查看更多>>摘要：The property that a nonlinear operator on a Banach space preserves an order relation, is subhomogeneous or order concave w.r.t. an order cone has profound consequences. In Nonlinear Analysis it allows to solve related equations by means of suitable fixed point or monotone iteration techniques. In Dynamical Systems the possible long term behavior of associate integrodifference equations is drastically simplified. This paper contains sufficient conditions for vector-valued Urysohn integral operators to be monotone, subhomogeneous or concave. It also provides conditions guaranteeing that these properties are preserved under spatial discretization of particularly Nystrom type. This fact is crucial for numerical schemes to converge, or for simulations to reproduce the actual behavior and asymptotics. (C) 2021 Published by Elsevier Inc.
查看更多>>摘要：A novel artificial neural network method is proposed for solving Cauchy inverse problems. Using multiple-layers network as an approximation we present a non-mesh discretization to solve the problems. The existence and convergence are shown to establish the well-posedness of neural network approximations for the Cauchy inverse problems. Numerical results on 2D to 8D cases show that compared to finite element method, the neural network approach easier extends to high dimensional case. The stability and accuracy of the proposed network approach are investigated by the experiments with noisy boundary and irregular computational domain. Our studies conclude that the neural network method alleviates the influence of noise and it is observed that networks with wider and deeper hidden layers could lead to better approximation. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The penalty projection algorithm (PP), which decouples pressure from the momentum equation of incompressible Navier-Stokes Equation (NSE), is among the most conventional approaches to simulate fluid flows. In a fluid-fluid decoupling setting, however, PP has never been employed but offers the potential for being one of the most typical candidates to compute two NSE's in each subdomain. Although pressure decoupling weakens the divergence constraint, the proposed algorithm operates with a well-known grad-div stabilization technique to retrieve this property. Theoretical and computational findings demonstrate how the proposed grad-div stabilized PP method settles concerns and outperforms when implemented with fluid-fluid decoupling. (c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The Meyer model has been successfully applied to decompose cartoon component and texture component for the gray scale image, where the total variation (TV) norm and the G-norm are respectively modeled to capture the cartoon component and the texture component in an energy minimization method. In this paper, we extend this model to the color image in the opponent color space, which is closer to human perception than the RGB space. It is important to extend the TV norm and the G-norm correspondingly because the color image is viewed as a vector-valued vector. We introduce the definition of the L-1 norm and L-infinity norm for the vector-valued vector and accordingly define the TV norm and the G-norm for the color image. In order to handle the numerical difficulty caused by the non-differentiability of the TV norm and G-norm, the dual formulations are used to represent these norm. Then the decomposition problem is reformulated into a minimax problem. A first-order primal-dual algorithm is readily applied to compute the saddle point of the minimax problem. Numerical results are shown the performance of the proposed model. (c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Individual selection, as an effective mechanism, is often used in spatial evolutionary games to promote cooperation. Previous research assumes that, individual selection usually occurs with people who fail to meet a certain criterion. However, individual selection is usually inevitable, regardless of whether players in population cooperate or defect. This paper studies the effects of wealth-based rule in costly public goods games when individual selection is inevitable. Specifically, we assume that only the top V individuals with relatively high cumulative payoffs in each group can be selected for costly PGG. The results show that when V is large, the increase of participation cost has slight inhibitory effects on the evolution of cooperation, but it alleviates the polarization of individuals. However, when V is small, the increase of participation cost within a certain range promotes cooperation prosperity, but it also causes an increase in the proportion of polarized individuals and a widening of the wealth gap between rich and poor individuals. (c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The solution to the third-kind Volterra integral equation (VIE3) usually has unbounded derivatives near the original point t = 0, which brings difficulties to numerical computation. In this paper, we analyze two kinds of modified multistep collocation methods for VIE3: collocation boundary value method with the fractional interpolation (FCBVM) and that with Lagrange interpolation (CBVMG). The former is developed based on the nonpolynomial interpolation which is particularly feasible for approximating functions in the form of t(eta) with the real number eta > 0. The latter is devised by using classical polynomial interpolation. The application of the boundary value technique enables both approaches to efficiently solve long-time integration problems. Moreover, we investigate the convergence properties of these two kinds of algorithms by Gronwall's inequality. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this article the polynomial stability for positive switching homogeneous systems with different degrees is investigated by proposing a logarithm contraction average dwell-time method. By introducing a class of logarithm contraction average dwell-time switching signals and a piecewise maximum Lyapunov function, we establish an explicit criterion for global polynomial stability of positive switching homogeneous systems whose degrees are greater than one. Especially, the main result is applicable to polynomial stability of Persidskii-type switching systems and consensus of multi-agent systems. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper introduces a C-0 weak Galerkin finite element method for a linear Cahn-Hilliard-Cook equation. The highlights of the proposed method are that the complexity of constructing the C-1 finite element space for fourth order problem is avoided and the number of degree of freedom is apparently reduced compared to the fully discontinuous weak Galerkin finite element method. With the redefined discrete weak Laplace operator and the classical C-0 Lagrange elements, the L-2 optimal error estimates in spatial variable are obtained. In time, the classical Euler scheme is then used to do the numerical simulation. Finally, numerical experiments are presented to demonstrate the efficiency of the proposed numerical method. (c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Poisson's equation has a lot of applications in various areas, such as Markov decision theory, perturbation theory, central limit theorems (CLTs), etc. Usually it is hard to derive the explicit expression of the solution of Poisson's equation for a Markov chain on an infinitely many state space. Here we will present a computational framework for the solution for both discrete-time Markov chains (DTMCs) and continuous-time Markov chains (CTMCs), by developing the technique of augmented truncation approximations. The censored Markov chain and the linear augmentation to some columns are shown to be effective truncation approximation schemes. Moreover, the convergence to the variance constant in CLTs are also considered. Finally the results obtained are applied to discrete-time single-birth processes and continuous-time single-death processes. (C) 2021 Elsevier Inc. All rights reserved.
Chellali, M.Sheikholeslami, S. M.Valenzuela-Tripodoro, J. C.Ahangar, H. Abdollahzadeh...
10页
查看更多>>摘要：A maximal double Roman dominating function (MDRDF) on a graph G = (V, E) is a function f : V(G) -> {0, 1, 2, 3} such that (i) every vertex v with f (v) = 0 is adjacent to least two vertices assigned 2 or to at least one vertex assigned 3, (ii) every vertex v with f (v) = 1 is adjacent to at least one vertex assigned 2 or 3 and (iii) the set {w subset of V vertical bar f(w) = 0} is not a dominating set of G. The weight of a MDRDF is the sum of its function values over all vertices, and the maximal double Roman domination number gamma(m)(dR)(G) is the minimum weight of an MDRDF on G. In this paper, we initiate the study of maximal double Roman domination. We first show that the problem of determining gamma(m)(dR)(G) is NP-complete for bipartite, chordal and planar graphs. But it is solvable in linear time for bounded cliquewidth graphs including trees, cographs and distance-hereditary graphs. Moreover, we establish various relationships relating gamma(m)(dR)(G) to some domination parameters. For the class of trees, we show that for every tree T of order n >= 4, gamma(m)(dR)(T) <= 5/4n and we characterize all trees attaining the bound. Finally, the exact values of gamma(m)(dR)(G) are given for paths and cycles. (C) 2021 Elsevier Inc. All rights reserved.
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