This paper proposes a numerical approximation combining finite difference method in time and finite element method in space to solve the two-dimensional time-space fractional Bloch-Torrey equation. Unlike the existing works which focus on the decoupled model, the proposed numerical scheme is established and discussed based on the coupled equations which is from the separation of real and imaginary

In this paper, we propose a new nonlinear finite volume (FV) scheme preserving the discrete maximum principle (DMP) for diffusion equations on distorted meshes. We introduce both cell-centered and vertex unknowns as primary ones. It is well-known that some restrictions on the diffusion coefficients and meshes have to be imposed for existing cell-centered schemes to preserve the DMP (see, e.g., Sheng

This paper considers prescribed-time observer (PTO) designs for a class of linear parameter-varying (LPV) systems. Firstly, a full-order prescribed-time observer with time-varying gains is developed. The existence conditions are given in terms of linear matrix inequalities (LMIs). In addition, the reduced-order PTO is also considered in this paper. Moreover, it is shown that the existence conditions

In this paper, a multi-fidelity surrogate model is created using co-kriging methodology to determine the natural frequencies of beams by combining the fidelities of Euler-Bernoulli (low-fidelity) and Timoshenko (high-fidelity) beam finite element models. This study of free vibration of beams involves uncertainties in material properties. The sampling space for the co-kriging surrogate model is created

Social distancing can be divided into two categories: spontaneous social distancing adopted by the individuals themselves, and public social distancing promoted by the government. Both types of social distancing have been proved to suppress the spread of infectious disease effectively. While previous studies examined the impact of each social distancing separately, the simultaneous impacts of them

The problem of full determination of trees with a minimal value of the ABC index is very hard and famous in mathematical chemistry. A well-known conjecture is that the big vertices (vertices of degree larger than 2, which are not adjacent to a vertex of degree 2) of a tree with a minimal value of the ABC index induce a star graph. Here we give an affirmative answer to this conjecture and thus make

We demonstrate the existence and uniqueness of solutions to a bilinear state system with locally essentially bounded coefficients on an unbounded time scale. We obtain a Volterra series representation for these solutions which is norm convergent and uniformly convergent on compact subsets of the time scale. We show the associated state transition matrix has a similarly convergent Peano-Baker series

Graham’s convex hull algorithm outperforms the others on those distributions where most of the points are on or near the boundary of the hull (Allison and Noga, 1984). To use this algorithm for finding an orthogonal convex hull of a finite planar point set, we introduce the concept of extreme points of a connected orthogonal convex hull of the set, and show that these points belong to the set. Then

This paper investigates a class of non-zero-sum stochastic differential game problems between two insurance companies. The surplus process of each company is modeled by a Brownian motion where drift and volatility depend on the continuous-time Markov regime switching process. Both companies have the option of paying dividends. The objective is to maximize the expected discount utility of surplus relative

This paper proposes a new method for designing a state-dependent switching law to stabilize a class of switched nonlinear system with two unstable subsystems. The main idea is to convert each subsystem to a second-order mechanical system by introducing a reversible transformation, thus the summation of its kinetic and potential energies is calculated as an energy function. Then, by defining a performance

This paper formulates the climate change dilemma as an adaption of public goods game. The Nash equilibrium of the climate change dilemma is analyzed in the cases of discrete contribution and continuous contribution. Analytic results show that environmental feedback promotes cooperation to a certain extent, but as the number of players increases, zero contribution becomes the only Nash equilibrium in

In this paper, the resolvent energy and spectral moment are investigated by the help of some special functions. Some sharp bounds are analyzed for these structures including its vertices, its edges, its degrees and its eigenvalues.

The extended adjacency matrix of graph G, Aex is a symmetric real matrix that if i≠j and uiuj∈E(G), then the ijth entry is dui2+duj2/2duiduj, and zero otherwise, where du indicates the degree of vertex u. In the present paper, several investigations of the extended adjacency matrix are undertaken and then some spectral properties of Aex are given. Moreover, we present some lower and upper bounds on

In this article, we combine the local projection stabilization (LPS) technique in space and the discontinuous Galerkin (DG) method in time to investigate the time-dependent convection-diffusion-reaction problems. This kind of stabilized space-time finite element (STFE) scheme, based on approximation space enriched by bubble functions that can increase stability, is constructed. The existence, uniqueness

The paper is focused on the surface wave field in functionally graded multi-layer transversely isotropic heterogeneous magneto-elastic reinforced media. The Geometry of the problem is formulated by considering the (n−1) finite layer composite structure over a semi-infinite substance, occupying the domain: −∞

