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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.

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.

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.

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.

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 current increasing global demand for low-carbon and environmentally friendly products, promoting the sustainability of closed-loop supply chains has become one of the key measures. However, consumers often do not regard remanufactured products as equivalent to new products. Therefore, this paper proposes a dynamic closed-loop supply chain that incorporates consumers' purchasing preferences to model a long-term game with product differentiation. Moreover, to enhance consumer acceptance of remanufactured products and reduce manufacturers' costs, low-carbon technologies and cost-sharing mechanisms are introduced. In this way, we construct a differential game in which the manufacturer sells new and remanufactured products through a retailer and makes decisions about the level of low-carbon technology in the remanufacturing process. Based on the theory of differential games, this paper analyzes three different power structures: the manufacturer-dominated Stackelberg game, the Nash game, and the retailer-dominated Stackelberg game. The optimal low-carbon technology level and pricing strategy are obtained by applying Pontryagin's maximum principle. The study shows that the retailer-led Stackelberg game helps retailers maximize profits, while the Nash game enables the entire closed-loop supply chain system to achieve the highest overall profits. This paper innovatively integrates low-carbon technologies into the dynamic game model of the remanufacturing process and reveals how the game behavior of supply chain participants affects the application of low-carbon technologies and the overall profit of the supply chain by comparing the cost-sharing mechanisms under different power structures. The results provide important theoretical support and practical references for closed-loop supply chain management with product differentiation.

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.

The paper discusses the inventory management problem with a single product stored in two warehouses, where each has its unique suppliers with certain lead times. Moreover, one of the warehouses may act as a backup supplier for the other. In other words, product exchange between two different warehouses within one company is allowed. The first warehouse operates under an a priori known time-variant contractual demand and a bounded random one. Its secondary goal is to accumulate emergency stock that can be delivered to the second warehouse within one time period. For this warehouse we use a desired trajectory generator to shape the required stock level and then utilize a trajectory following control law. The demand in the second warehouse is unknown but bounded, and its suppliers have limited delivery capacity. The challenge is to fulfill the customers’ needs, although they might exceed the order limit. Therefore, occasional backup supplies from the first warehouse are necessary. For the control of the second warehouse, a simple sliding mode (SM) scheme is applied. The paper proves that, with appropriate compensation of the emergency deliveries in the first warehouse, our proposed control scheme ensures full demand satisfaction in both warehouses despite the second one’s control limit.

In recent years, a variety of multiple zeta values (MZVs) variants have been defined and studied. One way to produce these variants is to restrict the indices in the definition of MZVs to some fixed parity pattern, which include Hoffman’s multiple t-values, Kaneko and Tsumura’s multiple T-values, and Xu and this paper’s author’s multiple S-values. Xu and this paper’s author have also considered the so-called multiple mixed values by allowing all possible parity patterns and have studied a few important relations among these values. In this paper, we turn to the finite analogs and the symmetric forms of the multiple mixed values, motivated by a deep conjecture of Kaneko and Zagier, which relates the finite MZVs and symmetric MZVs, and a generalized version of this conjecture by the author to the Euler sum (i.e., level two) setting. We present a few important relations among these values such as the stuffle, reversal, and linear shuffle relations. We also compute explicitly the (conjecturally smallest) generating set in weight one and two cases. In the appendix, we tabulate some dimension computations for various subspaces of the finite multiple mixed values and propose a conjecture.

The physical layer is implemented in the present communication era with new multicarrier modulation schemes such as Generalized Frequency Division Multiplexing with Multi-Input and Multi-Output (MIMO-GFDM) antenna systems to achieve good spectral efficiency and diversity order. This paper presents precoded Space-Time-Frequency MIMO-GFDM performance analysis to improve the bit error rate performance without increasing transmission power and bandwidth compared to conventional techniques. The proposed system also enhances the diversity order over frequency selective fading channels. In general, we need to perform channel matrix inversion operations at the receiver or channel precoding matrix operations at the transmitter to detect the symbols of MIMO-GFDM systems. This paper's proposed scheme completes the same task without performing channel matrix inversion. Orthogonal transform techniques such as Haar, Harley, Walsh-Hadamard, and Slant transforms are used as precoders at the transmitter for the proposed scheme. The simulation results are validated on the MATLAB working platform. We have compared the bit error rate of the PSTF-MIMO-GFDM system with Space-Time (ST) and Space Frequency (SF) as baseline schemes and different orthogonal transform precoding techniques.

