A cubic graph which has only hexagonal faces, and can be embedded into a torus is known as generalized honeycomb torus or honeycomb toroidal graph, abbreviated as nanotorus. This graph is determined by three parameters a,b, and c, and denoted by Ga,b,c. B. Alpspach in 2010 dedicated a survey paper to nanotori, wherein a number of open problems are suggested. In this article we deal with one of the

A multiple leaf-distance granular regular α-tree (abbreviated as LDR α-tree for short) is a tree (with at least α+1 vertices) where any two leaves are at some distance divisible by α. A connected graph's subtree which is additionally an LDR α-tree is known as an LDR α-subtree. Obviously, α=1 and 2, correspond to the general subtrees (excluding the single vertex subtrees) and the BC-subtrees (the distance

In this paper, we proposed three nonparametric kernel estimators for the overlapping Weitzman measure Δ. Due to the difficulty of finding a general expression for Δ when the nonparametric kernel method is adopted, we suggest using the numerical integration method as the first stage of our estimation process. In particular, three numerical integration rules are considered, which are known as, trapezoidal

Let D be a digraph with vertex set V(D) and arc set A(D). An antidirected spanning closed trail of D is a spanning closed trail in which consecutive arcs have opposite directions and each arc of D occurs at most once. If all vertices in this antidirected spanning closed trail are distinct, then the antidirected spanning closed trail is called an antidirected hamiltonian cycle. Grünbaum in 1971 conjectured

We deal with the problem of constructing, representing, and manipulating C3 quartic splines on a given arbitrary triangulation T, where every triangle of T is equipped with the quartic Wang–Shi macro-structure. The resulting C3 quartic spline space has a stable dimension and any function in the space can be locally built via Hermite interpolation on each of the macro-triangles separately, without any

A chaotic map plays a critical role in image encryption (IME). The map used to generate chaotic sequences should perform high dynamic characteristics. In this study, a new chaotic system depending on the Bessel function, so-called Bessel map, and a novel Bessel map-based IME scheme are proposed for the IME. The Bessel map has three control parameters, which provide superior ergodicity and diversity

In this paper, the output feedback H∞ control is investigated for the networked singularly perturbed systems (SPSs) with Markov lossy network, in which the packet loss probability varies in different modes. A new network mode-dependent round-robin-like protocol (RRLP) is introduced to the networked SPSs, which can dynamically adjust the number of the selected sensor nodes according to the network environment

In this article, the cooperative fault-tolerant tracking control (FTTC) is investigated for discrete-time multi-agent systems (MASs) with time-varying delays (TVDs) under multiple description encoding schemes (MDESs). First, a uniform channel model is proposed to describe the employed MDES subject to the effect of packet dropouts by introducing two independent random variables obeying the Bernoulli

In this paper, for variable coefficient Riesz fractional diffusion equations in one and two dimensions, we first design a second-order implicit difference scheme by using the Crank-Nicolson method and a fractional centered difference formula for time and space variables, respectively. With the compact operator acting on, a novel fourth-order finite difference scheme is subsequently constructed. Solvability

Climate change causing large seasonal fluctuations is likely to lead to an increase in the average threshold of the Allee effect as well as an increase in its seasonal variability. In this paper, we show that a seasonally synchronized predator-prey system can be strongly destabilized by these changes in the threshold of the Allee effect. The typical result first leads to two-year and multiyear cycles

Identifying the most influential individuals in structured populations is an important research topic throughout network science. Previous studies, whether identifying the initial cooperators in a network that can lead to the spread of cooperation or assessing the chances that an intrusive defector may lead to the collapse of cooperation, have assumed that all individual attributes are homogeneous

The Iterative Filtering method is a technique aimed at the decomposition of non-stationary and non-linear signals into simple oscillatory components. This method, proposed a decade ago as an alternative technique to the Empirical Mode Decomposition, has been used extensively in many applied fields of research and studied, from a mathematical point of view, in several papers published in the last few