This paper is concerned with the problem of asynchronous mode-dependent dissipative control for continuous-time semi-Markovian jump systems (S-MJSs), where the probability distribution functions of sojourn-time are established in a generic form to cover uncertainties that occur due to experimental limitations and errors. Further, based on a control-mode-dependent Lyapunov function, this paper proposes

In this paper, we study the dynamics of a delay differential model of predator-prey system involving teams of two-prey and one-predator, with Monod-Haldane and Holling type II functional responses, and a cooperation between the two-teams of preys against predation. We assume that the preys grow logistically and the rate of change of the predator relies on the growth, death and intra-species competition

Newton linearization is implemented for the discretized advection terms in the Navier-Stokes momentum equations. A modified Newton linearization algorithm is developed by analyzing how to properly account for mass conservation implicitly in the linearization. The numerical performance of the modified Newton linearization algorithm is investigated in terms of solution stability, convergence behaviour

In this paper, a novel collocation method is presented for the efficient and accurate evaluation of the two-dimensional elliptic partial differential equation. In the new method, the physical domain is discretized into a series of overlapping small (local) subdomains, and in each of the subdomain, a localized Chebyshev collocation method is applied in which the unknown functions at every node can be

A new definition of a multivalued logarithm on time scales is introduced for delta-differentiable functions that never vanish. This new logarithm arises naturally from the definition of the cylinder transformation that is also the wellspring of the definition of exponential functions on time scales. This definition will lead to a logarithm function on arbitrary time scales with familiar and useful

Viral infections remain a major cause of deaths globally. Here, we focus on Hepatitis B and C viruses (HBV and HCV) infection dynamics in the liver and blood cells, taking into account non-cytotoxic and cytotoxic mediated immune response as well as antiviral therapy. The analysis of the model is presented in terms of the reproduction number, R0. The system has a globally stable disease-free equilibrium

Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by the stochastic differential equations with drift term relying on some random effects. We obtain the Girsanov-type formula of the stochastic differential equation

In this paper, two implicit Backward Euler (BE) and Crank-Nicolson (CN) formulas of Ciarlet–Raviart mixed finite element method (FEM) are presented for the fourth order time-dependent singularly perturbed Bi-wave problem arising as a time-dependent version of Ginzburg-Landau-type model for d-wave superconductors by the bilinear element. The well-posedness of the weak solution and the approximation

Given a family of graphs F and a subgraph H of F∈F, let rb(F,H) denote the smallest number k so that there is a rainbow H in any k-edge-colored F. We call it rainbow number for H in regard to F. The set of all plane triangulations of order n is denoted by Tn. The wheel graph of order d+1 and the path of order k are denoted by Wd and Pk, respectively. In this paper, we establish lower bounds of rb(Tn

In the paper, we offer a qualitatively unimprovable oscillation result for half-linear several delay second-order differential equations, which improves and generalizes the one from the very recent study [8]. The sharpness of our newly obtained criterion is illustrated via Euler-type half-linear several delay differential equations.

In this paper we propose an eco-friendly optimization of banana or plantain yield by the control of the pest burrowing nematode Radopholus similis. This control relies on fallow deployment, with greater respect for the environment than chemical methods. The optimization is based on a multi-seasonal model in which fallow periods follow cropping seasons. The aim is to find the best way, in terms of profit

In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes are based on one or another additive splitting of the operator into “simpler” operators that are more convenient/easier for the computer implementation and use inhomogeneous

In the high-dimensional data setting, the sample covariance matrix is singular. In order to get a numerically stable and positive definite modification of the sample covariance matrix in the high-dimensional data setting, in this paper we consider the condition number constrained covariance matrix approximation problem and present its explicit solution with respect to the Frobenius norm. The condition

Understanding how information navigates through nodes of a complex network has become an increasingly pressing problem across scientific disciplines. Several approaches have been proposed on the basis of shortest paths or diffusive navigation. However, no existing approaches have tackled the challenges of efficient communication in networks without full knowledge of their global topology under external

This paper deals with phase lag (or time-lagged) heat conduction models: the Cattaneo-Vernotte (or thermal wave) model and the dual phase lag model. The main aim is to show that modal analysis of these second order partial differential equations provides a valid and effective approach for analysing and comparing the models. It is known that reliable values for the phase lags of the heat flux and the

