A physically realistic mathematical problem has been modelled to discuss the reflection and refraction phenomena of three-dimensional (3-D) plane waves. The considered composite structure comprises of water layer of finite width lying between isotropic and ice substrate has been considered. The mathematical analysis pertaining to this problem has been addressed analytically. The closed form expressions

Motivated by the advantage of exact discretization of a linear differential equation and the importance of symplectic numerical methods for conservative nonlinear oscillators, a modified Störmer-Verlet method relying on a parameter ω is proposed. The main idea is: firstly, based on some analytical approximation strategies, relating a linear equation with the corresponding nonlinear equation such that

For a graph G and a positive integer k, a k-list assignment of G is a function L on the vertices of G such that for each vertex v ∈ V(G), |L(v)| ≥ k. Let s be a nonnegative integer. Then L is a (k,k+s)-list assignment of G if |L(u)∪L(v)|≥k+s for each edge uv. If for each (k,k+s)-list assignment L of G, G admits a proper coloring φ such that φ(v) ∈ L(v) for each v ∈ V(G), then we say G is (k,k+s)-choosable

A dominating set in a graph G is a set S of vertices of G such that every vertex outside S is adjacent to a vertex in S. A connected dominating set in G is a dominating set S such that the subgraph G[S] induced by S is connected. The connected domination number of G, γc(G), is the minimum cardinality of a connected dominating set of G. A graph G is said to be k-γc-critical if the connected domination

The complex Ginzburg-Landau equation is considered using the traveling wave reduction. The first integral for the system of nonlinear differential equations is found. The first integrals is used to reduce the system of equations to the second-order ordinary differential equation. The general solutions for the five constraints on the parameters of the original complex Ginzburg-Landau equation are given

An extended generalized Darboux transformation method is proposed to construct the hybrid rogue wave and breather solutions for a classical nonlinear Schrödinger equation. Three types of hybrid wave solutions are obtained: (i) the hybrid first-order rogue wave and breather; (ii) the hybrid second-order rogue wave and first-order breather; (iii) the hybrid first-order rogue wave and second-order breather

We consider the non-isothermal fluid flow through a thin domain occupied by a saturated porous medium. The flow is governed by the Darcy-Brinkman system and the heat equation including the viscous dissipation term proposed by Al-Hadhrami et al. (2003). Using asymptotic analysis with respect to domain’s thickness, a second–order asymptotic approximation of the problem is built. The formally derived

We present a CUDA-based parallel implementation on GPU architecture of a modified version of the Smoothed Particle Hydrodynamics (SPH) method. This modified formulation exploits a strategy based on the Taylor series expansion, which simultaneously improves the approximation of a function and its derivatives with respect to the standard formulation. The improvement in accuracy comes at the cost of an

This paper is concerned with the problems of stochastic stability and control design for singular Markovian jump systems (SMJSs) with time varying delay. The derivative coefficient is considered to be mode dependent. A parameter-dependent reciprocally convex matrix inequality (PDRCMI) is constructed, which covers some existing ones as its special cases. Different from some existing ones, the introduced

Certificateless provable data possession (CL-PDP) protocol is an important tool to check the integrity of data outsourced to cloud service provider (CSP) since it is not necessary to consider the certificate management and key escrow problems. In 2017, He et al. proposed an efficient CL-PDP protocol (HKWWC-protocol, for short) with an additional good property: Privacy protection from the verifier [Appl

In practice, there exists numerous examples indicating the phenomenon that individuals are inclined to employ different strategies when interacting with the others. This is incurred by the fact that individuals are able to adjust their strategies adaptively under different interacting environments. Scholars have devoted their efforts to this topic; nevertheless, the impact of diverse interactions on

This paper investigates the global exponential stability of impulsive systems with infinite distributed delay. By introducing two auxiliary functions and two essential lemmas, some sufficient conditions of stability are presented based on flexible impulse frequency, where impulses are considered as perturbations. When the interval between two consecutive impulse times is very small in some time domains