An infrared camera is the best tool for identifying the temperatures in various parts of thermal power plants. In this paper, authors identified the probable faults in different parts of the Boiler using temperature. A well-liked and secure technique to use in condition monitoring and preventative maintenance is infrared thermography. This procedure is directly applied to determine whether the machine is operating normally or not and also to identify the heat pattern that indicates inefficiency and flaws within the machine. For the asset manager, it is the best practice. This procedure lowers the danger and increases operational dependability. Checking bearings and belts, and keeping an eye on electrical rooms, panel boards, rotating motors, boiler operations, etc., are all made easier using infrared thermography. This method helps pinpoint the precise site of the equipment or machine malfunction. It can avoid events that can happen due to destruction from heat radiation and save energy, money, time, and money on repairs. If the operations are prepared for the obstacles, they can be managed successfully. This paper presents details of an Expert system for Boilers in Thermal power plants.

In this paper, we study the weighted spaces $ L^p(\omega, \mathbb{R}^d) $ boundedness of certain class of maximal operators when their kernels belong to the space $ L^{q}(\mathbb{S} ^{d-1}) $, $ q > 1 $. Our results in this paper are improvements and extensions of some previously known results.

This paper contributes to the classification of flag-transitive 2-$ (v, k, \lambda) $ designs. Let $ \mathcal{D} $ be a non-trivial and non-symmetric $ 2 $-$ (v, k, \lambda) $ design with $ \lambda $ prime and $ G $ be a flag-transitive point-primitive automorphism group of $ \mathcal{D} $. A recent work by the first author and Chen has proven that the socle of $G$ is either a nonabelian simple group or an elementary abelian $ p $-group for some prime $ p $. In this paper, we focus on the case where the socle of $G$ is an exceptional group of Lie type and give all possible parameters of such 2-designs.

We investigate a system of linear ordinary differential equations containing point and integral loadings with nonlocal boundary conditions. Boundary conditions include integral and point values of the unknown function. An essential feature of the problem is that the kernels of the integral terms in the differential equations depend only on the integration variable. It is shown that similar problems arise during feedback control of objects with both lumped and distributed parameters during point and integral measurements of the current state of the controllable object. The problem statement considered in the paper generalizes a lot of previously studied problems regarding loaded differential equations with nonlocal boundary conditions. By introducing auxiliary parameters, we obtain necessary conditions for the existence and uniqueness of a solution to the problem under consideration. To solve the problem numerically, we propose to use a representation of the solution to the original problem, which includes four matrix functions that are solutions to four auxiliary Cauchy problems. Using solutions to the auxiliary problems in boundary conditions, we obtain the values of the unknown function at the loading points. This is enough to get the desired solution. The paper describes the application of the method using the example of solving a test model problem.

In this paper, we study the following Schrödinger equations with potentials and general nonlinearities \begin{equation*} \begin{cases} -\Delta u+V(x)u+\lambda u=|u|^{q-2}u+\beta f(u), \\ \int |u|^2dx=\Theta, \end{cases} \end{equation*} both on $\mathbb{R}^N$ as well as on domains $\Omega_r$ where $\Omega_r \subset \mathbb{R}^N$ is an open bounded convex domain and $r>0$ is large. The exponent satisfies $2+\frac{4}{N}\leq q\leq2^*=\frac{2 N}{N-2}$ and $f:\mathbb{R}\rightarrow \mathbb{R}$ satisfies $L^2$-subcritical or $L^2$-critical growth. This paper generalizes the conclusion of Bartsch et al. in [4]. Moreover, we consider the Sobolev critical case and $L^2$-critical case of the above problem.