The barycentric form of Lagrange interpolant is attractive due to its stability, fast convergent rate, high precision and so on. In this paper, we applies an algorithm based on two dimensional extension of barycentric Lagrange interpolant for solving two dimensional integro-differential equations (2D-IDEs) numerically. First, the solution of the 2D-IDEs is replaced by the extended two dimensional barycentric

Mineral precipitation and dissolution processes in a porous medium can alter the structure of the medium at the scale of pores. Such changes make numerical simulations a challenging task as the geometry of the pores changes in time in an apriori unknown manner. To deal with such aspects, we here adopt a two-scale phase-field model, and propose a robust scheme for the numerical approximation of the

We present a novel donation game model to investigate the impact of reputation on the evolution of tag-mediated altruistic behaviors, in which the donors need to simultaneously take the information of a recipient’s reputation and tag into account when making decisions. In detail, each individual can be randomly endowed with a tunable reputation value and a fixed tag at the initial stage, the donor’s

We develop precise bounds on the growth rates and fluctuation sizes of unbounded solutions of deterministic and stochastic nonlinear Volterra equations perturbed by external forces. The equation is sublinear for large values of the state, in the sense that the state–dependence is negligible relative to linear functions. If an appropriate functional of the forcing term has a limit L at infinity, the

In this paper, we consider the matrix inequality AXA≤?A in the star, sharp and core partial orders, respectively. We get general solutions of those matrix inequalities and prove D*⊆S* and D#⊆S#, although DO#⊈SO#.

Internet and smartphone are inventions that have brought significant benefits to humanity. However, many individuals have become addicted to using these technologies and, as a consequence, they experience negative mental effects. The home confinement due to the COVID-19 pandemic may have worsened this situation. Here, an epidemic model is proposed to represent the spread of the problematic technology

In this paper we studied the fractional Euler-Bernoulli beam equation including a composition of the left and right fractional Caputo derivatives. We analyzed the equation with two types of boundary conditions (for the fixed-supported and fixed-free ends). The differential equation is converted into an integral one, taking into account the assumed boundary conditions. The obtained exact solutions contain

A robust anti-disturbance control (RADC) strategy is investigated for the ship dynamic positioning (DP) systems with unknown time-varying disturbances. The disturbances are brought about by wind, second-order wave drift, ocean currents as well as unmodeled dynamics, which are modelled by the first-order Markov process. The disturbance observer (DO) is established to online estimate disturbances. Then

For any integers m≥0 and n≥2, we use Dm,n to denote the m-dimensional DCell with n-port switches. For a simple graph G=(V,E), an edge subset S⊂E(G) is said to be a λk-cut of G, if G−S is disconnected and each component of G−S has at least k vertices. The k-restricted edge-connectivity of G, denoted by λk(G), is the minimum cardinality of all λk-cuts of G. We prove that λk(Dm,n)=k(m+n−k) for m≥n≥2 and

Spectral and pseudo-spectral Galerkin techniques, by using the standard Jacobi polynomials, are implemented to calculate numerically the solutions of pantograph type Volterra delay integro-differential equations that have kernels with the property of weak singularity. Because of the complex structure of the considered problems, pseudo-spectral Galerkin approaches are more desirable with respect to

In this paper we recover a latent advantage of WENO-Z schemes. Taking the fifth-order WENO-Z scheme for instance, we realize that the scheme can be regarded as a nonlinear combination of a five-cell stencil and three three-cell stencils. The five-cell stencil is allotted a global higher-order indicator of smoothness than three-cell stencils. Then the five-cell stencil dominates the nonlinear combination

Social networks are flooded with different pieces of emotional information, the propagation of which helps to shape the development of public sentiment. To help designing effective communication strategies during the entire development of an event, we propose an emotion-based susceptible-forwarding-immune (E-SFI) propagation dynamic model, that takes into account of the categories of emotions into

In a graph G, cardinality of the smallest ordered set of vertices that distinguishes every element of V(G) is the (vertex) metric dimension of G. Similarly, the cardinality of such a set is the edge metric dimension of G, if it distinguishes E(G). In this paper these invariants are considered first for unicyclic graphs, and it is shown that the vertex and edge metric dimensions obtain values from two

We address the problem of minimizing the sum of a nonconvex, differentiable function and composite functions by DC (Difference of Convex functions) programming and DCA (DC Algorithm), powerful tools of nonconvex optimization. The main idea of DCA relies on DC decompositions of the objective function, it consists in approximating a DC (nonconvex) program by a sequence of convex ones. We first develop

