA protocols are inefficient here, as computational and communication complexities correlate with the size of larger datasets. Thus, adapting PSI-CA protocols to these imbalances is crucial.This paper explores unbalanced scenarios where one party (the receiver) has a relatively small dataset and limited computational power, while the other party (the sender) has a large amount of data and strong computational capabilities.This paper, based on the concept of commutative encryption, introduces Cuckoo filter, cloud computing technology, homomorphic encryption, among other technologies, to construct three novel solutions for unbalanced Private Set Intersection Cardinality (PSI-CA): an unbalanced PSI-CA protocol based on Cuckoo filter, an unbalanced PSI-CA protocol based on single cloud assistance, and an unbalanced PSI-CA protocol based on dual cloud assistance. Depending on performance and security requirements, different protocols can be employed for various applications.

Private Set Intersection (PSI) is a cryptographic method in secure multi-party computation that allows entities to identify common elements in their datasets without revealing their private data. Traditional approaches assume similar-sized datasets and equal computational power, overlooking practical imbalances. In real-world applications, dataset sizes and computational capacities often vary, particularly in the Internet of Things and mobile scenarios where device limitations restrict computational types. Traditional PSI protocols are inefficient here, as computational and communication complexities correlate with the size of larger datasets. Thus, adapting PSI protocols to these imbalances is crucial. This paper explores unbalanced PSI scenarios where one party (the receiver) has a relatively small dataset and limited computational power, while the other party (the sender) has a large amount of data and strong computational capabilities. It introduces three innovative solutions for unbalanced PSI: unbalanced PSI protocol based on Cuckoo filters, unbalanced PSI protocol based on single cloud assistance, and unbalanced PSI protocol based on dual cloud assistance, each addressing the shortcomings of the previous solution. These protocols primarily optimize database computational load, storage capacity, protocol execution time, and security. Depending on performance and security needs, different protocols can be employed for applications such as private contact discovery.

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control system with bounded disturbances. First, by constructing an appropriate Lyapunov-Krasovskii functional, we obtained a delay-dependent condition, which determed the admissible bounding ellipsoid for the reachable set of the system we considered. Then, a sufficient condition in form of liner matrix inequalities is given to solve the problem of controller design with reachable set estimation. Finally, by minimizing the volume of the ellipsoid and solving the liner matrix inequality, we obtain the desired ellipsoid and controller gain. A comparative numerical example is given to verify the usefulness of our result.

Given a set of distinct non-negative integers X^n and a target certificate S in parametrized form: ∃X^k⊆X^n,∑_(x_i∈X^k)▒x_i =S (k=|X^k |,n=|X^n |). We present a polynomial solution of the subset sum problem with time complexity T≤O(kn)≤O(n^2) and space complexity S≤O(((n-1)n)/2)≤O(n^2 ), so that P = NP.

With advances in information technology, big data, mobile communications, and robotics, digital technologies are increasingly being used in factories around the world. This digital transformation is named industry 4.0. Today, industrial companies are looking at how to adopt this era and implement these technologies 4.0 while improving their performance and generating more profits. The objective of this paper is to help companies to better choose the appropriate digital technologies according to their activities using a multi-experts-multi-criteria decision-making approach under hesitant fuzzy information. The proposed model is a generic model based on Multi-Agent Systems allowing to have an idea of the parameters necessary to apply the adopted approach. The adopted approach allows a better representation of uncertainty and subjectivity of experts’ judgments. It would be of great interest, especially, when exact quantitative data are not available. A real case company example is exposed (automotive company) towards putting into practice the proposed approach.

A construction for the systems of natural and real numbers is presented in Zermelo-Fraenkel Set Thoery, that allows for simple proofs of the properties of these systems, and practical and mathematical applications. A practical application is discussed, in the form of a Simple and Linear Fast Adder (Patent Pending). Applications to finite group theory and analysis are also presented. A method is illustrated for finding the automorphisms of any finite group $G$, which consists of defining a canonical block form for finite groups. Examples are given, to illustrate the procedure for finding all groups of $n$ elements along with their automorphisms. The canonical block form of the symmetry group $\Delta_4$ is provided along with its automorphisms. The construction of natural numbers is naturally generalized to provide a simple and sound construction of the continuum with order and addition properties, and where a real number is an infinite set of natural numbers. A basic outline of analysis is proposed with a fast derivative algorithm. Under this representation, a countable sequence of real numbers is represented by a single real number. Furthermore, an infinite $\infty\times\infty$ real-valued matrix is represented with a single real number. A real function is represented by a set of real numbers, and a countable sequence of real functions is also represented by a set of real numbers. In general, mathematical objects can be represented using the smallest possible data type and these representations are calculable. In the last section, mathematical objects of all types are well assigned to tree structures in a proposed type hierarchy.

Ramsey’s theory (RAM) from combinatorics and network theory goes looking for regularities and repeated patterns inside structures equipped with nodes and edges. RAM represents the outcome of a dual methodological commitment: by one side a top-down approach evaluates the possible arrangement of specific subgraphs when the number of graph’s vertices is already known, by another side a bottom-up approach calculates the possible number of graph’s vertices when the arrangement of specific subgraphs is already known. Since natural neural networks are often represented in terms of graphs, we suggest to utilize RAM for the analytical and computational assessment of a peculiar structure supplied with neuronal vertices and axonal edges, i.e., the human brain connectome. We discuss how a RAM approach in neuroscientific issues might be able to locate and trace unexplored motifs shared between different cortical and subcortical subareas. Furthermore, we will describe how notable RAM outcomes, such as the Ramsey’s theorem and the Ramsey’s number, could contribute to uncover still unknown anatomical connexions endowed in neuronal networks and unexpected functional interactions among grey zones of the human brain.