‎This paper addresses the problem of optimizing the reconstruction of links in a network in the aftermath of natural disasters or human errors‎, ‎such as landslides‎, ‎floods‎, ‎storms‎, ‎earthquakes‎, ‎bombing‎, ‎war‎, ‎etc‎. We aim to determine the optimal sequence for reconstructing the destroyed links within a specific time horizon, while simultaneously locating ‎‎(k)‎‎ portable emergency service centers (where ‎‎(k > 2) throughout the entire network. ‎In this paper‎, ‎the problem is considered in a tree structure‎. ‎A greedy algorithm and a heuristic method‎, ‎namely‎, ‎maximum radius‎, ‎are proposed to solve the problem‎. ‎We evaluate the performance of the proposed algorithms using randomly generated data‎. ‎The experimental results confirm the effectiveness of the proposed methods‎.

In this paper we are focusing on finding the transcendental entire solution of Fermat-type trinomial and binomial equations, by restricting the hyper-order to be less than one. As the hyper-order is a crucial parameter that characterizes the growth of entire functions, it will be interesting to investigate this unexplored domain, as far as practible, with certain restriction on hyper order. Our results are the improvements of previous results reported in recent papers [12], [13]. We have provided a series of examples to demonstrate and validate the effectiveness of our proposed solutions.

The gap between software design and implementation often results in a lack of clarity and precision. Formal languages, based on mathematical rules, logic, and symbols, are invaluable for specifying and verifying system designs. Various semi-formal and formal languages, such as JSON, XML, predicate logic, and regular expressions, along with formal models like Turing machines, serve specific domains. This paper introduces a new specification formal language, ObTFL (Object Transaction Formal Language), developed for general-purpose distributed systems, such as specifying the interactions between servers and IoT devices and their security protocols. The paper details the syntax and semantics of ObTFL and presents three real case studies—federated learning, blockchain for crypto and bitcoin networks, and the industrial PCB board with machine synchronization—to demonstrate its versatility and effectiveness in formally specifying the interactions and behaviors of distributed systems.

Scholars of English Literature unanimously say that J.R.R. Tolkien influenced C.S. Lewis’s writings. For the first time, we have investigated this issue mathematically by using an original multi-dimensional analysis of linguistic parameters, based on surface deep language variables and linguistic channels. To set our investigation in the framework of English Literature, we have considered some novels written by earlier authors, such as C. Dickens, G. MacDonald and others. The deep language variables and the linguistic channels, discussed in the paper, are likely due to writers’ unconscious design and reveal connections between texts far beyond the writers’ awareness. In summary, the capacity of the extended short-term memory required to readers, the universal readability index of texts, the geometrical representation of texts and the fine tuning of linguistic channels within texts—all tools largely discussed in the paper—revealed strong connections between The Lord of the Rings (Tolkien), The Chronicles of Narnia, The Space Trilogy (Lewis) and novels by MacDonald, therefore agreeing with what the scholars of English Literature say.

This paper explores the mathematical dynamics of consumer spending during a financial crisis using opponent process theory (OPT). Traditionally applied in psychology, OPT explains how initial emotional responses are followed by counteracting reactions to restore equilibrium. This study models the short-term boost in consumer spending and subsequent economic adjustments. Utilizing differential equations to represent these processes, this paper provides insights into the interplay between immediate policy effects and longer-term economic consequences. We focus on the United States (US) response to the 2008 Global Financial Crisis in this study. Results show evidence of diminishing response from prolonged stimuli due to demand saturation, resource allocation inefficiencies, and agent adaptation. Monetary stimuli may inflate debt/prices, outweighing benefits, and structural issues persist despite stimuli. Confidence and expectations impact response because perceived ineffectiveness weakens impact over time. Thus, while stimuli can initially boost activity, their sustained impact demands careful consideration of economic dynamics and agents’ responses.