In this paper, a weak Galerkin (WG) finite element method for one-dimensional nonlinear convection-diffusion equation with Dirichlet boundary condition is developed. Based on a special variational form featuring two built-in parameters, the semi-discrete and fully discrete WG finite element schemes are proposed. The backward Euler method is utilized for time discretization. The WG finite element method

For a graph, its path-index is the greatest eigenvalue of its path-matrix, whose (x,y)-entry for vertices x and y equals the connectivity of x and y if x≠y and 0 otherwise. Some upper and lower bounds are established on the path-index over graphs with prescribed parameters, and those graphs that attain the bounds are also identified.

In this manuscript, we present an innovative discretization algorithm designed to address the challenges posed by the three-dimensional (3D) Bratu problem, a well-known problem characterized by non-unique solutions. Our algorithm aims to achieve exceptional precision and accuracy in determining all potential solutions, as previous studies in the literature have only managed to produce limited accurate

We propose a numerical scheme for approximating the solution of the two dimensional acoustic wave problem. We use machine learning to find a stencil suitable even for high wavenumbers. The proposed scheme incorporates physics informed elements from the field of dispersion-relation-preserving (DRP) schemes into a convolutional optimization machine learning algorithm. We test the proposed method and

With the development of the Internet, the influence of rumors is more widespread. Studying the propagation law of rumors is an effective way to reduce the damage of rumors. We therefore propose a new two-layer rumor propagation model, which simultaneously introduces simplicial complexes into the online and offline network layers and considers the social adaptation of individuals. We derive the basic

We use P5 to denote a path of length 5 and C5 to denote a cycle of length 5. The aim of this paper is to prove that, if G is a connected graph satisfying (1). G has an induced C5 and no clique cut-set, (2). G has no induced subgraph isomorphic to P5 or K5−e, then G is max⁡{13,ω(G)+1}-colorable.

The output regulation problem has been studied based on a parameterization approach. Different from existing literature, the proposed method does not rely on prior knowledge of the system dynamics. Instead, it leverages state and input data to address the absence of information regarding unmodeled dynamics. Firstly, the output regulation problem is transformed into a stabilization problem by using

We propose a new numerical scheme for the game p-Laplacian, based on a semi-Lagrangian approximation. We focus on the 2D version of the game p-Laplacian, with the aim to apply the new scheme in the context of image processing. Specifically, we want to solve the so-called inpainting problem, which consists in reconstructing one or more missing parts of an image using information taken from the known

This article presents a mathematical model and a controller for a convertible fixed-wing Vertical Take-Off and Landing (VTOL). The mathematical model considers the aerodynamic forces generated by the motors. The developed Passivity-Based Control (PBC) law stabilizes the rotational and translational dynamics of a convertible Unmanned Aerial Vehicle (UAV) in the transition stages of cruise-stationary

Various techniques of integral inequality are widely used to establish the delay-dependent conditions for the dynamics of differential systems so that the conservatism of conditions can be reduced. In the integer-order systems, the integral term of ∫τωp˙T(s)Sp˙(s)ds often appears in the derivative of Lyapunov−Krasovskii functional, and how to scale down this term to obtain less conservative condition

Uncertain discrete-time noncausal systems are uncertain singular systems that are supposed to be regular along. This study examines optimal control problems (OCPs) using the optimistic value criterion in the context of uncertain discrete-time noncausal systems. Recurrence equations for tackling these OCPs are provided in terms of uncertainty theory. These equations have effectively addressed OCPs involving

This paper researches the stability issue of generalized neural networks (GNN) with time-varying delay. For the delay, its derivative has an upper bound or is unknown. Firstly, the augmented Lyapunov-Krasovskii functional (LKF) is constructed based on the state vectors of the third order integral inequalities. Then, by introducing two sets of state vectors, the LKF derivative is presented as the quadratic

This article presents the problem of distributed training with a decentralized execution policy as a safe, optimal formation control for a heterogeneous nonlinear multi-agent system. The control objective is to guarantee safety while achieving optimal performance. This objective is achieved by introducing novel distributed optimization problems with cost and local control barrier functions (CBFs).

