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Automatic test paper design is critical in education to reduce workloads for educators and facilitate an efficient teaching process. However, current designs fail to satisfy the realistic teaching requirements of educators, including the consideration of both test quality and efficiency. This is the main reason why teachers still manually construct tests in most teaching environments. In this paper, the quality of tests is quantitatively defined while considering multiple objectives, including a flexible coverage of knowledge points, cognitive levels, and question difficulty. Then, a model based on the technique of linear programming is delicately designed to explore the optimal results for this newly defined problem. However, this technique is not efficient enough, which cannot obtain results in polynomial time. With the consideration of both test quality and generation efficiency, this paper proposes a genetic algorithm (GA) based method, named dynamic programming guided genetic algorithm with adaptive selection (DPGA-AS). In this method, a dynamic programming method is proposed in the population initialization part to improve the efficiency of the genetic algorithm. An adaptive selection method for the GA is designed to avoid prematurely falling into the local optimal for better test quality. The question bank used in our experiments is assembled based on college-level calculus questions from well-known textbooks. The experimental results show that the proposed techniques can construct test papers with both high effectiveness and efficiency. The computation time of the test assembly problem is reduced from 3 hours to 2 seconds for a 5000-size question bank as compared to a linear programming model with similar test quality. The test quality of the proposed method is better than the other baselines.

Background:Understanding fractions in mathematics often poses greater complexity compared to integral numbers. The primary difficulty lies in students' inadequate grasp of fractional basics, notably in comparing and sequencing fractions. Aim: This research seeks to create and evaluate a learning pathway's effect on fourth graders' comprehension of fractions, with a focus on their comparison and sequencing. Method: Employing a design research validation study approach, the research progresses through preliminary design, experimental design, and retrospective analysis. Conducted in a Palembang school involving six fourth graders recommended by their teacher, data collection encompassed essay-based pre and post-tests, Student Activity Sheets, observations, interviews, and documentations. The data analysis was retrospectively carried out, anchored on HLT as the benchmark. Result: Findings reveal a student learning trajectory encompassing three principal activities. Initially, students used folding and gluing of paper to discern fraction values. Subsequently, they engaged in coloring and illustrating folds for fraction comparison. The final activity involved drawing, coloring boxes, and fraction comparison and sequencing. Overall, students showed proficiency in understanding and determining fraction values and comparing them, yet struggled with ordering certain fractions. Conclusion: The structured learning path facilitated students' understanding of basic fraction concepts, especially in comparing them. Nevertheless, reinforcing methods or approaches for teaching fraction ordering is essential.

In 1921 Mellin published a Comptes Rendu paper computing the principal solution of a polynomial using generalized hypergeometric functions of its coefficients. He used an integral transform nowadays bearing his name. Slightly over three pages, the paper is written in French in a terse style befitting the language. This article makes Mellin’s landmark result accessible to people who are not experts in hypergeometric functions and complex analysis by deriving detailed proofs that were omitted in Mellin’s paper.

In this paper we extend the SuperHyperAlgebra, SuperHyperGraph, SuperHyperTopology, SuperHyperSoft Set, endowed with SuperHyperOperations, SuperHyperAxioms, and SuperHyperFunctions, to the most general form of structure, from our real world, called SuperHyperStructure in any field of knowledge. A practical application of the SuperHyperStructure is presented at the end. The prefix “Hyper” [Marty, 1934] stand for the codomain of the functions and operations to be P(H), or the powerset of the set H. While the prefix “Super” [Smarandache, 2016] stands for using the Pn (H), n ≥ 2, or the n-th PowerSet of the Set H {because the set (or system) 𝐻 (that may be a set of items, a company, institution, country, region, etc.) is organized in sub-systems, which in their turn are organized in sub-sub-systems, and so on} in the domain and/or codomain of the functions and operations.

Paper-cut elements in the design of boat space can effectively improve the homogenisation tendency of existing boat space design, effectively enhance the characteristics of traditional Chinese culture and enrich the development ideas of boat space design. Therefore, based on the Chinese folk art of paper cutting, this paper combines theoretical analysis and empirical research to deeply analyse the artistic expression of paper-cut elements in the spatial design of boats. This paper mainly studies the artistic integration of paper-cut elements in the decorative design of boats and the artistic integration of paper-cut elements in the practical design of boats. Through the calculation and analysis of the sparse autoencoder algorithm model, it can be seen that the decorative integration of paper-cut elements in wallpaper is 82%, which is higher than that of traditional materials (24%). The integration of paper-cut elements in the space design of cabins and guest rooms is as high as 97% and 94%, respectively, which is far better than the integration of traditional materials in the space design of cabins and guest rooms. This shows that the application of folk paper-cut elements to the space design of boats not only highlights the theme of boats but also enhances the cultural value of boats.