The persistence and extinction (PE) are interesting topics in mathematics. This research analyzed PE of stochastic Logistic equations (SLE) by incorporating the Ornstein-Uhlenbeck process (SLOP) and stochastic delay Logistic equation (SDLE) by incorporating the Ornstein-Uhlenbeck process (SLDOP). Firstly, we proved that SLOP and SLDOP have positive solutions. Likewise, for stochastic permanence (SP)

We consider a contact model with power-law friction in the antiplane context. Our study focuses on the boundary optimal control, paying special attention to optimality conditions and computational methods. Depending on the exponent of the power-law friction, we are able to deduce an optimality condition for the original problem or for a regularized version of it. Furthermore, we introduce and analyze

Due to instability being induced easily by parameter disturbances of network systems, this paper investigates the multistability of memristive Cohen-Grossberg neural networks (MCGNNs) under stochastic parameter perturbations. It is demonstrated that stable equilibrium points of MCGNNs can be flexibly located in the odd-sequence or even-sequence regions. Some sufficient conditions are derived to ensure

The aim of this work is to study the oscillatory properties of the solutions of fourth-order delay differential equations with a p-Laplacian like operator of the form(r(ν)|w″′(ν)|p1−2w″′(ν))′+q(ν)|w(η(ν))|p2−2w(η(ν))=0.The results obtained are based on the comparison with first and second-order differential equations and the use of a Riccati transformation. Some examples are provided to illustrate

In this paper, we present a discrete dynamic system which describes an epidemic spreading within a single farm, where animals are separated into batches. In this model, we consider an indirect transmission of the disease coming from the bacteria remaining in the reservoir and taking into account the transfer of bacteria between adjacent compartments. In our model, tridiagonal matrices of non-negative

Continuous time Markov Chain (CTMC) approximation techniques have received increasing attention in the option pricing literature, due to their ability to solve complex pricing problems, although existing approaches are mostly limited to one or two dimensions. This paper develops a general methodology for modeling and pricing financial derivatives which depend on systems of stochastic diffusion processes

In this paper we consider the Pure and Impure Prisoner’s Dilemmas. Our purpose is to theoretically extend them when using non-Archimedean quantities and to work with them numerically, potentially on a computer. The recently introduced Sergeyev’s Grossone Methodology proved to be effective in addressing our problem, because it is both a simple yet effective way to model non-Archimedean quantities and

Given a hypergraph H of order n with rank k ≥ 2, denote by D(H) and A(H) the degree diagonal tensor and the adjacency tensor of H, respectively, of order k and dimension n. For real number α with 0 ≤ α < 1, the α-spectral radius of H is defined to be the spectral radius of the symmetric tensor αD(H)+(1−α)A(H). First, we establish a upper bound on the α-spectral radius of connected irregular hypergraphs

For a set S⊆V(G) in a network G, the Steiner distance dG(S) of S is the minimum size among all connected subnetworks whose vertex sets contain S. The Steiner k-eccentricity ɛk(v) of a vertex v of G is the maximum Steiner distance among all k-vertex set S which contains the vertex v, i.e., εk(v)=max{d(S)|S⊆V(G),|S|=k,v∈S}. Based on Steiner k-eccentricity, the connective Steiner k-eccentricity index

Strategy-updating rules play fundamental roles for the persistence of cooperation in groups composed by selfish individuals. In this paper, we study the spatial evolutionary prisoner’s dilemma game with the introduction of the strategy-updating cost for players, where each player is able to update its strategy if its payoffs is greater than a critical threshold. We show that there exist sudden increases

This paper presents a study on the drafting, kissing, tumbling (DKT) phenomenon between two circular and impermeable interacting particles of different sizes and densities in a confined medium in 2D using Immersed Boundary (IB) method. There are two different cases considered in this study. The first case, Case 1, deals with the scenario when the trailing particle was larger in size than the leading

The paper investigates the issue of mixed H∞ and dissipative asynchronous controller design for a class of Markov jump singularly perturbed systems (MJSPSs). A suitable dynamic event-triggered rule is offered to further mitigate the transmission burden of communication network. Since the mode information of Markov chain is extremely difficult to get, an asynchronous controller is well constructed.