The report details out programming approach for automating warehouse using Answer Set Programming.

Background: Although National Licensing Examinations (NLEs) may be a costly process, they can predict better performance for many following years. The current licensing requirements will not entail and new requirements will be requested. Therefore, this study suggests a framework for the development of the Medical Licensing Exam by exploring the opinions of Egyptian medical practitioners and educators regarding the exam format and criteria. Objective and methods: to describe the needed steps to develop the EMLE through a two-phase exploratory mixed-method study that had been conducted among the Egyptian medical sectors: medical practitioners and educators. Results: There were 50 clinical and academic educators shared in the online discussion about EMLE development. Then, a survey was carried out on 266 participants with various working places in which 198 of the participants were staff in the Higher Education Ministry and 68 physicians in the Ministry of Health. The input from both had contributed to the development of the following framework that is divided into two main sections; the Exam Logistics and the Exam Set up. The exam Logistics included the exam committee, prerequisites for the exam, the admission criteria and fees, and the validity of the license. While the Exam Set up included exam setting, structure, standard-setting, pass marks and reset policy. Conclusion: A Multidisciplinary team resources for the exam setting. Fairness and objectivity were highlighted through several factors; development of the exam blueprint, types of assessment methods, post-exam analysis, and standard-setting. Finally, the reset policy, fees, and validity of the license were recommended with a student-centered perspective that was suggested for the exam committee.

We provide an axiomatic base for the set of natural numbers, that has been proposed as a canonical construction, and use this definition of $\mathbb N$ to find several results on finite group theory. Every finite group $G$, is well represented with a natural number $N_G$; if $N_G=N_H$ then $H,G$ are in the same isomorphism class. We have a linear order, on the quotient space of isomorphism classes of finite groups, that is well behaved with respect to cardinality. If $H,G$ are two finite groups such that $|H|=m<n=|G|$, then $H<\mathbb Z_n\leq G\leq\mathbb Z_{p_1}^{n_1}\oplus\mathbb Z_{p_2}^{n_2}\oplus\cdots\oplus\mathbb Z_{p_k}^{n_k}$ where $n=p_1^{n_1}p_2^{n_2}\cdots p_{k}^{n_k}$ is the prime factorization of $n$. We find a canonical order for the objects of $G$ and define equivalent objects of $G$, thus finding the automorphisms of $G$. The Cayley table of $G$ takes canonical block form, and we are provided with a minimal set of independent equations that define the group. We show how to find all groups of order $n$, and order them. We give examples using all groups with order smaller than $10$, and we find the canonical block form of the symmetry group $\Delta_4$. In the next section, we extend our results to the infinite case, which defines a real number as an infinite set of natural numbers. A real function is a set of real numbers, and a sequence of real functions $f_1,f_2,\ldots$ is well represented by a set of real numbers, as well. In general, we represent mathematical objects using the smallest possible data-type. In the last section, mathematical objects are well assigned to tree structures. We conclude with brief comments on type theory and future work on computational aspects of these representations.

A new approach is presented to defining the amount of information, in which information is understood as the data about a finite set as a whole, whereas the average length of an integrative code of elements serves as a measure of information. We obtain a formula for the syntropy of reflection, that is, the information that two intersecting finite sets reflect about each other. The specificities of reflection of discrete systems through the combination of their parts are considered, and it is shown that the additive syntropy and entropy of reflection are measures of structural order and chaos. Three information laws have been established: the law of conservation of the sum of chaos and order; information law of reflection; the law of conservation and transformation of information. An assessment of the structural organization and the level of development of discrete systems is presented. It is shown that various measures of information are structural characteristics of integrative codes of elements of discrete systems. The conclusion is made that, from the informational-genetic positions, the synergetic theory of information is primary in relation to the Hartley-Shannon information theory. In the appendix we consider the asymmetry of the mutual reflection of finite sets and the proportionality of arbitrary quantities.

We consider Pisot family substitution tilings in $\R^d$ whose dynamical spectrum is pure point. There are two cut-and-project schemes(CPS) which arise naturally: one from the Pisot family property and the other from the pure point spectrum respectively. The first CPS has an internal space $\R^m$ for some integer $m \in \N$ defined from the Pisot family property, and the second CPS has an internal space $H$ which is an abstract space defined from the property of the pure point spectrum. However it is not known how these two CPS's are related. Here we provide a sufficient condition to make a connection between the two CPS's. In the case of Pisot unimodular substitution tiling in $\R$, the two CPS's turn out to be same due to [5, Remark 18.5].

Various factors and constraints should be considered when developing a manufacturing production schedule, and such a schedule is often based on rules. This paper develops a composite dispatching rule based on heuristic rules that comprehensively consider various factors in a semiconductor production line. The composite rule is obtained by exploring various states of a semiconductor production line (machine status, queue size, etc.), where such indicators as makespan and equipment efficiency are used to judge performance. A model of the response surface, as a function of key variables, is then developed to find the optimized parameters of a composite rule for various production states. Further, dynamic scheduling of semiconductor manufacturing is studied based on support vector regression (SVR). This approach dynamically obtains a composite dispatching rule (i.e. parameters of the composite dispatching rule) that can be used to optimize production performance according to real-time production line state. Following optimization, the proposed dynamic scheduling approach is tested in a real semiconductor production line to validate the effectiveness of the proposed composite rule set.