Journal of Applied Mathematics and Computing最新文献

This paper studies several types of robust control cycles (RCCs) for the Boolean control networks (BCNs) affected by disturbances using semi-tensor product of matrices, and provides their computing methods. First, the cycles of a BCN are classified as strong RCCs and weak RCCs according to their ability to resist disturbances. Secondly, the properties of the states on a cycle for the BCNs are revealed, based on which all the RCCs whose weak connecting degree is not more than one with certain length are obtained. Moreover, the controls to ensure that the state trajectories form RCCs are designed. Finally, some examples are given to demonstrate the effectiveness of the obtained theoretical results, as well as to show the applications of these results.

Malaria, a lethal protozoan disease transmitted through the bites of female Anopheles mosquitoes infected with Plasmodium parasites, remains a significant global health concern. This study introduces a compartmental mathematical model to explore the impact of insecticide use and malaria treatment based on awareness initiatives. The model incorporates the influence of media-based awareness on the effectiveness of insecticide utilization for malaria control. Key mathematical properties, such as positivity, boundedness of solutions, feasibility, and stability of equilibria, are systematically investigated. Our analysis demonstrates that all solutions to the system are positive and bounded within a specified set of initial conditions, establishing the mathematical soundness and epidemiological relevance of the model. The basic reproduction number (R_0) is determined through the next-generation matrix method. Stability analysis reveals that the disease-free equilibrium is globally asymptotically stable when (R_0) is less than one, while it becomes unstable if (R_0) exceeds one. Global stability of the endemic equilibrium is established using an appropriate quadratic Lyapunov function in cases where (R_0) surpasses one. We identify the most sensitive parameters of the model through normalized forward sensitivity indices. In addition, numerical simulations employing the Runge–Kutta method in Python software further validate our findings. Both analytical and numerical results collectively suggest that the integration of awareness-based insecticide usage with malaria treatment holds the potential for malaria elimination. This comprehensive approach not only contributes to the mathematical rigor of the model but also underscores its practical implications for effective malaria control strategies.

Maximum distance separable (MDS) matrices play a crucial role not only in coding theory but also in the design of block ciphers and hash functions. Of particular interest are involutory MDS matrices, which facilitate the use of a single circuit for both encryption and decryption in hardware implementations. In this article, we present several characterizations of involutory MDS matrices of even order. Additionally, we introduce a new matrix form for obtaining all involutory MDS matrices of even order and compare it with other matrix forms available in the literature. We then propose a technique to systematically construct all (4 times 4) involutory MDS matrices over a finite field (mathbb {F}_{2^m}). This method significantly reduces the search space by focusing on involutory MDS class representative matrices, leading to the generation of all such matrices within a substantially smaller set compared to considering all (4 times 4) involutory matrices. Specifically, our approach involves searching for these representative matrices within a set of cardinality ((2^m-1)^5). Through this method, we provide an explicit enumeration of the total number of (4 times 4) involutory MDS matrices over (mathbb {F}_{2^m}) for (m=3,4,ldots ,8).

A single machine scheduling problem takes into account a common due window assignment, including delivery time, resource allocation and learning effect. The basic processing time, position and allotted resources are all linked to the actual processing time. We take into consideration three goal functions, which minimize the costs of earliness, tardiness, start time of window, window size, resource allocation and makespan. The aim is to find the optimal sequence and distribution of resources. Polynomial time algorithms are provided for each of the three issues. The algorithms have (O(n^3)) levels of complexity, where n is the number of jobs. Special cases with the same learning rates are also considered. Polynomial time algorithms are also provided for each of the special cases. The algorithms have (O(ntextrm{log}n)) levels of complexity.

Rapidly developing machine learning methods have stimulated research interest in computationally reconstructing differential equations (DEs) from observational data, providing insight into the underlying mechanistic models. In this paper, we propose a new neural-ODE-based method that spectrally expands the spatial dependence of solutions to learn the spatiotemporal DEs they obey. Our spectral spatiotemporal DE learning method has the advantage of not explicitly relying on spatial discretization (e.g., meshes or grids), thus allowing reconstruction of DEs that may be defined on unbounded spatial domains and that may contain long-ranged, nonlocal spatial interactions. By combining spectral methods with the neural ODE framework, our proposed spectral DE method addresses the inverse-type problem of reconstructing spatiotemporal equations in unbounded domains. Even for bounded domain problems, our spectral approach is as accurate as some of the latest machine learning approaches for learning or numerically solving partial differential equations (PDEs). By developing a spectral framework for reconstructing both PDEs and partial integro-differential equations (PIDEs), we extend dynamical reconstruction approaches to a wider range of problems, including those in unbounded domains.