This paper addresses the nonfragile H∞ observer design problem for uncertain nonlinear switched systems with quantization. The measurement output signals are quantized by a static quantizer before being transmitted. The sector bound approach is applied to obtain the quantization error. To address the problem of observer parameter perturbation, a set of observers with gain variations are constructed

To recover a sparse signal from a noised linear measurement system Ax=b+e, convex lp regularization methods (i.e., 1 ≤ p < 2, in particular, p=1) are commonly used under certain conditions. Recently, however, more attentions have been paid to nonconvex lq regularization methods (i.e., 0 < q < 1, in particular, q=1/2) for recovering a sparse signal. In this paper, we use proximal methods to study both

In this paper, we propose an iterative splitting method to solve the partial differential equation (PDE) in option pricing problems. We focus on the Heston stochastic volatility model and the derived two-dimensional PDE. We take the European option as an example and conduct numerical experiments using different boundary conditions. The iterative splitting method transforms the two-dimensional equation

This paper handles a design of event-triggered H∞ filter for T-S fuzzy systems in the connection of network communication. The sampled-data fuzzy filter, which take into account both the measurement output and the fuzzy consequent parameter as the sampled signal, is expressed as a fuzzy system with a time-varying delay including the event-triggering variable. Under these considerations, a novel pr

Information source selection (ISS) is ubiquitous across a myriad of scientific disciplines. Previous studies mainly viewed the issue of ISS as a multi-criteria decision making (MCDM) problem, and therefore used MCDM methods to investigate it. However, many important aspects, for example, the dynamic process of ISS, the impact of different kinds of factors on ISS, and the stability of the solution of

This paper investigates the problem of reachable set estimation for a general class of continuous-time singular linear systems with time-varying delay. By employing a new Lyapunov functional candidate, a criterion with the help of linear matrix inequalities (LMIs) is developed utilizing the new inequality scaling method, free-weighting matrix and the time-delay segmentation method. The reachable set

A gradually implicit method with deferred correction (GIMDC) and adaptive relaxation factors (ARFs) is developed for simulation to nonlinear heat transfer with temperature-dependent properties. GIMDC is equivalent to explicit method initially and approaches implicit method gradually. The theoretical analyses of convergence, error and stability indicate that the accuracy and stability of GIMDC are close

The Turán number of a graph G, denoted by ex(n, G), is the maximum number of edges of an n-vertex simple graph having no G as a subgraph. Let Sℓ denote the star on ℓ+1 vertices. In this paper, we investigate to determine the Turán number for Sℓ1∪Sℓ2, where ℓ1 > ℓ2. We give a new lower bound on ex(n,Sℓ1∪Sℓ2). Moreover, if ℓ2+1≤ℓ1≤2ℓ2+1 (or if ℓ1 ≥ 3 and ℓ2=2), we determine the exact values ex(n,Sℓ1∪Sℓ2)

The longitudinal dispersion and cross-sectional concentration distribution of chemical species through an annular tube have been studied for oscillatory flows in the presence of heterogeneous reactions between the species and tube wall along with homogeneous reaction in the bulk flow. The species is supposed to undergo kinetic reversible phase exchange and irreversible absorptive reactions at the outer

This paper investigates the finite-time stability (FTS) for a class of stochastic Markovian reaction-diffusion systems (SMRDSs). First, a boundary control strategy is put forward. Under the designed boundary controller, a sufficient condition of FTS for SMRDSs is provided based on the method of Lyapunov-Krasovskii functional combined with inequality techniques.When there exists the incompleteness of

Temperature has distinct impact on the activation of neural activities by adjusting the excitability and channel conductance. Some biological neurons can percept slight changes of temperature and then appropriate firing modes are induced under different temperatures. Indeed, the temperature-dependent property can be described by using thermistors, which can be included to build functional neural circuits

Manifestation of Küppers–Lortz secondary instability in rotating Rayleigh–Bénard convection in a Newtonian liquid (water) and in homogeneous and heterogeneous nanoliquids is reported for rigid-isothermal and free-isothermal boundaries. Water–alumina and water–alumina–copper are used as representative homogeneous and heterogeneous nanoliquids. Experimental data on thermal conductivity and dynamic viscosity