English is a universal language and is widely used. In order to deepen the cognition of language, this paper proposes to analyse the variation of metadiscourse verb patterns in English academic papers from within and between disciplines. By comparing the metadiscourse chunks used in various disciplines, it is concluded that there are obvious differences in the verb types of the subject papers. Analysing various identification algorithms of verb types, it is obtained that the combination of the word movement distance (WMD) model and the R&L density peak clustering algorithm is the best. Using the R&L density peak clustering, identification parameters are easy to determine, and when combined with the WMD model to calculate the similarity of words, it improve the accuracy of verb pattern clustering. By comparison, it is proved that the accuracy of the algorithm combining the WMD model and R&L density peak clustering reaches 30.06%, and the effect of identifying verb pattern variation is the best.

In this paper, through the collection and analysis of data, the art of Guangling paper-cutting is theoretically researched, and the general features and shapes of Guangling paper-cutting are summarized. In order to overcome the limitations of traditional algorithms in the extraction of features of Guangling paper-cutting, the combination of spatial pyramid matching and context-dependent histogram methods are used to extract the shape features of paper-cutting images with stronger differentiation. The support vector machine is used to solve the problem of recognizing and classifying the image patterns in the digitized display. The design of the digital promotion of the Shanxi Guangling paper-cutting brand is carried out. Research variables are designed to analyze the effect of digital transformation and promotion of paper-cutting brands. The results show that the discrepancy of Guangling paper-cutting features extracted by the algorithm in this paper is very low, the e1 difference is maintained within 0.1, and the total recognition rate of SVM on Guangling paper-cutting features can reach 88.06%, and the overall effect is more satisfactory, and the regression equation of the influence of paper-cutting = −0.807+0.111*history+0.122* style+0.234*paper-cutting+0.216*display+0.136 * linkage, and propose strategies to enhance the influence of paper-cutting brand. The technical methods used in this study guarantee the quality of the digital transformation of Guangdong paper-cutting from the source.

To deeply analyze the performance of paper-cutting elements in interior space design, this paper explores the artistic expression of paper-cutting elements. The BIM model is constructed based on the TVL algorithm, and a noise-reducing style migration method with an additional total variable loss function is used to fuse the texture features of a specific paper-cutting style so that the paper-cutting texture is generated in the target object area more intensively. The algorithm is supplemented with a U-shaped network structure to obtain the mask map of the target object, modify and expand the ScanNet training data set, and input a content map and a style map to generate the stylized paper cutout image automatically. The results show that compared with other elements, the stability of paper-cut elements reaches 96.31%, the image smoothness reaches 89.34%, and the retention of significant regions reaches 93.26%. In modern design, the peak signal-noise of paper-cut elements improved by 13.418d on average, the structural similarity also improved by 0.34807, and the recognition rate of paper-cut elements in the furnishing category reached 95%. Applying paper-cut art in interior space design can give interior furnishing design better visual effects, provide inspiration and ideas for interior space design innovation, and contribute to improving aesthetics.

In the realm of Chinese traditional arts, paper-cutting symbols embody deep-seated aesthetic and cultural values. Within the framework of artificial intelligence, the fusion of these conventional symbols with contemporary pattern design through intelligent reconstruction processes promotes innovation in modern design. This paper introduces a novel pattern feature extraction algorithm specifically designed for identifying and extracting the essence of traditional paper-cutting art. Utilizing Deep Convolutional Generative Adversarial Networks (DCGAN), an automated method for generating woven patterns is developed, integrating conventional motifs with modern design elements. Additionally, a segmentation model based on DeepLabV3+ semantics is constructed to facilitate this integration. The study focuses on the fusion of traditional paper-cutting symbols with fabric patterns, providing a new direction for textile design research. The empirical evaluation involved seven experimenters who predominantly favored patterns that blended abstract and traditional styles, with the average style rating exceeding 3.2. Moreover, the color performance analysis of the reconstructed fabric patterns across five regions showed color difference values greater than 4, indicating superior color fidelity. These findings underscore the potential of combining AI-driven techniques with traditional art forms to enhance and revolutionize modern design practices.

The study of metadiscourse word resources is an important way to reveal academic knowledge constructs and genre features in English papers. This paper selects intra- and interdisciplinary English academic papers as data samples, and the text representation is based on the vector space model. The text similarity is calculated using the word movement distance model to complete the clustering based on the density peak, and then the semantic annotation of metadiscourse verb patterns is performed using the conditional random field. Then, the intra- and interdisciplinary metadiscourse annotations are compared to analyze the variation of verb patterns. The intra-disciplinary variation of metadiscourse verb patterns was mainly found using attitude markers, where the log-likelihood ratios of 48.56, 30.25, and 35.64 were obtained for affirmative, critical, and critical declarative attitudes, respectively. In interdisciplinary studies, basic disciplines preferred to use verb patterns as transitions, while applied disciplines preferred to express the author’s point of view. The study of metadiscourse verb patterns effectively enriches the linguistic resources in academic English teaching and deepens the understanding of the characteristics of disciplinary essay genres.

In this paper, we consider a robust combinatorial optimization problem with uncertain weights and propose an uncertainty set that generalizes interval uncertainty by imposing lower and upper bounds on deviations of subsets of items. We prove that if the number of such subsets is fixed and the family of these subsets is laminar, then the robust combinatorial optimization problem can be solved by solving a fixed number of nominal problems. This result generalizes a previous similar result for the case where the family of these subsets is a partition of the set of items.