This study focuses on the fixed-time event-triggered leader-following consensus issue for nonlinear multi-agent system with uncertain disturbances. First, two distributed fixed-time controllers based on event-triggered mechanism are put forward to address this issue. Different from the existing finite-time control techniques, the proposed controller can guarantee that the settling time does not depend

An ongoing rapid development in single particle tracking techniques has opened new possibilities for analysis of particles dynamics inside living cells. Assuming that the motion is governed by a fractional Brownian motion, we have generated a synthetic video resembling a real one from an experimental video of G-proteins and coupled with them receptors inside living cells. Next, we applied Brownian

In this paper, the fault estimation problem is considered for nonlinear system with process fault, sensor fault and unknown input. A novel adjustable dimension augmented descriptor observer is designed. Based on the proposed observer, the system state, process and sensor faults can be estimated simultaneously, and the unknown input can be decoupled from the error dynamic. The observer parameters are

Let D(G) and Tr(G) be the distance matrix and diagonal matrix with vertex transmissions of a connected graph G, separately. Define matrix Dα(G) as Dα(G)=αTr(G)+(1−α)D(G), 0≤α≤1. Let Un={G|G is a simple connected graph with |V(G)|=|E(G)|=n}, Tn={T|T is a tree of order n} and their complement sets be Unc and Tnc, separately. In this paper, we generalize the conclusions in Qin et al. (2020) to Dα-matrix:

This work concentrates on addressing the sliding mode control problem of continuous-time nonlinear networked control systems. Considering the state information may not be utterly available in practice, a state observer model is designed to estimate the state information. Meanwhile, a type of discrete-time event-triggered mechanism is utilized to filter the sampled signal for reducing the occupation

The authors found a minor incorrect citation (Lemma 3.3) in their above titled paper which should be corrected in this Corrigendum.

For the non-Hermitian generalized saddle point problems, we propose a new constraint preconditioner. The new constraint preconditioner is constructed based on the preconditioned generalized shift-splitting (PGSS) iteration method. We also analyze the invertibility condition of the new preconditioner in detail. Moreover, the convergence properties of the new constraint preconditioning iteration method

In this paper, the nonsingular CUPL-Toeplitz linear system from Markov chain is solved. We introduce two fast approaches whose complexity could be considered to be O(nlogn) based on the splitting method of the CUPL-Toeplitz matrix which equals to a Toeplitz matrix minus a rank-one matrix. Finally, we confirm the performance of the new algorithms by three numerical experiments.

In this paper, we propose two models to describe the spatial dynamic of vole populations together with their finite volumes discretization. The models are based on age-structured transport equations set on a graph. The local evolution of the population occurs at the nodes, while transmission between nodes represents spatial dynamics and is a gradual process in the first model, an instantaneous one

Mathematical models for predicting the geographical distribution of areas with high rates of home burglary and numerical experiments to evaluate the effectiveness of police patrol routing strategies in reducing crime can support security policymakers in planning more effective patrol routes. We give an overview of the model formulated by Jones et al. (2010) to study the effects of the presence of law

In this article we consider an aggregate loss model with dependent losses. The loss occurrence process is governed by a two-state Markovian arrival process (MAP2), a Markov renewal process that allows for (1) correlated inter-loss times, (2) non-exponentially distributed inter-loss times and, (3) overdisperse loss counts. Some quantities of interest to measure persistence in the loss occurrence process

In this article, we propose a new family of methods, such as Jarratt, with the fifth and sixth order. This includes some popular methods as special cases. We propose four different selection for parameter matrix Tk. The main advantage of the proposed methods is that they work well for any value of parameter “a” in the first stage of iterations, while the existing methods work only for some a (2/3or1/2)

In this paper, a Cournot model and its dual Bertrand model where firms have comprehensive preferences are developed. The preference was proposed by Bowles (2004) based on the results of Rabin (1993) and Lebine (1998). Comparable static method is used to illustrate the impact of parameters on equilibrium. Three scenarios are classified by preference parameter: completely cooperative, hostile to each

The joint distribution of a geometric Brownian motion and its time-integral was derived in a seminal paper by Yor (1992) using Lamperti’s transformation, leading to explicit solutions in terms of modified Bessel functions. In this paper, we revisit this classic result using the simple Laplace transform approach in connection to the Heun differential equation. We extend the methodology to the geometric

Algebraic multigrid (AMG) is an efficient iterative method for solving linear equation systems arising from the elliptic partial differential equations. The coarsening algorithm, which determines the coarse-variable set in the classical AMG, is a critical component. This paper targets at reducing the overall solution time of the classical AMG by improving the quality of the coarse-variable set obtained