This study is devoted to the inverse spectral problems of the Sturm-Liouville operator with many frozen arguments. Under certain assumptions, the authors obtained the uniqueness theorems for recovering the operator from one spectrum. Finally, a numerical simulation of the inverse problem is given.

An important theorem about the spectral Turán problem of Ka,b was largely developed in separate papers. Recently it was completely resolved by Zhai and Lin [J. Comb. Theory, Ser. B 157 (2022) 184-215], which also confirms a conjecture proposed by Tait [J. Comb. Theory, Ser. A 166 (2019) 42-58]. Here, the prior work is fully stated, and then generalized with a self-contained proof. The more complete

The main contribution of this manuscript is to introduce to the scientific community the concept of maximally efficient damped composed Newton-type method and the design of two schemes of this class of orders four and six. It is obtained from a different and new extension of the vectorial optimal fourth-order Ermakov's Hyperfamily, in the sense of Cordero-Torregrosa conjecture. We call this class biparametric

In this paper we prove some Lp-type Heisenberg-Pauli-Weyl uncertainty principles for complex signals with respect to fractional Fourier transform, 1≤p≤2. We also discuss the effect of shifting and scaling on the uncertainty principles. Moreover, some numerical simulations are given to demonstrate our results.

In this paper, we introduce a high-precision Hermite neural network solver which employs Hermite interpolation technique to construct high-order explicit approximation schemes for fractional derivatives. By automatically satisfying the initial conditions, the construction process of the objective function is simplified, thereby reducing the complexity of the solution. Our neural networks are trained

In this paper, we focus on numerical approximations of Piecewise Diffusion Markov Processes (PDifMPs), particularly when the explicit flow maps are unavailable. Our approach is based on the thinning method for modelling the jump mechanism and combines the Euler-Maruyama scheme to approximate the underlying flow dynamics. For the proposed approximation schemes, we study both the mean-square and weak

In this paper, an online policy iteration algorithm is adopted to solve the linear quadratic tracking control problem for a class of partially unknown Markov jump singular interconnected systems. Firstly, due to the singular systems consisting of dynamic parts and static parts, Markov jump singular interconnected systems can be described as regular systems composed of dynamic parts by utilizing a linear

Matrix completion is a challenging problem in computer vision. Recently, quaternion representations of color images have achieved competitive performance in many fields. The information on the coupling between the three channels of the color image is better utilized since the color image is treated as a whole. Due to this, researcher interest in low-rank quaternion matrix completion (LRQMC) algorithms

Let G be a graph and X⊆V(G). Then, vertices x and y of G are X-visible if there exists a shortest x,y-path where no internal vertices belong to X. The set X is a mutual-visibility set of G if every two vertices of X are X-visible, while X is a total mutual-visibility set if any two vertices from V(G) are X-visible. The cardinality of a largest mutual-visibility set (resp. total mutual-visibility set)

Recognizing the threshold dynamics of highly developed animals with memory is significant for the governance of species within a specific domain. To investigate how the memory threshold affects population behavior, we formulate a spatially heterogeneous predator-prey system with memory-based diffusion and hunting cooperation on predators. In homogeneous environments, the occurrence conditions of Turing

Strategy update rules play an important role in repeated Prisoner's Dilemma games. This work proposes a modified strategy update rule based on the traditional Fermi function, in which individual past performance is taken into account in strategy update. Then, the consistency aspiration α serves as a benchmark to measure an individual's past performance, and the past performance score is dynamically

This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special cases. Therefore, the proposed method serves as a general framework that includes not only the classical and cubic RNMs but also a novel RNM with elastic net regularization

Let G be a graph and M⊆V(G). Vertices x,y∈M are M-visible if there exists a shortest x,y-path of G that does not pass through any vertex of M∖{x,y}. We say that M is a mutual-visibility set if each pair of vertices of M is M-visible, while the size of any largest mutual-visibility set of G is the mutual-visibility number of G. If some additional combinations for pairs of vertices x,y are required to

In the ecosystem, the chase of the predator with cooperation contributes to fear psychology in the prey, resulting in behavioral changes such as a decrease in the birth rate. We construct a spatially diffusive model with delay to investigate the combined perturbation of these factors. Initially, we establish the existence of positive solutions and examine the stability of steady-state solutions under

Understanding human responses to epidemic outbreaks—particularly to control measures such as vaccination—is essential for accurately modeling the complex interplay between epidemics and human behavior. Through the framework of evolutionary vaccination games, we explore how individuals' opinions influence vaccine uptake attitudes under imperfect vaccination and, in turn, how this affects to the spread

In the era of rapid development of the Internet, in order to reflect the evolution process of users' viewpoints on network relations, a Bayesian viewpoint evolution model based on Weibo data mining is proposed by studying the relationship between the viewpoints of the author and those of the forwarders on the Sina Weibo platform. Firstly, Python crawler technology was used to crawl the comments and

