This work deals with the study of structured backward error analysis of Hankel and symmetric-Toeplitz matrix pencils. These structured matrix pencils belong to the class of symmetric matrix pencils with some additional properties that a symmetric matrix pencil does not have in general. The perturbation analysis of these two structures is discussed one by one to depict the additional properties explicitly

In this paper, a drug-sensitive and drug-resistant mixed strains of HIV infection model with saturated incidence and distributed infection delays is proposed. The drug-sensitive strain could mutate and become drug-resistant strain during the process of reverse transcription (i.e., SR conversion in short). The nonnegativity and boundedness of solutions are discussed, by introducing two kinds of principle

We investigate solvability theory and numerical simulation for two-side conservative fractional diffusion equations (CFDE) with a variable-coefficient a(x). We introduce σ=−aDp as an intermediate variable to isolate a(x) from the nonlocal operator, and then apply the least-squares method to obtain a mixed-type variational formulation. Correspondingly, solution space is split into a regular space and

A set D of vertices in a graph G is a dominating set if every vertex in V(G)−D is adjacent to a vertex in D. If the subgraph induced by the set D is connected, then D is a connected dominating set in G. The connected domination number of G, γc(G), is the minimum cardinality of a connected dominating set of G. A graph G is k-γc-critical if γc(G)=k and γc(G+uv)

This paper investigates representations of outer matrix inverses with prescribed range and/or null space in terms of inner inverses. Further, required inner inverses are computed as solutions of appropriate linear matrix equations (LME). In this way, algorithms for computing outer inverses are derived using solutions of appropriately defined LME. Using symbolic solutions to these matrix equations it

An arc-colored digraph D is properly (properly-walk) connected if, for any ordered pair of vertices (u,v), the digraph D contains a directed path (a directed walk) from u to v such that arcs adjacent on that path (on that walk) have distinct colors. The proper connection number pc→(D) (the proper-walk connection number wc→(D)) of a digraph D is the minimum number of colours to make D properly connected

Since the 2007/2008 financial crisis, the total value adjustment (XVA) should be included when pricing financial derivatives. In the present paper, the derivative values of European and American options have been priced where we take into account counterparty risk. Whereas European and American options considering counterparty risk have already been priced under Black-Scholes dynamics in [2], here

This paper deals with boundary feedback control for a fractional reaction-diffusion equation with varying coefficient coupled with fractional ordinary differential equations with delay, which is a generalization of integer order coupled system. By designing a state feedback controller, we transform an unstable system into an asymptotic stable system via the backstepping method. The exact solution of

In this paper, the issue of non-fragile control is addressed for the positive discrete-time Roesser model with uncertain parameters, where the switching mechanism obeys the persistent dwell time (PDT) constraint. First of all, in order to reduce the resource occupancy, a event-triggered (E-T) mechanism is introduced for the considered positive Roesser model. Then two kinds of non-fragile controllers

Cross-efficiency measurement is an extension of Data Envelopment Analysis that allows for tie-breaking ranking of the Decision Making Units (DMUs) using all the peer evaluations. In this article we examine the theory of cross-efficiency measurement by comparing a selection of methods popular in the literature. These methods are applied to performance measurement of European warehouses. We develop a

This paper studies deterministic constraint optimization problem with two competitive agents in which the following objective functions on a single machine: the total weighted late work and the total completion time. We show that the constraint optimization problem is the binary NP-hard by Knapsack problem reduction. Furthermore, we present a pseudo-polynomial time algorithm by early due date maximum

In order to study the influence of communication structure on opinion dynamics in social networks with multiple true states, a social learning model is proposed in which the social network is composed of strongly connected communities and some uninformed individuals outside the communities. Multiple communities correspond to multiple underlying true states. At each time step, the individual in a community

In network analysis, centrality measures identify the most important vertices within a graph. In a connected graph, the transmission of a vertex u is the sum of the lengths of the shortest paths between the node and all other nodes in the graph. In this paper, we discuss a method to uniquely identify a vertex in a plane nanosheet. Using this approach, we compute the transmission of every vertex in

In this work we look for characteristics and mobility patterns in the cities of Rome and London, from a dataset of private vehicle movements in those cities. Based on mobility data and other data related to the urban public transport network, commercial activity and tourist information, a multiplex network with three layers is constructed for each city. The construction of the multiplex network allows

We find closed form formulas for the Kemeny’s constant and the Kirchhoff index for the cluster G1{G2} of two highly symmetric graphs G1, G2, in terms of the parameters of the original graphs. We also discuss some necessary conditions for a graph to be highly symmetric.