This investigation delves into the evolving patterns and regional variances in industry-academia collaboration (IAC) within Functional Nucleic Acids (FNAs) research. Analyzing publications and patents from 1990 to 2021, we dissected IAC at individual and collective levels, documenting the count and share of IAC endeavors, key partners, and regional differences. Results indicate a rising trend in IAC publications and collaborating institutions, while patent trends display a mix of increases, decreases, and steady states. The United States leads in IAC activities, correlating with its prowess in scientific research and technological innovation. Notably, regional discrepancies in IAC are mainly due to intra-regional variations, with Asia and Europe experiencing the most pronounced disparities.

In an era overwhelmed by academic big data, students grapple with identifying academic papers that resonate with their learning objectives and research interests, due to the sheer volume and complexity of available information. This study addresses the challenge by proposing a novel academic paper recommendation system designed to enhance personalized learning through the nuanced understanding of academic social networks. Utilizing the theory of social homogeneity, the research first constructs a sophisticated academic social network, capturing high-order social relationships, such as co-authorship and advisor–advisee connections, through hypergraph modeling and advanced network representation learning techniques. The methodology encompasses the development and integration of a hypergraph convolutional neural network and a contrastive learning framework to accurately model and recommend academic papers, focusing on aligning with students’ unique preferences and reducing reliance on sparse interaction data. The findings, validated across multiple real-world datasets, demonstrate a significant improvement in recommendation accuracy, particularly in addressing the cold-start problem and effectively mapping advisor–advisee relationships. The study concludes that leveraging complex academic social networks can substantially enhance the personalization and precision of academic paper recommendations, offering a promising avenue for addressing the challenges of academic information overload and fostering more effective personalized learning environments.

Predicting stock prices is contained in the basic approach is fundamental and technical analysis which is needed by entrepreneurs who invest their capital, this analysis is to determine the company's financial performance and must continue to be carried out, to carry out this analysis we use the help of several financial ratios where several types of ratios Return on Assets, Debt to Equity Ratio, Return on Equity, and Book Value per Share are some examples. The authors applied a quantitative descriptive approach to companies listed on the Indonesia Stock Exchange in the Pulp & Paper sector for this study. According to the Correlation and Regression tables, all of the variables ROA, ROE, DER, and BVS have an effect on stock prices, but the stock session obtained on the variables ROA, ROE, and DER has a very significant effect on stock prices but has no significant effect on stock prices on the BVS variable. So in the long term the company must implement one of two policies, namely low solvency means using less debt than own capital and a low solvency policy will not cause high interest expenses to be borne by the company so that it will affect growth.

We construct a two discrete parameter family of compact minimal surfaces embedded in the Berger sphere which may be considered as the analogue of the helicoidal Karcher-Scherk surfaces.

Frank and Wolfe’s celebrated conditional gradient method is a well-known tool for solving smooth optimization problems for which minimizing a linear function over the feasible set is computationally cheap. However, when the objective function is nonsmooth, the method may fail to compute a stationary point. In this work, we show that the Frank–Wolfe algorithm can be employed to compute Clarke-stationary points for nonconvex and nonsmooth optimization problems consisting of minimizing upper-$C^{1,\alpha }$ functions over convex and compact sets. Furthermore, under more restrictive assumptions, we propose a new algorithm variant with stronger stationarity guarantees, namely directional stationarity and even local optimality.

Standards are a set of guidelines or criteria used to ensure consistency, quality, safety, and compatibility in products, services, and processes [...]

Abstract Very recently Jain et al. (J. Inequal. Appl. 2022:73, 2022) introduced the concept of multivalued F-contraction with altering distance function and investigated the existence of best proximity points for this class of mappings. In this article we prove that the existence of best proximity points for multivalued F-contraction non-self mappings can be obtained from the corresponding fixed point result for multivalued F-contraction self mappings, and so the main conclusion due to Jain et al. is not a real generalization of fixed point theory.

A scheme for the integration of $ \, {}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)} $-type fractional differential equations (FDEs) is presented in this paper. The approach is based on the expansion of solutions to FDEs via fractional power series. It is proven that $ \, {}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)} $-type FDEs can be transformed into equivalent $ \left(\, {}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)}\right)^n $-type FDEs via operator calculus techniques. The efficacy of the scheme is demonstrated by integrating the fractional Riccati differential equation.

From time to time, we hear in the news about a breach or attack on some well-known companies as just news, but it is a serious problem because it is the privacy of citizens, their money in trade and managing their businesses and projects. In this paper, we offer a review of the honey encryption planner. Honey Encryption is the encryption system that ensures flexibility versus the brute-force attack through the provision of plain reasonable text, but false for each key is invalid utilized by a trespasser to decrypt a message, two key areas are open it is difficult to create a compelling message trap that's perfect enough to deceive the striker even when he believes that he has the message in its original form. The next problem, the typo issue, where a valid phony plain text seem to a lawful user when he accidentally enters the wrong key. Our goal is to have more satisfaction disguised tricks that are perfect enough to prevent a trespasser from getting the original message, We also need new security methods because the attackers are looking for new ways to attack the systems, so we proposed a new way to protect messages and passwords well and difficult to break and take all the possibilities of attack, including the brute-force, and then the data is hidden in an image with a public secret key.