This paper introduces a proximal bundle scheme to solve generalized variational inequalities with inexact data. Under optimality conditions, the problem can be equivalently represented as seeking out the zero point of the sum of two multi-valued operators whose domains are the real Hilbert space. The two operators denoted by T and f, respectively, are the monotone operator and the subdifferential of

The article proposes a dynamic event-triggered adaptive predefined time output feedback control technique for uncertain switching multi-input multi-output (MIMO) nonlinear systems with strict feedback forms. In contrast to previous event-triggered output feedback control, the control technique proposed in this study not only enables the system to reach steady state within a predefined time, but also

In this paper, we consider the utility maximization problem of an agent regarding optimal consumption-investment, job-switching strategy, and the optimal early retirement date. The agent can switch between two jobs or job categories at any time before retirement, but incurs a cost when switching to a position offering higher labor income. The agent's utility maximization involves a combination of stochastic

In this paper we investigate the calculation and analysis for a class of the highly oscillatory generalized Bessel transform with endpoint singularities of algebraic type. First, when the oscillator has either zeros or stationary points, we give many asymptotic expansions for the transform. On the basis of these results, we construct a new and good modified Filon-type method. Moreover, based on the

This paper proposes a heterogeneous traffic model based on the intelligent driver model (IDM), which is composed of connected autonomous vehicles (CAVs) and human-driven vehicles (HDVs). Since these CAVs are equipped with V2V (Vehicle-to-vehicle communications), we consider the velocity and acceleration of multi-vehicle ahead under the communication area to describe the following behavior of CAVs.

This article is concerned with the predictor-based event-triggered learning control of networked control systems (NCSs) with false data injection attacks (FDIAs) and output delay. Firstly, by applying the prediction method, a new state observer including an output predictor is employed to get the estimation of delayed sampled-data output in the context of sampling. To improve the efficiency of limited

In the context of method of approximate particular solutions (MAPS), we propose a novel meshless computational scheme based on hybrid radial basis function (RBF)-polynomial bases to solve both parabolic and hyperbolic partial differential equations over a large terminal time interval on irregular spatial domain. By using space–time approach, the original time-dependent problem is firstly reformulated

This paper investigates a collective defined contribution (CDC) pension fund scheme in continuous time, where members' contributions are fixed in advance, and benefit payments depend on the final salary rate. We take account of the co-integration between labor income and the stock market by letting the difference between logs of labor and dividends follow a mean-reverting process. Further, labor income

Ecological compensation plays an important role in the governance of renewable resource. When the resource stock is not higher than the compensation threshold, the defector of excessive effort pays compensation cost to restore resources. This paper establishes a coupled social ecosystem based on the ecological compensation mechanism by using evolutionary game theory. It is found that ecological compensation

The kernel polynomial method based on Jacobi polynomials Pn(α,β)(x) is proposed. The optimal-resolution positivity-preserving kernels and the corresponding damping factors are calculated. The results provide a generalization of the Jackson damping factors for arbitrary Jacobi polynomials. For α=±1/2, β=±1/2 (Chebyshev polynomials of the first to fourth kinds), explicit trigonometric expressions for

This paper proposes a verification method for sparse linear systems Ax=b with general and nonsingular coefficient matrices. A verification method produces the error bound for a given approximate solution. Practical methods use one of two approaches. One approach is to verify the computed solution of the normal equation ATAx=ATb by exploiting symmetric and positive definiteness; however, the condition

This paper is addressed to the study of a novel impulsive fractional differential hemivariational inclusions (IFDHI) with a nonlocal condition, comprising an impulsive fractional differential inclusion (IFDI) with a nonlocal condition and a hemivariational inequality (HVI), within separable reflexive Banach spaces. Initially, we establish the unique solvability of the HVI by adopting the surjectivity

For a non-decreasing sequence S=(s1,s2,…) of positive integers, a partition of the vertex set of a graph G into subsets X1,…,Xℓ, such that vertices in Xi are pairwise at distance greater than si for every i∈{1,…,ℓ}, is called an S-packing ℓ-coloring of G. The minimum ℓ for which G admits an S-packing ℓ-coloring is called the S-packing chromatic number of G. In this paper, we consider S-packing colorings

This article addresses the issue of global asymptotic stabilization (GAS) for a group of linearly uncontrollable and unobservable time-delayed systems with uncertain control gains. As a result of the use of a nonsingular transformation and time rescaling, the group of nonlinear integrators with large delays are transformed into nonlinear integrators with small delays. Then, after applying both the

In this paper, we introduce the top predator into the Filippov pest-natural enemy system, and propose a three-dimensional Filippov food chain model to address the impact of integrated pest management (IPM) strategies on the sliding dynamics and pest control as well as food chain ecosystems. In particular, the proposed model exists multiple pseudo-equilibria in the sliding region, which result in rich