In this paper, a wavelet immersed boundary (IB) method is proposed to solve fluid-structure interaction (FSI) problems with two-variable coupling, in which it is an interaction between fluid force and boundary deformation. This wavelet IB method is developed by introducing a wavelet finite element method to calculate the FSI force affected by the two-variable coupling. Furthermore, a boundary influence

In this paper, we study the pth moment exponential stability (p-ES) and the almost sure exponential stability (a-ES) of neutral stochastic delay differential equations (NSDDEs). By using the vector Lyapunov function (VLF) method, we can prove that the global solution of NSDDEs exists when the linear growth condition is removed, and we also get some stability criteria for NSDDEs. In the presented stability

This paper studies the asymptotic behavior of a solution of dispersive shallow water waves modeled by coupling the Rosenau-RLW equation and the Rosenau-Burgers equation. The energy decay rates of the solution to the model are examined through the Fourier transform method. Moreover, we develop a pseudo-compact finite difference scheme for solving the model, study solution behavior, and confirm our theoretical

This paper researches the problem of p-norm fixed-time synchronization for a class of delayed inertial complex-valued neural networks (ICVNNs). By using reduced-order transformation and separating real and imaginary parts of complex-valued parameters, the second-order ICVNNs can be converted into the form of first-order real-valued differential equations. Then some new flexible and adjustable algebraic

In this paper, a general Filippov-type predator-prey model with a refuge is presented. We propose a discontinuous predator-prey model incorporating a threshold policy by extending a general continuous predator-prey model. By employing the qualitative analysis theory related to Filippov systems, the necessary and sufficient conditions for the global asymptotical stability of a standard cycle, a touching

In this paper, the orbital stability of dn periodic solutions for the generalized symmetric regularized-long-wave equation with two nonlinear terms is investigated. First, the existence of dn periodic solution to the equation is obtained. Then, according to the Floquet theory and Lame equation, the spectral properties of corresponding linear operators are given. Last, according to the classical theory

In this work, we adopt the generalized Kudryashov method to produce exact wave solutions for some space-time fractional partial differential equations. The Jumaries modified Riemann-Liouville is considered. The proposed method is implemented to the fractional Sharma-Tasso-Olver equation and the fractional Bogoyavlenskii’s breaking soliton equations. Various solutions containing hyperbolic tangent function

This article presents a saturation controller design method for a type of nonlinear time-delay systems. Different from the current works, the nonlinear systems considered herein satisfy an incremental quadratic constraint, which is a more general nonlinearity. Firstly, for the constraint in the actuator, the convex set theory is employed to transform the saturated feedback law into a parameterized

In this paper, we use the phase field method to deal with the compliance minimization problem in topology optimization. A modified Allen-Cahn type equation with two penalty terms is proposed. The equation couples the diffusive interface dynamics and the linear elasticity mechanics. We propose the first- and second-order unconditionally energy stable schemes for the evolution of phase field modeling

Due to the current COVID-19 pandemic, much effort has been put on studying the spread of infectious diseases to propose more adequate health politics. The most effective surveillance system consists of doing massive tests. Nonetheless, many countries cannot afford this class of health campaigns due to limited resources. Thus, a transmission model is a viable alternative to study the dynamics of the

The main purpose of this work is to develop a numerical solution method for solving a class of nonlinear free final time fractional optimal control problems. This problem is subject to equality and inequality constraints in canonical forms, and the orders in the fractional system can be different. For this problem, we first show that, by a time-scaling transformation, the problem can be transformed

In the paper, a prescribed chattering reduction control using aperiodic signal updating is presented for quadrotors subject to parameter uncertainties and external disturbances. Using estimation errors instead of tracking errors to update adaptive laws, estimator-based minimum learning parameter (EMLP) observers capable of relaxing computational complexity are respectively explored in translational

This work studies edge-transitive bi-circulants of order 2n with Zn being a Hall subgroup of the full automorphism groups. The automorphism groups of such graphs are completely determined. As an application, a classification is given of bipartite edge-transitive bi-circulants of order 2n with valency less than the smallest prime divisors of n. This also leads to a new construction of an infinite family

In a family of real quadratic three dimensional systems symmetric with respect to a plane we look for subfamilies having center manifolds filled with isochronous periodic orbits. Eleven such subfamilies are detected and it is shown that for ten of them there are Darboux type substitutions transforming the subfamilies to systems which are linear on center manifolds. We also give an example of a 3-dim

At the present work, we propose a new numerical scheme for the solution of two and three dimensional time fractional nonlinear damped Klein–Gordon equation (DKGE). To this end, we use the Legendre spectral element method to discretize the equation in the spatial directions and for the time stepping, an alternating direction implicit (ADI) method based on a scheme of order O(τ2) is considered. We prove

In this paper we propose and study a new structural invariant for graphs, called distance-unbalancedness, as a measure of how much a graph is (un)balanced in terms of distances. Explicit formulas are presented for several classes of well-known graphs. Distance-unbalancedness of trees is also studied. A few conjectures are stated and some open problems are proposed.