Let $ R $ be a commutative ring with the identity $ 1_{R} $, and let $ R^* $ be the multiplicative group of units in $ R $. An element $ a\in R^* $ is called an exceptional unit if there exists a $ b\in R^* $ such that $ a+b = 1_{R} $. We set $ R^{**} $ to be the set of all exceptional units in $ R $. In this paper, we consider the residue-class ring $ \mathbb{Z}_n $. For any positive integers $ n, s $, and $ c\in\mathbb{Z}_n $, let $ {\mathcal N}_{s}(n, c): = \sharp\big\{(x_1, ..., x_s)\in (\mathbb{Z}_n^{**})^s : x_1+...+x_s\equiv c \pmod n\big\} $. In 2016, Sander (J.Number Theory 159 (2016)) got a formula for $ {\mathcal N}_{2}(n, c) $. Later on, Yang and Zhao (Monatsh. Math. 182 (2017)) extended Sander's theorem to finite terms by using exponential sum theory. In this paper, using matrix theory, we present an explicit formula for $ {\mathcal N}_{s}(n, c) $. This extends and improves earlier results.

The purpose of this paper is to solve the problem of the sharp estimation of the modulus of the third Taylor coefficient on the class of holomorphic bounded nonvanishing in the unit disk functions (hereafter referred to as the class of bounded nonvanishing functions). The problem of sharp estimation of the moduli of all Taylor coefficients depending on the coefficient number on this class is usually called the Krzyz problem. Consider the class of normalized holomorphic bounded functions in the unit disk (hereafter referred to as the class of bounded functions). The coefficient problem on this class is posed as follows: find the necessary and sufficient conditions to impose on a sequence of complex numbers so that the power series with coefficients from this sequence is the Taylor series of some function from the class of bounded functions. In this paper, by means of the solution of the coefficient problem for the class of bounded functions, we solve the problem of obtaining the sharp estimates of moduli of the first three Taylor coefficients on the class of bounded functions. It is pointed out that it is possible to visualize the first three coefficient bodies of the subclass of the class of bounded functions, consisting of functions with real coefficients. Next, we solve the problem of obtaining the sharp upper estimation of the modulus of the third Taylor coefficient on the class of bounded nonvanishing functions, by reducing it to the functional over the class of bounded functions. On the basis of the above-mentioned estimates on the class of bounded functions, it was possible to obtain a functional that majorizes the original one. The problem is then reduced to the problem of finding the conditional maximum of the function of three real variables with inequality-type constraints, which made it possible to apply standard methods of differential calculus to obtain this main result.

Neyman’s 1923 paper introduced the potential outcomes framework and the foundations of randomization-based inference. We discuss the influence of Neyman’s paper on four introductory to intermediate-level textbooks by Berkeley faculty members (Scheffé; Hodges and Lehmann; Freedman, Pisani, and Purves; and Dunning). These examples illustrate that Neyman’s key insights can be explained in intuitive and interesting ways to audiences at all levels, including undergraduates in introductory statistics courses. We have found Freedman, Pisani, and Purves’s box-of-tickets model to be a valuable expository tool, and we also find their intuitive explanation of Neyman’s variance result helpful: It is a “minor miracle” that in randomized experiments, the two-sample zz-test is conservative because of “two mistakes that cancel.” All four books take a more positive view of Neyman’s results than Neyman himself did. We encourage educators and researchers to explore ways to communicate Neyman’s ideas that are helpful for their own audiences.

This paper investigates rumor propagation in a multilingual environment, taking into account language usage variations. Firstly, a 2I2S2R model is proposed within a heterogeneous network framework that incorporates both immunologic and cross-transmitted mechanisms. Secondly, the paper calculates the basic reproduction number $ R_0 $ by the next-generation matrix method. Thirdly, the local asymptotic stability and the global asymptotic stability are further explored, which indicate that whether the rumor continuously spreads or becomes extinct is determined by the threshold. Finally, the numerical simulation and sensitivity analysis are given to illustrate the effectiveness of theoretical results and the influence of model parameters on rumor spreading.