This paper proposes an adaptive distributed event-triggered secure consensus control scheme for achieving fully distributed self-triggered secure consensus control of nonlinear multiagent systems with sequential communication link scaling attacks. Firstly, attacks on the communication link for nonlinear multiagent systems are modeled by sequential communication link scaling attacks, which include communication

This paper presents a sparse optimization method for the simultaneous orthogonal tensor diagonalization. The model treats off-diagonal elements of tensors as entities requiring sparsity, guided by an ℓ1 norm regularizer to optimize the diagonalization process. A gradient-based alternating multi-block Jacobi-AMB algorithm is developed to address the optimization problem on the product of orthogonal

The search for a highly discriminating and easily computable invariant to distinguish graphs remains a challenging research topic. Here we focus on cospectral graphs whose complements are also cospectral (generalized cospectral), and on coinvariant graphs (same Smith normal form) whose complements are also coinvariant (generalized coinvariant). We show a new characterization of generalized cospectral

A graph G is 2-edge Hamiltonian connected if for any edge set E⊆{uv:u,v∈V(G),u≠v} with |E|≤2, G∪E has a Hamiltonian cycle containing all edges of E, where G∪E is the graph obtained from G by including all edges of E. The problem of determining whether a graph is 2-edge Hamiltonian connected is challenging, as it is known to be NP-complete. This property is stronger than Hamiltonian connectedness, which

The present work deals with the problem of prescribed-time control of non-linear impulsive systems consisting of external perturbations. Lyapunov-like sufficient conditions for prescribed-time and practical prescribed-time stability are provided for vanishing and non-vanishing perturbations, respectively. Depending on the user's requirements, some sequences of stabilizing impulses are constructed in

Gamma-positivity is one of the basic properties that may be possessed by polynomials with symmetric coefficients, which directly implies that they are unimodal. It originates from the study of Eulerian polynomials by Foata and Schützenberger. Then, the alternatingly gamma-positivity for symmetric polynomials was defined by Sagan and Tirrell. Later, Ma et al. further introduced the notions of bi-gamma-positive

This paper aims to design the fully distributed event-triggered secondary voltage resilient tracking control strategy for microgrids subject to denial-of-service (DoS) attacks. The fully distributed method is employed to remove the requirement of the smallest nonzero eigenvalue of the Laplacian matrix, which is the global information. In addition, an attack compensation with the latest successful transmission

In this paper, we propose a new class of second-order one-step time-splitting schemes for scalar and systems of conservation laws. The strategy is based on a relaxation approximation which consists in introducing a relaxation system with linearly degenerate characteristic fields to approximate the original system and deal with its nonlinearities. The numerical schemes are based on the use of arbitrarily

As a generalization of strongly regular graphs, van Dam and Omidi [8] introduced the concept of strongly walk-regular graphs. A graph is called strongly ℓ-walk-regular if the number of walks of length ℓ from a vertex to another vertex depends only on whether the two vertices are adjacent, not adjacent, or identical. They proved that this class of graphs falls into several subclasses including connected

The incidence Q-spectral radius of a k-uniform hypergraph G with n vertices and m edges is defined as the spectral radius of the incidence Q-tensor Q⁎:=RIRT, where R is the incidence matrix of G, and I is an order k dimension m identity tensor. Since the (i1,i2,…,ik)-entry of Q⁎ is involved in the number of edges in G containing vertices i1,i2,…,ik simultaneously, more structural properties of G from

The total σ-irregularity is given by σt(G)=∑{u,v}⊆V(G)(dG(u)−dG(v))2, where dG(z) indicates the degree of a vertex z within the graph G. It is known that the graphs maximizing σt-irregularity are split graphs with only a few distinct degrees. Since one might typically expect that graphs with as many distinct degrees as possible achieve maximum irregularity measures, we modify this invariant to σtf(n)(G)=∑{u

This work aims to solve a fuzzy initial value problem for fractional difference equations and to study a class of discrete fractional cobweb models with fuzzy data under the Caputo granular difference operator. Based on relative-distance-measure fuzzy interval arithmetic, we first present several new concepts for fuzzy functions in the field of fuzzy discrete fractional calculus, such as the forward

This research note establishes a specific framework for transforming nonlinear multi-input and multi-output diffeomorphism systems into extended observable normal forms without using differential geometry techniques. For this purpose, the nonlinear MIMO systems whose nonlinear terms do not need to be Lipschitz, are proposed. First, a change of coordinates is designed to eliminate the square items and

In this study, a novel reproducing kernel Hilbert space (RKHS) method is introduced to show that high-order linear Fredholm integro-differential equations (IDEs) with variable coefficients can be transformed into ordinary differential equation (ODEs). The RKHS method constructs multiple types of RKHSs related to the given terms based on the H-HK formulation, which are utilized to determine solutions