Recently, the systems of e-learning are improved technologically and the led to the emergence of e-learning systems that reached the level of adaptation to students. Through which, it changed the entire education system during the Internet era. Nonetheless, the use of rule-based, assumption-based, and network-based method have some vital methodologies used to implement learner models across adaptive learning systems. The so common way to structure the learner models approaches rely on the personalization and user modelling. However, personalization and user modeling found out to be the best approaches-not only in developing students' talents but also in allowing students to take their own learning direction and making sure that they are using their potential to the fullest. The mismatching in viewpoints and perceptions between teachers and technicians along with a lack of appropriate technical knowledge have been identified as some of the major challenges affecting the learner model development. the main objective of this article is to show the use of different approaches through the recent scholars’ in implementing learner models within adaptive e-learning systems. Moreover, approaches and challenges in implementing learner models are also described

The human capability to react or adapt to upcoming changes strongly relies on the ability to forecast them [...]

Perception is an individual's ability to respond, interpret, and distinguish a view of any information to a stimulus. So the aims of this study was to find out: (1) students' perceptions of the use of an equation editor in writing mathematical notation as assignments for calculus class I papers, (2) students' perceptions of writing calculus I paper assignments using the manual method (handwriting). The research subjects consisted of 16 students majoring in Extension Informatics Engineering (afternoon class) Semester I. The type of research was descriptive qualitative. Data collection techniques are interviews. The analysis stage is to analyze the results of the interviews. The results of the study concluded that: (1) 11 (eleven) students agreed to use the equation editor in writing calculus I paper assignments,the rest were still confused about the use of the equation editor; and (2) all students do not agree if the paper is written using the manual method (handwriting) because the results are not neat and take a long time.

This Special Issue comprises the first collection of papers submitted by the Editorial Board Members (EBMs) of the journal Mathematical and Computational Applications (MCA), as well as outstanding scholars working in the core research fields of MCA [...]

This issue of featured papers from 2020 is related to the study of symmetry phenomena in various different fields, but mainly in theoretical physics [...]

This editorial is a short review of papers accepted in the Mathematics and Symmetry/Asymmetry section in 2020–2021 about the symmetry methods [...]

We investigated the influence of mental imagery expertise in 15 pen and paper role-players as an expert group compared to the gender-matched control group of computer role-players in the difficult Vandenberg and Kuse mental rotation task. In this task, the participants have to decide which two of four rotated figures match the target figure. The dependent measures were performance speed and accuracy. In our exploratory investigation, we further examined midline frontal theta band activation, parietal alpha band activation, and parietal alpha band asymmetry in EEG as indicator for the chosen rotation strategy. Additionally, we explored the gender influence on performance and EEG activation, although a very small female sample section was given. The expected gender difference concerning performance accuracy was negated by expertise in pen and paper role-playing women, while the gender-specific difference in performance speed was preserved. Moreover, gender differences concerning electro-cortical measures revealed differences in rotation strategy, with women using top-down strategies compared to men, who were using top-down strategies and active inhibition of associative cortical areas. These strategy uses were further moderated by expertise, with higher expertise leading to more pronounced activation patters, especially during successful performance. However, due to the very limited sample size, the findings of this explorative study have to be interpreted cautiously.

Investigating the research trends within a scientific domain by analyzing semantic information extracted from scientific journals has been a topic of interest in the natural language processing (NLP) field. A research trend evaluation is generally based on the time evolution of the term occurrence or the term topic, but it neglects an important aspect—research publication latency. The average time lag between the research and its publication may vary from one month to more than one year, and it is a characteristic that may have significant impact when assessing research trends, mainly for rapidly evolving scientific areas. To cope with this problem, the present paper is the first work that explicitly considers research publication latency as a parameter in the trend evaluation process. Consequently, we provide a new trend detection methodology that mixes auto-ARIMA prediction with Mann–Kendall trend evaluations. The experimental results in an electronic design automation case study prove the viability of our approach.

This Special issue contains top-tier physics-related and mathematical research, among other topics, written by scholars who are well-known in their field [...]

Leveraging artificial intelligence (AI), this study revolutionizes examination management and education in universities by developing an intelligent system encompassing comprehensive management, pre-examination activities, scheduling, and preparation. The system also features a quality management component for educational outcomes. An enhanced genetic algorithm introduces an adaptation function to optimize intelligent grouping, facilitating effective exam paper distribution. Applied at Y University, our innovative approach significantly refines exam paper difficulty (ranging between 0.5016 and 0.5581) and differentiation (0.3845 to 0.4596), showcasing the intelligent algorithm’s effectiveness in exam management and contributing valuable insights to educational research.