This paper is concerned with the issue of finite-time control for Markovian jump systems randomly occurring quantization. By absorbing the phenomena of unmeasurable state and randomly occurring quantization, a novel nonhomogeneous Markovian switching system is constructed, and an observer-based controller and non-fragile observer are designed. By utilizing Lyapunov function method, sufficient admissibility

This paper focuses on the problem of global exponential stability analysis for high-order delayed discrete-time Cohen–Grossberg neural networks. Multiple time-varying delays are considered. First, a technique lemma is obtained based on the properties of nonsingular M-matrices. Second, the delay-dependent and -independent criteria under which the zero equilibrium is globally exponentially stable are

In this paper, TCP/AWM network congestion control problem is investigated. First, a new funnel boundary (FB) is proposed. And then, in the framework of backstepping, a new control technique is given by virtue of free-will arbitrary time stability and the novel FB, which guarantees that the tracking error converges to the origin within an arbitrary setting time. Besides, the transient performances of

In this study we propose a novel adaptive finite element method for the ground state solution of Bose-Einstein Condensates (BEC). Different from the classical adaptive scheme applied to BEC which needs to solve a nonlinear eigenvalue model directly on each adaptive finite element space, our scheme requires to solve a linear elliptic boundary value problem on current adaptive space and a nonlinear eigenvalue

This paper is devoted to the adaptive state-feedback tracking control for stochastic nonlinear systems disturbed by unknown covariance noise under the condition of full-state constraints and parametric uncertainties. Different from the related literatures, nonlinear functions in the diffusion terms are allowed to be unknown in this paper. The parametric uncertainties and unknown covariance noise are

In this study, we concentrate on the design problem of robust reliable control for uncertain semi-Markovian jump systems with input saturation over a specified finite interval of time. To exhibit the reality, a delay function that varies with respect to time and a more practical actuator fault model are included in the addressed system and the control design, respectively. By coupling the linear matrix

This paper investigates the output feedback secure control problem for a class of cyber-physical-system (CPSs) under sparse sensor attacks. The considered CPSs are modeled as complex dynamical networks(CDN) with linear couplings. First, by defining a novel quadratic cost index, an optimal control policy consisting of a feedback control and a compensated feedforward control is obtained in the attack-free

A contragenic function in a domain Ω⊆R3 is a reduced-quaternion valued (i.e the last quaternionic coordinate is zero) harmonic function, which is orthogonal in L2(Ω) to all reduced-quaternion monogenic functions and their conjugates. Contragenicity is not a local property. For spheroidal domains of arbitrary eccentricity, we relate standard orthogonal bases of harmonic and contragenic functions for

In this work we propose a two-dimensional multi-species model to describe the dynamics of biofilms formed by the pathogenic bacteria Listeria monocytogenes. Different Listeria monocytogenes strains produce biofilms with different structures, namely flat, honeycomb and clustered. Previous works showed that glucose impaired uptake and the appearance of damaged or dead cells are critical mechanisms underlying

In this paper, we consider the optimal harvesting controls for a diffusive predator-prey system, which is formulated by prey refuge and modified Leslie-Gower functional response. The locally and globally asymptotic stability of unique positive constant steady state is discussed under homogeneous Neumann boundary condition. The nonexistence and existence of nonconstant steady states are obtained by

Dimensionally reduced models are effective approximations of flow and transport processes in structures containing thin layers. We propose and analyse such a model for flow in fractured porous media. The fractures can store and transport fluid and they are modelled as lower-dimensional entities in the surrounding porous medium. The flow system of interest in this work is single-phase, isothermal and

We propose a cooperative evolution model in which successive behaviors influence reputation. There are two mechanisms to form reputation. One is enhancing the reputation of players who cooperate insistently, and reducing it when they defect continuously. The other is increasing reputation when defection is transformed into cooperation, and decreasing when cooperation is turned into defection. These