The interconnection network between the storage system and the multi-core computing system is the bridge for communication of enormous amounts of data access and storage, which is the critical factor in affecting the performance of high-performance computing systems. By enforcing additional restrictions on the definition of R-structure and R-substructure connectivities to satisfy that each remaining

An event-triggered formation control strategy is proposed for a multi-agent system (MAS) suffered from unknown disturbances. In identifier-critic-actor neural networks (NNs), the strategy only needs to calculate the negative gradient of an approximated Hamilton-Jacobi-Bellman (HJB) equation, instead of the gradient descent method associated with Bellman residual errors. This simplified method removes

The evolution of cooperation is a pivotal area of study, essential for understanding the survival and success of complex biological and social systems. This paper investigates the dynamics of cooperation in spatial public goods games (SPGG) through a model that incorporates a fairness-driven migration mechanism. In this model, agents move towards environments perceived as fairer, influencing the spatial

Among unrelated individuals, the emergence and maintenance of trust has always been a pressing issue to address, one that has garnered considerable attention through the framework provided by trust games. However, few studies have considered the effects of time delay in trust games. Given that decision-makers in trust games inherently exhibit lagged responses when observing the market, we explore the

The Müntz polynomials are defined by contour integral associated to a complex sequence Λ={λ0,λ1,λ2,⋯}, which are large extensions of the algebraic polynomials. In this paper, we derive new recurrence formulas for Müntz polynomials, aimed at facilitating the computation of these polynomials and their related integrals. Additionally, we construct a novel class of orthogonal polynomials with respect to

Zero-determinant strategies are a class of strategies in repeated games which unilaterally control payoffs. Zero-determinant strategies have attracted much attention in studies of social dilemma, particularly in the context of evolution of cooperation. So far, not only general properties of zero-determinant strategies have been investigated, but zero-determinant strategies have been applied to control

In this paper, a simultaneous inversion problem for the Riesz-Feller space-fractional diffusion equation with inexact operators is investigated, which is to identify the source term and initial value from two over-specified measurements. The problem model is well known to be ill-posed. We propose a regularization method to deal with the inverse problem using the idea of mollification. Under an a priori

This paper addresses the challenge of change point detection in temporal networks, a critical task across various domains, including life sciences and socioeconomic activities. Continuous analysis and problem-solving within dynamic networks are essential in these fields. While much attention has been given to binary cases, this study extends the scope to include change point detection in weighted networks

This paper studies the bumpless transfer (BT) control issue for switched systems with event-triggered (ET) control input. The aim is to reduce the jumps in control input at both switching and triggering points, while capturing the stability of the switched systems. First, a dynamic ET program is constructed with the triggering condition based on the level of suppression of input signal jumps. This

Multi-state Boolean networks model the behavior of interrelated (non-binary) Boolean entities over time. These networks can be used in several contexts, and extend the usual (simpler) binary-state Boolean networks. Leveraging the established knowledge of binary-state Boolean networks, we explore the dynamics of sequential multi-state Boolean networks, where their entities or nodes have states which

In this paper, we derive a decomposition formula for spectra of the distance Laplacian matrix DL and distance signless Laplacian matrix DQ of n-Cayley graphs by using group representation theory. Besides, we compute the DL and DQ spectra of the n-gonal n-cone graph and the n-sunlet graph. Finally, we present some examples of DL-integral graphs and DQ-integral graphs.

The coupling between neuronal oscillators plays an intriguing role in understanding the dynamics of the biological neurons present in realistic situations. Importantly, when the coupling between these neurons assumes an asymmetric nature, it can lead to profound changes in their overall behavior. In order to explore the impact of asymmetrical coupling on neuron models subjected to magnetic flux induction

One of the crucial aspects of patient-specific blood flow simulations is to specify material parameters and boundary conditions. The choice of boundary conditions can have a substantial impact on the character of the flow. While no-slip is the most popular wall boundary condition, some amount of slip, which determines how much fluid is allowed to flow along the wall, might be beneficial for better

This paper aims to present the virtual element method (VEM) for solving the Davey–Stewartson equations with application in fluid mechanics. The VEM is a recent technology that can be regarded as a generalization of the standard finite element method (FEM) to general meshes without the need to integrate complex nonpolynomial functions on the elements. This method only utilizes degrees of freedom associated

This paper focuses on the dissipative control design problem for a class of Markov jump systems (MJSs) via two-dimensional (2D) Roesser models. In terms of Lyapunov functional methods and linear matrix inequalities techniques, sufficient conditions are established to obtain the dissipative controller, such that the closed-loop system is finite-region bounded with (Q, S, R)-κ-dissipative performance