With the innovation and development of commercial shopping centers in China, the shopping environment is becoming more and more colorful. However, in today’s social environment, the central function of low-level consumption experience can no longer meet the needs of the masses. Therefore, in the design of indoor environment, we should start from a new perspective, focusing on the difference of internal space and the experience of consumption mode, so as to meet the development needs of commercial shopping in the future. Based on the research on the indoor environment of comprehensive commercial shopping center, comprehensive commercial shopping center in a certain area as the research target, the corresponding mathematical model was constructed, and using the measured method validation build the model of reliability and validity, thus obtains using CFD numerical simulation software of thermal and moisture environment of building an in-depth exploration, The effective countermeasures are put forward for the original air distribution mode. Comparing the improved scheme with the original scheme, it is found that the former can provide effective basis for the interior environment design of similar comprehensive commercial shopping malls.

Abstract Cloudiness or formation is a concept routinely used in industry to address deviations from homogeneity in nonwovens and papers. Measuring a cloudiness index based on image data is a common task in industrial quality assurance. The two most popular ways of quantifying cloudiness are based on power spectrum or correlation function on the one hand or the Laplacian pyramid on the other hand. Here, we recall the mathematical basis of the first approach comprehensively, derive a cloudiness index, and demonstrate its practical estimation. We prove that the Laplacian pyramid as well as other quantities characterizing cloudiness like the range of interaction and the intensity of small-angle scattering are very closely related to the power spectrum. Finally, we show that the power spectrum can be measured easily by image analysis methods and carries more information than the alternatives.

The operation space of the vertical lift shaft is small, the components are complex, the occluding and different behavior space characteristics are similar, and the unsafe behavior is not easy to detect, which makes the operation safety of maintenance personnel in the elevator greatly threatened. This paper proposes an elevator maintenance personnel behavior detection algorithm based on the first-order deep network architecture (FOA-BDNet). First, a lightweight backbone feature extraction network is designed to meet the online real-time requirements of elevator maintenance environment monitoring video stream detection. Then, the feature fusion network structure of "far intersection and close connection" is proposed to fuse the fine-grained information with the coarse-grained information and to enhance the expression ability of deep semantic features. Finally, a first-order deep target detection algorithm adapted to the elevator scene is designed to identify and locate the behavior of maintenance personnel and to correctly detect unsafe behaviors. Experiments show that the detection accuracy rate on the self-built data set in this paper is 98.68%, which is 4.41% higher than that of the latest target detection model YOLOv8-s, and the reasoning speed reaches 69.51fps/s, which can be easily deployed in common edge devices and meet the real-time detection requirements for the unsafe behaviors of elevator scene maintenance personnel.

Let [Formula: see text] be the principal eigenvector corresponding to the spectral radius [Formula: see text] of a graph G of order n. In this paper, we find some bounds on the ratio of the maximal component [Formula: see text] to the minimal component [Formula: see text] of the principal eigenvector X in terms of the graph parameters such as the independence number [Formula: see text], the minimum vertex cover number of the vertex [Formula: see text] and the chromatic number [Formula: see text]. Also, we present some bounds on the extremal component [Formula: see text] of the principal eigenvector X. An upper bound of the spectral radius [Formula: see text] of G in terms of the minimum vertex cover number [Formula: see text] and order of the graph n is also introduced in this paper.

Recently, in the field of periodic nonuniform sampling, researchers (Wang et al., 2019; Asharabi, 2023) have investigated the incorporation of a Gaussian multiplier in the one-dimensional series to improve its convergence rate. Building on these developments, this paper aimed to accelerate the convergence of the two-dimensional periodic nonuniform sampling series by incorporating a bivariate Gaussian multiplier. This approach utilized a complex-analytic technique and is applicable to a wide range of functions. Specifically, it applies to the class of bivariate entire functions of exponential type that satisfy a decay condition, as well as to the class of bivariate analytic functions defined on a bivariate horizontal strip. The original convergence rate of the two-dimensional periodic nonuniform sampling is given by $ O(N^{-p}) $, where $ p \geq 1 $. However, through the implementation of this acceleration technique, the convergence rate improved drastically and followed an exponential order, specifically $ \mathrm{e}^{-\alpha N} $, where $ \alpha > 0 $. To validate the theoretical analysis presented, the paper conducted rigorous numerical experiments.

In this current paper, we developed a new predator-prey model accompanying delay based on the earlier works. By applying inequality strategies, fixed point theorem, and a suitable function, we got new necessary conditions for the existence, uniqueness, nonnegativeness, and boundedness of the solution to the developed delayed predator-prey model. The bifurcation behavior and stability nature of the defined delayed predator-prey model were investigated by using stability and bifurcation theory of delayed differential equations. We have modified the Hopf bifurcation's appearance time and stability domain by building two distinct hybrid delayed feedback controllers for the delayed predator-prey model. The time of Hopf bifurcation appearance and stability domain of the model were explored. Matlab experiment diagrams were given to support the learned important results. The derived outcomes in this paper were original and have significant theoretical implications for maintaining equilibrium between the densities of the three species.