In this paper, we determine the maximum size of a graph of fixed order without isolated vertices which contains (fractional) matching of given size, which is a variation of some known results involving the maximum size of all graphs of fixed order containing matching of given size by Erdős and Gallai. As corollaries of our results, Turán-type results for a connected graph on (fractional) matching are

The asymptotic stability and long time decay rates of solutions to linear Caputo time-fractional ordinary differential equations are known to be completely determined by the eigenvalues of the coefficient matrices. Very different from the exponential decay of solutions to classical ordinary differential equations, solutions of time-fractional ordinary differential equations decay only polynomially

By means of a complex representation of a commutative quaternion matrix, the singular value decomposition and the generalized inverse problems of a commutative quaternion matrix are studied, and the corresponding theorems and algorithms are given. In addition, based on the singular value decomposition and generalized inverse of a commutative quaternion matrix, the numerical experiments for solving

In the real world, a single homogeneous or heterogeneous network is very rare, so we consider a compound model which contains two different types of subnetworks. The compound model may be applied to analyze the contagion dynamics of two different communities where they have a probability to communicate. The global infection threshold is obtained, and many factors affecting spread of epidemics are analyzed

This paper takes into consideration the H∞ filtering problem based on L2-gain analyses for switched descriptor systems. To start with, the state jumps that have been ignored for the existing results in the literature are precisely characterized for the filtering error system at the switching moments utilizing a mode-dependent coordinates transformation for the first time. Next, by utilizing multiple

The theory of inverse location involves modifying parameters in such a way that the total cost is minimized and one/several prespecified facilities become optimal based on these perturbed parameters. When the modifying parameters are grouped into sets, with each group's cost measured under the rectilinear norm and the overall cost measured under the Chebyshev norm, the resulting problem is known as

To improve mathematical models of epidemics it is essential to move beyond the traditional assumption of homogeneous well–mixed population and involve more precise information on the network of contacts and transport links by which a stochastic process of the epidemics spreads. In general, the number of states of the network grows exponentially with its size, and a master equation description suffers

Splines over triangulations and splines over quadrangulations (tensor product splines) are two common ways to extend bivariate polynomials to splines. However, combination of both approaches leads to splines defined over mixed triangle and quadrilateral meshes using the isogeometric approach. Mixed meshes are especially useful for representing complicated geometries obtained e.g. from trimming. As

We propose two conservative fourth-order compact finite difference (CFD4C) schemes and give the rigorous error analysis for the Klein-Gordon-Zakharov system (KGZS) with ε∈(0,1] being a small parameter. In the case 0<ε≪1, i.e., the subsonic limit regime, the solution of KGZS propagates waves with wavelength O(ε) in time and O(1) in space, respectively, with amplitude at O(εα†) with α†=min⁡{α,β+1,2}

Let i be a positive integer. A complete bipartite graph K1,i is called an i-star, denoted by Si. An {S2,S3}-packing of a graph G is a collection of vertex-disjoint subgraphs of G in which each subgraph is a 2-star or a 3-star. The maximum {S2,S3}-packing problem is to find an {S2,S3}-packing of a given graph containing the maximum number of vertices. The perfect {S2,S3}-packing problem is to answer

In this work we present a new construction of basis functions that generate the space of geometrically smooth splines on an unstructured quadrilateral mesh. The basis is represented in terms of biquintic Bézier polynomials on each quadrilateral face. The gluing along the face boundaries is achieved using quadratic gluing data functions, leading to globally G1–smooth spaces. We analyze the latter space