This paper is devoted to determine the fractional order, the initial flux speed and the boundary Neumann data simultaneously in a one-dimensional time-fractional diffusion-wave equation from part boundary Cauchy observation data. We prove the uniqueness result for this inverse problem by using a new result for the Mittag-Leffler function and Laplace transform combining with analytic continuation. Then

A two-level stabilized quadratic equal-order variational multiscale method based on the finite element discretization is proposed for numerically solving the steady incompressible Navier-Stokes equations at high Reynolds numbers. In this method, a stabilized solution is first obtained by solving a fully stabilized nonlinear system on a coarse grid, and then the solution is corrected by solving a stabilized

A (k, r)-coloring of a graph G is a proper k-vertex coloring of G such that the neighbors of each vertex of degree d will receive at least min{d, r} different colors. The r-hued chromatic number, denoted by χr(G), is the smallest integer k for which a graph G has a (k, r)-coloring. Let f(r)=r+3 if 1 ≤ r ≤ 2, f(r)=r+5 if 3 ≤ r ≤ 7 and f(r)=⌊3r/2⌋+1 if r ≥ 8. In [Discrete Math., 315-316 (2014) 47-52]

The Q-graph of a graph G is defined to be the graph obtained from G by inserting a new vertex into each edge of G, and joining by edges those pairs of new vertices which lie on adjacent edges of G. In this paper, we investigate the existence of Laplacian perfect state transfer and Laplacian pretty good state transfer in Q-graphs of r-regular graphs for r ≥ 2. We prove that there is no Laplacian perfect

A star edge coloring of a graph G is a proper edge coloring of G without bichromatic paths or cycles of length four. The star chromatic index, χst′(G), of G is the minimum number k for which G has a star edge coloring by k colors. In [2], L. Bezegova´ et al. conjectured that χst′(G)≤⌊3Δ2⌋+1 when G is an outerplanar graph with maximum degree Δ ≥ 3. In this paper we obtained that χst′(G)≤Δ+6 when G is

We use Newton’s method to approximate locally unique solutions for a class of boundary value problems by applying the shooting method. The utilized operator is Fréchet-differentiable between Banach spaces. These conditions are more general than those that appear in previous works. In particular, we show that the old semilocal and local convergence criteria for Newton’s method involving Banach space

In this article, the problem of stabilization for the switched positive linear system (SPLS) with impulse and marginally stable subsystems is studied, in which both the continuous time case and the discrete time case are taken into account. By the usage of a piecewise weak linear copositive Lyapunov function (LCLF) and the mode-dependent dwell time (MDT), time-dependent switching control laws are designed

This paper investigates the finite-time H∞ adaptive control of linear systems with unknown mismatched uncertainties. To deal with outage and stuck failures on the actuator and the uncertainties, a new finite-time adaptive H∞ control strategy is proposed. With the established strategy, the resultant closed-loop system is finite-time bounded with the required H∞ level. The validity of the proposed method

We study the Vasyunin-type cotangent sum c0(h/k)=−∑m=1k−1(m/k)cot(πhm/k), where h and k are positive coprime integers. This sum is related to Estermann zeta function. By applying the Euler-Maclaurin summation formula to a suitable function, we improve a previous large-k asymptotic approximation of c0(h/k). We also provide a procedure to compute an arbitrary number of terms of the approximation.

In the numerical methods for the Laplace transform inversion the errors quantification in computational processes is a crucial issue. In this paper, we propose two inversion methods based on smoothing splines combined with a procedure for the derivation of error bounds. In particular, we numerically study the impact of the fitting error amplification through the analysis of several sources of error

The present study proposes a new fractional-order hyperchaotic memristor oscillator. The proposed system is studied through numerical simulations and analyses, such as the Lyapunov exponents, bifurcation diagrams, and phase portraits. Then, using the sliding mode concept, a robust adaptive control scheme is designed to synchronize the proposed system. The adaptation mechanism is implemented to estimate

This paper further investigates the design problem of the functional interval observer for discrete-time systems with disturbances. Two methods are given to design functional interval observers. Given monotone system theory, a Luenberger-like functional interval observer is constructed and sufficient conditions are achieved by Sylvester equations in the first method. The second approach is known as