In this paper, we first introduced systems of generalized vector quasi-variational equilibrium problems as well as systems of vector quasi-variational equilibrium problems as their special cases in abstract convex spaces. Next, we established some existence theorems of solutions for systems of generalized vector quasi-variational equilibrium problems and systems of vector quasi-variational equilibrium problems in non-compact abstract convex spaces. Furthermore, we applied the obtained existence theorem of solutions for systems of vector quasi-variational equilibrium problems to solve the existence problem of Nash equilibria for noncooperative games. Then, as applications of the existence result of Nash equilibria for noncooperative games, we studied the existence of weighted Nash equilibria and Pareto Nash equilibria for multi-objective games. The results derived in this paper extended and unified the primary findings presented by some authors in the literature.

This paper introduces a subclass of Markov renewal processes (MRPs) and presents a solution to the optimal filtering problem in a stochastic observation system, where the state is modeled by an MRP and observed indirectly through noisy measurements. The MRPs considered here can be interpreted as continuous-time Markov chains (CTMCs) with a finite set of abstract states representing distributions of random vectors. The paper outlines the probabilistic properties of MRPs, emphasizing the ability to express any arbitrary function of the MRP as the solution to a linear stochastic differential system (SDS) with a martingale on the right-hand side (RHS). Using these properties, an optimal filtering problem is formulated in stochastic observation systems, where the hidden state belongs to the class of MRPs, and the observations consist of both diffusion and counting components. The drift terms in all observations depend on the system state. An optimal filtering estimate for a scalar function of the MRP is provided through the solution of an SDS with innovation processes on the RHS. Additionally, the paper presents a version of the Kushner-Stratonovich equation, describing the evolution of the conditional probability density function (PDF). To demonstrate the practical application of the estimation method, the paper presents a communications-related example, focusing on monitoring the qualitative state and numerical characteristics of a network channel using noisy observations of round-trip time (RTT) and packet loss flow. The paper also highlights the robustness of the filtering algorithm in scenarios where the MRP distribution is uncertain.

In this paper, we focus on two relative aging classes, namely increasing (decreasing) relative failure rate and increasing (decreasing) failure rate relative to average failure rate. We studied some reliability properties and connections with other classes of lifetime distributions. The main objective of this paper was to investigate the preservation properties of decreasing relative failure rate class and decreasing failure rate relative to average failure rate class under the structure of ($ n-k+1 $)-out-of-$ n $ system. We give some examples of parametric distributions to evaluate the correctness of the results.

In this paper, polynomial equations with real coefficients and in one variable were considered which contained a small, positive but specified and fixed parameter $ \varepsilon_0 \neq 0 $. By using the classical asymptotic method, roots of the polynomial equations have been constructed in the literature, which were proved to be valid for sufficiently small $ \varepsilon $-values (or equivalently for $ \varepsilon \to 0 $). In this paper, it was assumed that for some or all roots of a polynomial equation, the first few terms in a Taylor or Laurent series in a small parameter depending on $ \varepsilon $ exist and can be constructed. We also assumed that at least two approximations $ x_1(\varepsilon) $ and $ x_2(\varepsilon) $ for the real roots exist and can be constructed. For a complex root, we assumed that at least two real approximations $ a_1(\varepsilon) $ and $ a_2(\varepsilon) $ for the real part of this root, and that at least two real approximations $ b_1(\varepsilon) $ and $ b_2(\varepsilon) $ for the imaginary part of this root, exist and can be constructed. Usually it was not clear whether for $ \varepsilon = \varepsilon_0 $ the approximations were valid or not. It was shown in this paper how the classical asymptotic method in combination with the bisection method could be used to prove how accurate the constructed approximations of the roots were for a given interval in $ \varepsilon $ (usually including the specified and fixed value $ \varepsilon_0 \neq 0 $). The method was illustrated by studying a polynomial equation of degree five with a small but fixed parameter $ \varepsilon_0 = 0.1 $. It was shown how (absolute and relative) error estimates for the real and imaginary parts of the roots could be obtained for all values of the small parameter in the interval $ (0, \varepsilon_0] $.

In this paper, we introduced a new contraction principle via altering distance and $ C $-class functions with rational forms which extends and generalizes the existing version provided by Hasan Ranjbar et al. [H. Ranjbar, A. Niknam, A fixed point theorem in Hilbert $ C^\ast $-modules, Korean J. Math., 30 (2022), 297–304]. Specifically, the rational forms involved in the contraction condition we presented involve the $ p $-th power of the displacements which can exceed the second power mentioned in Hasan Ranjbar et al.'s paper. Moreover, we also proved a fixed point theorem for this type of contraction in the Hilbert $ C^\ast $-module. Some adequate examples were provided to support our results. As an application, we applied our result to prove the existence of a unique solution to an integral equation and a second-order $ (p, q) $-difference equation with integral boundary value conditions.