This work emphasizes the computational and analytical analysis of integral-differential equations, with a particular application in modeling avoidance learning processes. Firstly, we suggest an approach to determine a unique solution to the given model by employing methods from functional analysis and fixed-point theory. We obtain numerical solutions using the approach of Picard iteration and evaluate their stability in the context of minor perturbations. In addition, we explore the practical application of these techniques by providing two examples that highlight the thorough analysis of behavioral responses using numerical approximations. In the end, we examine the efficacy of our suggested ordinary differential equations (ODEs) for studying the avoidance learning behavior of animals. Furthermore, we investigate the convergence and error analysis of the proposed ODEs using multiple numerical techniques. This integration of theoretical and practical analysis enhances the domain of applied mathematics by providing important insights for behavioral science research.

The resolvability parameter is an essential component, especially in the context of network research, due to its theoretical and practical significance. Its importance is evident in several applications and outcomes, including social network analysis, network security, facility location and site selection, and effective routing. We introduce a novel resolvability parameter, Fault-Tolerant Mixed Metric Dimension, in this paper, and this defined as let (R_{m,f}) be a set that nodes on a graph as both an edge-resolving set and a resolving set. If (R_{m,f}) can uniquely represent the graph’s edges and vertices, then it is referred to as a mixed resolving set, and its all subsets cardinality is called the mixed metric dimension. If all of the graph’s vertices and edges are uniquely represented by (R_{m,f}^{prime },) and all subsets of (R_{m,f}^{prime }) with of cardinality one less than (R_{m,f}) likewise have unique representations for all of the graph’s vertices and edges, then (R_{m,f}) is referred to as a Fault-Tolerant Mixed Resolving Set, and If two such sets (R_{m,f}^{1}) and (R_{m,f}^{2}) exist such that (R_{m,f}^{1}cap R_{m,f}^{2}ne 0) then we say that the graph has exchange property. (R_{m,f})’s minimum cardinality is known as its fault-tolerant mixed Metric Dimension. These definitions offer a means of measuring a collection of vertices’ capacity to represent graph structures uniquely, taking fault-tolerant and resolution into account. Furthermore, a problem related to the lab’s system network is also discussed and linked with this topic in this work. Like a lab engineer is embarking on the creation of a new circular lab, intending to establish where and how many devices within it to supply internet with wire to all systems. A solution to this problem is proving this novel topic authenticity.

The article studies fixed/preassigned-time synchronization in a fuzzy inertial neural network characterized by discontinuous activation functions and mixed delays. First, we adopt a more accurate method to calculate the settling-time. Then, we extend the result of fixed-time synchronization (FXS) to preassigned-time synchronization (PAS). Next, by designing event-triggered controller and applying the non-smooth theory, the stability criterion of FXS/PAS are obtained. Finally, in the simulation section, we illustrate the validity and practicability of the results by listing a specific example.

In the context of hyperbolic spaces, our study presents a novel iterative approach for approximating common fixed points satisfying general contractive condition involving a pair of mappings with weak compatibility. Also, we notice that our iterative procedure approximates to a point of coincidence if the weak compatibility condition is violated. We provide theorems to demonstrate the (Delta -)convergence, stability, and efficiency of this iteration process. Additionally, we provided some immediate corollaries that involve mappings with contractive condition, instead of general contractive condition. Furthermore, we demonstrate with examples and graphs that our iteration process is faster than all previous procedures, including those of Jungck-SP, Jungck-CR, and Jungck-DK, utilizing MATLAB software. Also, we compare the impact of the initial values and the parameters on the convergence behavior of the proposed iterative process with existing iterative schemes using an example. Finally, we focus on using our iterative technique to approximate the solution of a non-linear integral equation with two delays.

This paper exploits the good features of the Dai-Liao (DL) conjugate gradient (CG) method in connection with the inertial interpolation and the projection technique to propose an efficient algorithm for solving the convex-constrained monotone system by avoiding the direction of maximum magnification (MM). It is well-known that if the gradient lies in the direction of MM by the search direction matrix, the algorithm may result in unnecessary computational errors and may likely not be convergent. Avoiding this direction will accelerate the convergence of the proposed algorithm theoretically and numerically. The proposed DL algorithm avoids the direction of MM and uses the inertial extrapolation and hyperplane projection steps to accelerate its convergence at every given iteration. The theoretical analysis proved that the proposed algorithm is globally convergent under some standard assumptions and has a linear convergence rate. Lastly, the numerical experiment on some test problems demonstrated that the algorithm is time-efficient and has less computational cost.