The main target of this paper is to present a new and efficient method to solve a nonlinear free boundary mathematical model of atherosclerosis. This model consists of three parabolic, one elliptic and one ordinary differential equations that are coupled together and describes the growth of a plaque in the artery. We start our discussion by using the front fixing method to fix the free domain and simplify

In this paper, the sampled-data resilient H∞ control problem is concerned for networked stochastic systems with multiple attacks. Multiple attacks consisting of denial-of-service (DoS) attacks and random deception attacks are first described. Then on the basis of these attacks, a new switched stochastic time-delay closed-loop system is proposed under sampled-data and full state feedback controller

Motivated from the study of eccentricity, center, and sum of eccentricities in graphs and trees, we introduce several new distance-based global and local functions based on the smallest distance from a vertex to some leaf (called the “uniformity” at that vertex). Some natural extremal problems on trees are considered. Then the middle parts of a tree is discussed and compared with the well-known center

State constraints are very common in actual networked systems. The main purpose of this article is to investigate the constrained set controllability of k-valued logical control networks (KVLCNs), the states of which are within a finite set. At first, the dynamics of KVLCNs with state constraints (SC-KVLCNs) can be equivalently written as an bilinear system by applying algebraic state space representation

The turbulent hydromagnetic dynamo is a process of magnetic field generation by chaotic flow of an electrically conducting fluid (plasma, liquid iron etc.). It is responsible for generation of large-scale magnetic fields of astrophysical objects such as planets, stars, accretion discs, galaxies, galaxy clusters etc. In particular, the dynamical process of induction of large-scale fields is strongly

We investigate solutions to the system of linear equations (SoLE) in both the time-varying and time-invariant cases, using both gradient neural network (GNN) and Zhang neural network (ZNN) designs. Two major limitations should be overcome. The first limitation is the inapplicability of GNN models in time-varying environment, while the second constraint is the possibility of using the ZNN design only

In this paper we use the orbital normal form of the nondegenerate Hopf-zero singularity to obtain necessary conditions for the existence of first integrals for such singularity. Also, we analyze the relation between the existence of first integrals and of inverse Jacobi multipliers. Some algorithmic procedures for determining the existence of first integrals are presented, and they are applied to some

Given graphs G and H, the generalized Turán number ex(G,H) is the maximum number of edges in an H-free subgraph of G. In this paper, we obtain an asymptotic upper bound on ex(CTn,C2ℓ) for any n≥3 and ℓ≥2, where C2ℓ is the cycle of length 2ℓ and CTn is the complete transposition graph which is defined as the Cayley graph on the symmetric group Sn with respect to the set of all transpositions of Sn.

Let G be an edge-colored connected graph, a path (trail, walk) of G is said to be a proper-path (trail, walk) if any two adjacent edges of it are colored distinctly. If there is a proper-path (trail, walk) between each pair of different vertices of G, then G is called proper-path (trail, walk) connected. The edge-coloring which makes G proper-path (trail, walk) connected is called a proper-path (trail

Nonlinear science is very common and important natural phenomenon in our surroundings. It is quite possible to find a large number of phenomena, which become a cause of the formulation of a non-linear partial differential equation. Due to the presence of non-linear partial differential equations in each branch of science, these equations have become a useful tool to deal with complex natural phenomena

In this paper, we extend the discrete unified gas kinetic scheme (DUGKS) to simulate conjugate heat transfer flows. The conjugate interface that separates two media with different thermophysical properties is handled by a ghost-cell (GC) immersed boundary method. Specifically, fictitious cells are set in both domains to implement the continuity conditions of both temperature and heat flux at the conjugate

An outbreak of respiratory disease caused by a novel coronavirus is ongoing from December 2019. As of December 14, 2020, it has caused an epidemic outbreak with more than 73 million confirmed infections and above 1.5 million reported deaths worldwide. During this period of an epidemic when human-to-human transmission is established and reported cases of coronavirus disease 2019 (COVID-19) are rising

The paper aims at applications of a decoupled wavelet method for investigating multiple physical steady flow fields of binary nanofluids in double-diffusive mixed convection. The Buongiorno’s mathematical model of nanofluids is further perfected in the presence of Dufour and Soret effects, incorporating with linear and nonlinear diffusiophoresis effects based on experiments [Chemical Engineering Science

In this paper, the stability problem of neural networks is addressed by considering time-varying delays. By proposing novel geometry-based negative conditions for the form of quadratic function and constructing new augmented Lyapunov-Krasovskii functionals, a novel stability criterion is derived. Finally, to show the effectiveness of the proposed criterion, several numerical examples are given.