This paper is motivated by the paper [2]. The main aim of this paper is to extend the stability result from [16], related to the θ-Euler- Maruyama method (θ ∈ (12{1 \over 2}, 1)) for a class of neutral stochastic differential equations with time-dependent delay. The theta method is defined such that, in general case, it is implicit in both drift coefficient and neutral term. Sufficient conditions of the a.s. exponential stability of the θ-Euler-Maruyama method, including the linear growth condition on the drift coefficient of the equation, are revealed. The stability result is established for larger class of neutral terms than that considered in the second cited paper. An example is provided to support the main results of the paper.

Abstract This paper deals with the attraction–repulsion chemotaxis system with nonlinear productions and logistic source, u t = ∇ ⋅ ( D ( u ) ∇ u ) − ∇ ⋅ ( Φ ( u ) ∇ v ) + ∇ ⋅ ( Ψ ( u ) ∇ w ) + f ( u ) , v t = Δ v + α u k − β v , τ w t = Δ w + γ u l − δ w , τ ∈ { 0 , 1 } , $$\begin{aligned}& u_{t} = \nabla \cdot \bigl( D(u) \nabla u \bigr) - \nabla \cdot \bigl( \Phi (u) \nabla v \bigr) + \nabla \cdot \bigl( \Psi (u) \nabla w \bigr) + f(u),\\& v_{t} = \Delta v+\alpha {{u}^{k}}-\beta v,\qquad \tau w_{t} = \Delta w+\gamma {{u}^{l}}-\delta w,\quad \tau \in \{0,1 \}, \end{aligned}$$ in a bounded domain Ω ⊂ R n $\Omega \subset {{\mathbb{R}}^{n}}$ ( n ≥ 1 $n \ge 1 $ ), subject to the homogeneous Neumann boundary conditions and initial conditions, where D , Φ , Ψ ∈ C 2 [ 0 , ∞ ) $D,\Phi ,\Psi \in {{C}^{2}}[0,\infty )$ are nonnegative with D ( s ) ≥ ( s + 1 ) p $D(s)\ge {{(s+1)}^{p}}$ for s ≥ 0 $s\ge 0$ , Φ ( s ) ≤ χ s q $\Phi (s)\le \chi {{s}^{q}}$ , ξ s g ≤ Ψ ( s ) ≤ ζ s j $\xi {{s}^{g}}\le \Psi (s) \le \zeta s^{j}$ , s ≥ s 0 $s\ge {{s}_{0}}$ , for s 0 > 1 ${{s}_{0}}>1$ , the logistic source satisfies f ( s ) ≤ s ( a − b s d ) $f(s)\le s(a-b{{s}^{d}})$ , s > 0 $s>0$ , f ( 0 ) ≥ 0 $f(0)\ge 0$ , and the nonlinear productions for the attraction and repulsion chemicals are described via α u k $\alpha {{u}^{k}}$ and γ u l $\gamma {{u}^{l}}$ , respectively. When k = l = 1 $k=l=1$ , it is known that this system possesses a globally bounded solution in some cases. However, there has been no work in the case k , l > 0 $k,l>0$ . This paper develops the global boundedness of the solution to the system in some cases and extends the global boundedness criteria established by Tian, He, and Zheng (2016) for the attraction–repulsion chemotaxis system.

The discrete Hopfield neural network 3-satisfiability (DHNN-3SAT) model represents an innovative application of deep learning techniques to the Boolean SAT problem. Existing research indicated that the DHNN-3SAT model demonstrated significant advantages in handling 3SAT problem instances of varying scales and complexities. Compared to traditional heuristic algorithms, this model converged to local minima more rapidly and exhibited enhanced exploration capabilities within the global search space. However, the model faced several challenges and limitations. As constraints in SAT problems dynamically increased, decreased, or changed, and as problem scales expanded, the model's computational complexity and storage requirements may increase dramatically, leading to reduced performance in handling large-scale SAT problems. To address these challenges, this paper first introduced a method for designing network synaptic weights based on fundamental logical clauses. This method effectively utilized the synaptic weight information from the original SAT problem within the DHNN network, thereby significantly reducing redundant computations. Concrete examples illustrated the design process of network synaptic weights when constraints were added, removed, or updated, offering new approaches for managing the evolving constraints in SAT problems. Subsequently, the paper presented a DHNN-3SAT model optimized by genetic algorithms combined with K-modes clustering. This model employed genetic algorithm-optimized K-modes clustering to effectively cluster the initial space, significantly reducing the search space. This approach minimized the likelihood of redundant searches and reduced the risk of getting trapped in local minima, thus improving search efficiency. Experimental tests on benchmark datasets showed that the proposed model outperformed traditional DHNN-3SAT models, DHNN-3SAT models combined with genetic algorithms, and DHNN-3SAT models combined with imperialist competitive algorithms across four evaluation metrics. This study not only broadened the application of DHNN in solving 3SAT problems but also provided valuable insights and guidance for future research.

In this paper, we apply the powerful sine-Gordon expansion method (SGEM), along with a computational program, to construct some new traveling wave soliton solutions for two models, including the higher-order nonlinear Boussinesq dynamical wave equation, which is a well-known nonlinear evolution model in mathematical physics, and the (1+1)-dimensional framework of the Van der Waals gas system. This study presents some new complex traveling wave solutions, as well as logarithmic and complex function properties. The 3D and 2D graphical representations of all obtained solutions, unveiling new properties of the considered model are simulated. Additionally, several simulations, including contour surfaces of the results, are performed, and we discuss their physical implications. A comprehensive conclusion is provided at the end of this paper.