With the development of urban architecture, the growing demand for larger public buildings is becoming challenging for indoor human evacuation under emergencies such as fires. However, the indoor fire evacuation behaviour of heterogeneous crowds when including individuals with disabilities have not been adequately explained. Therefore, this paper aims to study indoor evacuation characteristics of a

As a typical class of Cyber-Physical Systems (CPSs), microgrids (MGs) are susceptible to malicious cyber attacks and disturbances that can compromise their security and reliability. To address this issue, an event-triggered distributed resilient control method is proposed in this paper to mitigate the impacts of disturbances, FDI and DoS attacks on MGs. The proposed approach employs a piecewise control

In this paper, we present the method of integral transforms and the Gauss-Chebyshev quadrature methods to solve the problem of a crack parallel to a fixed boundary under remote tension. We derive a system of singular integral equations of the first kind, specific to the problem at hand, which we numerically solve using Gauss-Chebyshev integration. We specialize our results to the problem of a crack

A geodesic packing of a graph G is a set of vertex-disjoint maximal geodesics. The maximum cardinality of a geodesic packing is the geodesic packing number gpack(G). It is proved that the decision version of the geodesic packing number is NP-complete. We also consider the geodesic transversal number, gt(G), which is the minimum cardinality of a set of vertices that hit all maximal geodesics in G. While

This paper investigates the problem of adaptive event-triggered filtering for a class of semi-Markov jump systems. A more general scenario of semi-Markov jump systems under communication constraints is explored, where the output signal occurs with saturation nonlinearity, packet loss, and quantization. The saturation nonlinearity and packet dropout are described by two random variables subject to Bernoulli

As a measure of vertex importance according to the graph structure, PageRank has been widely applied in various fields. While many PageRank algorithms have been proposed in the past decades, few of them take into account whether the graph under investigation is directed or not. Thus, some important properties of undirected graph—symmetry on edges, for example—is ignored. In this paper, we propose a

In the framework of partial unknown states, this paper studies the exponential stability problem of nonlinear systems. A novel event-triggered mechanism (ETM) just involving partial known states is designed to guarantee the exponential stability of considered system, where forced impulse with great freedom degree is introduced in ETM. What's more, the information of known states of the system is fetched

Serendipity elements are a class of simplified forms of the double-k element in 2D or the triple-k element in 3D. The main advantage is that serendipity elements can maintain a proper order of convergence of the interpolation error under the condition of regularity, while reducing the number of inner freedoms. In practice, it is necessary to analyze their interpolation error on anisotropic meshes.

Globalization has led to increasingly interconnected interactions among individuals. Their payoffs are affected by the investment decision of themselves and their neighbors, which will cause conflicting interests between individual and social investment. Such problems can be modeled as a networked public goods game (NPGG). In this paper, we study the Best-shot NPGG model by introducing three mechanisms:

For many application problems that are modeled by partial differential equations (PDEs), not only it is important to obtain accurate approximations to the solutions, but also accurate approximations to the derivatives of the solutions. In this study, some new high order compact (HOC) finite difference schemes are derived to approximate the first and second derivatives of the solution to some elliptic

Weakly delayed planar linear discrete systems with multiple delaysx(k+1)=Dx(k)+∑l=1nHlx(k−ml),k=0,1,… are considered where m1,m2,…,mn are fixed integers, D, H1, …, Hn are nonzero 2×2 real constant matrices and x:{−mn,−mn+1,…}→R2. Formulas for general solutions are found and simplified, equivalent non-delayed planar linear discrete systems are constructed and conditional stability is analyzed. Results

In this paper, we present an efficient and stable fractional-step 2D immersed boundary (IB) method for solving the interaction problems between bulk fluid and elastic interface, in particular, when the fluid inertia and the interfacial elasticity are the significant factors affecting its dynamics. In myriads of real-world applications, the effects of high inertia and elasticity are dominant. So the