Abstract In this paper we propose an algorithm for testing whether the independent observations come from finite-variance distribution. The preliminary knowledge about the data properties may be crucial for its further analysis and selection of the appropriate model. The idea of the testing procedure is based on the simple observation that the empirical cumulative even moment (ECEM) for data from finite-moments distribution tends to some constant whereas for data coming from heavy-tailed distribution, the ECEM exhibits irregular chaotic behavior. Based on this fact, in this paper we parameterize the regular/irregular behavior of the ECEM and construct a new test statistic. The efficiency of the testing procedure is verified for simulated data from three heavy-tailed distributions with possible finite and infinite variances. The effectiveness is analyzed for data represented in time domain. The simulation study is supported by analysis of real vibration signals from rotating machines. Here, the analyses are provided for data in both the time and time-frequency domains.

Thermal-aware virtual machine (VM) placement has emerged as a critically significant research domain in response to the escalating demand for energy-efficient and dependable cloud data centers. Addressing the imperative need for resource optimization and reduced energy consumption, the virtual machine placement problem seeks to strategically allocate VMs to physical servers while adhering to stringent thermal constraints. This paper intricately surveys the state-of-the-art techniques employed in thermal-aware VM placement, encompassing both static and dynamic approaches. Our comprehensive analysis delves into influential factors, including workload characteristics, server heterogeneity, and advanced thermal management techniques. By elucidating the intricacies of these considerations, our review offers a nuanced understanding of the complex VM placement landscape. Importantly, we spotlight key challenges and identify open research issues, presenting a roadmap for future investigations. This review paper stands as a pivotal resource, providing invaluable insights for researchers and practitioners navigating the evolving landscape of thermal-aware virtual machine placement in cloud data centers.

The aim of this paper is to introduce the cyclic-Fibonacci hybrid sequence and give some properties. By taking into account the cyclic-Fibonacci hybrid sequence modulo $m$, the method will be given to determine the period lengths of this sequence according to the different $m$ values. In the final part of this paper, we study the cyclic-Fibonacci hybrid sequence in groups and then we calculate the cyclic-Fibonacci hybrid lengths of polyhedral groups $(2,2,2)$, $(2,n,2)$ and $(n,2,2)$ as applications of the results produced.

In manufacturing industries, reliability analysis of cutting tools is of paramount importance, as their frequent failures may result in enhanced downtime of production lines, leading to reduced throughput, enhanced process cycle times, and low profits. There are numerous factors that govern the desired operations of cutting tools, e.g., tool cutting speed, feed, depth of cut, and many others. Existing literature on cutting tools’ reliability estimation emphasizes mainly three variables, as mentioned earlier while neglecting other important factors. Including a greater number of factors in the process of estimating reliability increases the number of covariates, hence rendering the data acquisition costlier and estimation models highly complex. This work initially utilizes Analytical Hierarchy Process (AHP) to assess the importance of various factors that are responsible for the cutting tool’s performance, followed by the reliability estimation of the cutting tools using proportional hazards model (PHM) considering the four “critical to reliability” factors as obtained through AHP as covariates. The proposed method also helps in determining the relationship of these sub-factors with the hazard rate and reliability of the cutting tools. Experimental results are then used to verify the model’s predictions through response surface methodology (RSM) and Weibull fit. Furthermore, the paper also presents a proposed technique to estimate the required number of cutting tools for one machine per day and the number of job completions that can be an essential takeaway for various industries. Thus, this research paper proposes an integrated AHP-RSM-PHM based approach for a comprehensive reliability analysis of cutting tools.

This paper investigates the complexities surrounding uncertain portfolio selection in cases where security returns are not well-represented by historical data. Uncertainty in security returns is addressed by treating them as uncertain variables. Portfolio selection models are developed using the quadratic-entropy of these uncertain variables, with entropy serving as a standard measure of diversification. Additionally, the study underscores the superior risk estimation accuracy of Average Value-at-Risk (AVaR) compared to variance. The research concentrates on the computational challenges of portfolio optimization in uncertain environments, utilizing the Mean-AVaR-Quadratic Entropy paradigm to meet investor requirements and assuage concerns. Two illustrative examples are provided to show the efficiency of the proposed models in this paper.