The Internet of Things (IoT) has become increasingly popular, opening vast application possibilities in different fields including smart cities, healthcare, manufacturing, agriculture, etc. IoT comprises resource-constrained devices deployed in Low Power and Lossy Networks (LLNs). To satisfy the routing requirements of these networks, the Internet Engineering Task Force (IETF) created a standardised Routing Protocol for low-power and Lossy Networks (RPL). However, this routing protocol is vulnerable to routing attacks, prompting researchers to propose several techniques to defend the network against such attacks. Machine learning approaches demonstrate effective ways to detect such attacks in large quantities. Therefore, this paper systematically synthesised 17 publications to compare the performance of traditional and advanced machine learning algorithms to identify the best algorithm for detecting RPL-based IoT routing attacks. The findings of this paper show that machine learning algorithms are capable of effective detection of many routing attacks with high accuracy and a low False Positive Rate. Furthermore, the results demonstrate that on average, advanced machine learning algorithms can achieve an accuracy of 96.03% compared to traditional machine learning algorithms which achieved 91.67%. Traditional machine learning algorithms demonstrated the best performance on average False Positive Rate by achieving 2.75% compared to their counterparts which gained 4.79%. However, Random Forest showed the best performance and outperformed all the algorithms in the selected publications by achieving over 99% accuracy, precision and recall.

In this computational paper, we focused on the efficient numerical implementation of semi-implicit methods for models in materials science. In particular, we were interested in a class of nonlinear higher-order parabolic partial differential equations. The Cahn-Hilliard (CH) equation was chosen as a benchmark problem for our proposed methods. We first considered the Cahn-Hilliard equation with a convexity-splitting (CS) approach coupled with a backward Euler approximation of the time derivative and tested the performance against the bi-harmonic-modified (BHM) approach in terms of accuracy, order of convergence, and computation time. Higher-order time-stepping techniques that allow for the methods to increase their accuracy and order of convergence were then introduced. The proposed schemes in this paper were found to be very efficient for 2D computations. Computed dynamics in 2D and 3D are presented to demonstrate the energy-decreasing property and overall performance of the methods for longer simulation runs with a variety of initial conditions. In addition, we also present a simple yet powerful way to accelerate the computations by using MATLAB built-in commands to perform GPU implementations of the schemes. We show that it is possible to accelerate computations for the CH equation in 3D by a factor of 80, provided the hardware is capable enough.

This paper aims to formulate a class of nonlinear hybrid stochastic time-delay neural networks (STDNNs) with Lévy noise. Specifically, the coefficients of networks grow polynomially instead of linearly, and the time delay of given neural networks is non-differentiable. In many practical situations, nonlinear hybrid STDNNs with Lévy noise are unstable. Hence, this paper uses feedback control based on discrete-time state and mode observations to stabilize the considered nonlinear hybrid STDNNs with Lévy noise. Then, we establish stabilization criteria of $ H_{\infty} $ stability, asymptotic stability, and exponential stability for the controlled nonlinear hybrid STDNNs with Lévy noise. Finally, a numerical example illustrating the usefulness of theoretical results is provided.

The paper deals with the estimation of sensor faults for dynamic systems as well as the assessment of the uncertainty of the resulting estimates. For that purpose, it is assumed that the external disturbances are bounded within an ellipsoidal domain. This allows considering both stochastic and deterministic process and measurement uncertainties. Under such an assumption, a fault diagnosis scheme is developed with a prescribed convergence rate and accuracy. To achieve fault estimation, a conversion into an equivalent descriptor system is utilized. The paper provides a full stability and convergence analysis of the estimator including observability analysis. As a result, a set of complementary fault uncertainty intervals is obtained, which are minimized in such a way as to obtain a minimum detectable sensor fault. The final part of the paper exhibits a numerical example concerning fault estimation of a multi-tank system. The obtained results clearly confirm the performance of the proposed estimator expressed in the minimum detectable fault intervals.

The paper proposes a non-iterative training algorithm for a power efficient SNN classifier for applications in self-learning systems. The approach uses mechanisms of preprocessing of signals from sensory neurons typical of a thalamus in a diencephalon. The algorithm concept is based on a cusp catastrophe model and on training by routing. The algorithm guarantees a zero dispersion of connection weight values across the entire network, which is particularly important in the case of hardware implementation based on programmable logic devices. Due to non-iterative mechanisms inspired by training methods for associative memories, the approach makes it possible to estimate the capacity of the network and required hardware resources. The trained network shows resistance to the phenomenon of catastrophic forgetting. Low complexity of the algorithm makes in-situ hardware training possible without using power-hungry accelerators. The paper compares the complexities of hardware implementations of the algorithm with the classic STDP and conversion procedures. The basic application of the algorithm is an autonomous agent equipped with a vision system and based on a classic FPGA device.