We investigate the Laplacian eigenvalues about unit graph G(Zn) on Zn and show the case whenever n is an even number or an odd prime power, G(Zn) would be Laplacian integral. We also prove that if n>1, then the Laplacian spectral radius of G(Zn) is equal cardinal number of V(G(Zn)) if and only if n=pk, here p is a prime integer, k is an integer that positive. In addition, this paper also characterizes

Let G and H be two graphs. The maximum integer k, for which there exists an edge coloring ϕ:E(G)→{1,2,…,k} that makes every copy of H has at least two edges with the same color, is the anti-Ramsey number of G with respect to H. Mycielski developed an interesting graph transformation that transforms G into the Mycielskian μ(G) of G. In this paper, we determine the anti-Ramsey number of μ(Cn) with respect

In multiple applications, from Statistics to Particle Physics and notably in Cryptography and Computer Security, it is necessary to obtain long sequences of random numbers. In order to verify the properties of these sequences, different statistical tests are commonly applied, which are usually included in the so-called test batteries or test suites. The batteries need to be both effective and efficient

The n-dimensional HSDC with the logic graph Hn is one of the most attractive server-centric data center networks for high incremental scalability. The routing design in network topology is very important for information transmission. In particular, the application of disjoint path covers can solve various problems such as program code optimization and mapping parallel programs to parallel structures

Let G be a maximal planar graph with diameter two and maximum degree Δ. Let χ(G2) denote the chromatic number of the square of G. In this paper, we prove that χ(G2)=Δ+1 if 2≤Δ≤3; χ(G2)≤6 if Δ=4; χ(G2)≤9 if Δ=5; χ(G2)≤Δ+5 if 6≤Δ≤7; and χ(G2)≤⌊3Δ/2⌋+1 if Δ≥8. All bounds are tight. This confirms the Wegner's conjecture for maximal planar graphs with diameter two.

In this paper, we present a Markov chain model to study infectious disease outbreaks assuming that healthcare facilities, specifically the number of hospital beds for infected individuals, are limited. Therefore, only a restricted number of infected individuals can be admitted to a hospital ward and receive medical care at the same time. Since the pathogen spreads both inside and outside the ward,

The distributed task allocation problem, as one of the most interesting distributed optimization challenges, has received considerable research attention recently. Previous works mainly focused on the task allocation problem in a population of individuals, where there are no constraints for affording task amounts. The latter condition, however, cannot always be hold. In this paper, we study the task

NP problems act essential roles in modelling and analysing various complex systems, and representation learning of system individuals and relations has faced the kernel difficulty in understanding the complexity and solving the NP problems. In this paper, solution space organisation of minimum vertex-cover problem is deeply investigated using the famous König-Egérvary (KE) graph and theorem, in which

The problem of distributed filtering for a class of discrete-time nonlinear complex networks subject to the network bandwidth limitation is investigated. In order to reduce the network transmission burden, the round-robin protocol is employed. Under which, a quantization-based encoding-decoding mechanism is introduced to protect the security of measurements. Taking into account the quality of transmission

While Hopfield networks are known as paradigmatic models for memory storage and retrieval, modern artificial intelligence systems mainly stand on the machine learning paradigm. We show that it is possible to formulate a teacher-student self-supervised learning problem with Boltzmann machines in terms of a suitable generalization of the Hopfield model with structured patterns, where the spin variables

In this paper, we develop a prisoner's dilemma game model with three types of strategies and six types of emotions. We propose a direct emotional interaction mechanism considering memory effect in which a player's favorability serves as an index of emotions and directly impacts payoffs and emotions. Our model enables that individuals gradually increase the tendency to loneliness or defection in the

This paper presents an adaptive event-triggered control method for linear systems subject to input saturation. At the first, using convex hull properties, an observer-based controller is designed and then a generalized event-triggering mechanism is regarded. In order to extend more time interval between any two successive events, an adaptive event-triggered control method is also proposed. The proposed