This paper studies the stability problem of time-varying delay systems. Firstly, By constructing a delay-product Lyapunov-Krasovskii functional, a stability criterion is established, where the advantages of convexity properties are being exploited. This stability criterion in terms of linear matrix inequality (LMI) can be checked exactly using an improved negativity condition of quadratic polynomials

The purpose of this paper is the prediction of the behaviour of multilayer elastomeric bearings by the finite element analysis. First, the finite element formulation of equilibrium equations of incompressible elasticity problem is presented. This approach is based on the modified potential energy taking into account the incompressibility. The linearized system obtained is solved by the Newton–Raphson

Pharmacokinetics is the study of the time course of drug concentrations in body compartments. The majority of drugs are eliminated at first order kinetics with a nonconstant elimination rate due to spontaneous erratic variations in the metabolic processes and individual difference. Noting the paradox of stochastic pharmacokinetic models, this paper proposes an uncertain pharmacokinetic model for mono-compartmental

In this paper, we apply spline quasi-interpolating operators on a bounded interval to solve numerically linear Fredholm integral equations of second kind by using superconvergent Nyström and degenerate kernel methods introduced in [4]. We give convergence orders associated with approximate solutions and their iterated versions in terms of spline quasi-interpolating order. Moreover, asymptotic expansions

A kinetic exchange model is used to investigate the evolution of wealth distribution in a financial market. Assume that the market is characterized by a risky asset (a stock) and a risk-less asset (a bond). The model captures wealth exchanges and speculative trading to affect the dynamics of wealth distribution. We embed a suitable value function into the interactions of wealth to describe that agents

Image deblurring is an important pre-processing step in image analysis. The research for efficient image deblurring methods is still a great challenge. Most of the currently used methods are based on integer-order derivatives, but they typically lead to texture elimination and staircase effects. To overcome these drawbacks, some researchers have proposed fractional-order derivative-based models. However

We first verify the global well-posedness of the impulsive reaction-diffusion equations on infinite lattices. Then we establish that the generated process by the solution operators has a pullback attractor and a family of Borel invariant probability measures. Furthermore, we formulate the definition of statistical solution for the addressed impulsive system and prove the existence. Our results show

For any bipartite graph B, the bipartite Ramsey number brk(B) is defined to be the smallest integer N such that any edge-coloring of complete bipartite graph KN,N by k colors contains a monochromatic B. In this note, it is shown that brk(K2,s)∼(s−1)k2 for fixed s≥2 and brk(K3,3)∼k3 as k→∞.

Scalar multiplication is the main operation in the implementation of hyperelliptic curve cryptosystems, where the basic arithmetic of reduced divisor classes is required. In this work, some explicit formulas are proposed for the arithmetic of reduced divisor classes by exploiting Jacobian coordinates when the degenerate divisor is involved. Moreover, an efficiency analysis shows that the degenerate

In a graph G, the cardinality of the smallest ordered set of vertices that distinguishes every element of V(G)∪E(G) is called the mixed metric dimension of G, and it is denoted by mdim(G). In [12] it was conjectured that every graph G with cyclomatic number c(G) satisfies mdim(G)≤L1(G)+2c(G) where L1(G) is the number of leaves in G. It is already proven that the equality holds for all trees and more

Based on the invariant energy quadratization approach, we propose a linear implicit and local energy preserving scheme for the nonlinear Schrödinger equation with wave operator, that describes the solitary waves in physics. In order to overcome the difficulty of designing an efficient scheme for the imaginary functions of the nonlinear Schrödinger equation with wave operator, we transform the original

For general three-dimensional piecewise linear systems, some explicit sufficient conditions are achieved for the existence of a heteroclinic loop connecting a saddle-focus and a saddle with purely real eigenvalues. Furthermore, certain sufficient conditions are obtained for the existence and number of periodic orbits induced by the heteroclinic bifurcation, through close analysis of the fixed points

We consider a version of the N-player snowdrift game in which the payoffs obtained by the players are delayed. The delay in payoffs is shown to lead to a Hopf bifurcation with an associated critical value of the time delay in the replicator dynamics. For time delays larger than the critical time delay, the replicator dynamics oscillate around the equilibrium instead of asymptotically approaching it

This paper studies a discrete-time formation containment tracking control problem of a linear heterogeneous multi-unmanned system under the leader-follower formation with switching directed topology and unknown external disturbance. To solve the containment tracking control of the heterogeneous multi-unmanned system with switching directed topology, distributed containment control strategies are presented

A new integral inequality method is put forward to analyze the general decay stability for Markovian switching neutral stochastic functional differential systems. At first, in order to get around the dynamic analyses difficulty induced by the coinstantaneous presence of neutral term, Markovian switching and Brownian motion noise, an new integral inequality as a powerful tool is gained. Then, based