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• In this paper, we used Kansa's method to solve nonlinear radiation diffusion problems. The full-implicit discretization is adopted in time, and Wendland's radial basis function is used in space. We presented two new algorithms, DL and SPI for 1D and 2D radiation diffusion problems. Both of them are efficient and accurate. Numerical experiments show that the presented algorithms can obtain small error and good numerical results for nonlinear problems. Moreover, SPI algorithm is better than DL algorithm for 1D and 2D case with the lower errors and small iteration numbers when interior points N is large. Radiation diffusion is a phenomenon of interest in the field of astrophysics, inertial confinement fusion and so on. Since it is modeled by nonlinear equations that are usually solved in complex domains, it is difficult to solve by means of finite element method and finite difference method and so on. In the paper, we will provide a kind of new fast meshfree methods based on radial basis functions. At first, the part of diffusion terms for 1D and 2D radiation diffusion equations are linearized directly on time to form the new implicit schemes, and Kansa's non-symmetric collocation method with the compactly supported radial basis function is used to solve the radiation diffusion problem. Second, the successive permutation iterative algorithms for full-implicit discretization on time are constructed furtherly, which are more efficient than the former algorithm. In the end, the accuracy and efficiency of the presented algorithms are verified by 1D and 2D numerical experiments. The new meshfree methods not only avoid the complexity of mesh generation, but also solve the radiation diffusion problem with high accuracy. [ABSTRACT FROM AUTHOR]

Given a closed linear operator A in a Banach space X and a multi-valued function with convex, closed values F : [ 0 , b ] × C ( [ - τ , 0 ] ; X ) → 2 X , we consider the Cauchy problem c D t α u ( t ) ∈ Au ( t ) + F ( t , u t ) , t ∈ [ 0 , b ] , u ( t ) = φ ( t ) , t ∈ [ - τ , 0 ] , where τ ⩾ 0 , c D t α , 0 < α < 1 , represents the regularized Caputo fractional derivative of order α . We concentrate on the case when the semigroup generated by A is noncompact and obtain nonemptyness of the solution set if, in particular, X is reflexive and F is weakly upper semicontinuous with respect to the second variable. Furthermore, in this situation topological properties of the set of all solutions are considered. [ABSTRACT FROM AUTHOR]

Abstract: A quaternion matrix A is called η-Hermitian if , where is the conjugate transpose of A. In this paper, we consider the following system of linear real quaternion matrix equations involving η-Hermicity: where Y and Z are required to be η-Hermitian. We obtain some necessary and sufficient conditions for the existence of a solution to above system, and give an expression of the general solution when the system is solvable. Our results include the main result of He and Wang (2013) [2] and other well-known results as special cases. [Copyright &y& Elsevier]

Abstract: The weighted essentially non-oscillatory (WENO) methods are a popular high-order spatial discretization for hyperbolic partial differential equations. Typical treatments of WENO methods assume a uniform mesh. In this paper, we give explicit formulas for the finite-volume, fifth-order WENO (WENO5) method on non-uniform meshes in a way that is amenable to efficient implementation. We then compare the performance of the non-uniform mesh approach with the classical uniform mesh approach for the finite-volume formulation of the WENO5 method. We find that the numerical results significantly favor the non-uniform mesh approach both in terms of computational efficiency as well as memory usage. We expect this investigation to provide a basis for future work on adaptive mesh methods coupled with the finite-volume WENO methods. [Copyright &y& Elsevier]

Abstract: Quadratic programming has been widely applied to solving real world problems. The conventional quadratic programming model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This paper discusses the interval quadratic programming problems where the cost coefficients, constraint coefficients, and right-hand sides, are represented by interval data. Since the parameters are interval-valued, the objective value is interval-valued as well. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the interval quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into conventional one-level quadratic program. Solving the pair of quadratic programs produces the interval of the objective values of the problem. An example illustrates the whole idea and sheds some light on interval quadratic programming. [Copyright &y& Elsevier]

Research on cooperative evolution behavior based on memory mechanism has been a hot topic of many scholars in recent years. However, most previous studies have considered neighbors' historical payoffs when individuals choose role models whom they will learn from, but paid less attention to the stability of neighbors' strategy which indicates how frequently they change their strategies in memory length. In this paper, we study the memory length M and the strategy persistence level u of individuals and the change rate of cooperative tendency δ on the cooperative evolution under the mixed strategy of the prisoner's dilemma. Strategy persistence level is measured by the number of times which the strategy in neighbor's memory length is continuous and consistent with neighbor's current strategy, and can determine the probability that the individual learns the neighbor's strategy when updating the strategy; the change rate of cooperative tendency δ is described by the standard deviation of the normal distribution. We investigate the effects of M and δ on the evolutionary of cooperation. The results show that the persistence strategy mechanism which we proposed in the memory length can improve network reciprocity and facilitate the generation and maintenance of cooperation, the larger the memory length is, the smaller the standard deviation value is, the more conducive to cooperation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we develop an improved version of the mapped weighted essentially non-oscillatory (WENO) method in Henrick et al. (2005) [10] for hyperbolic partial differential equations. By rewriting and making a change to the original mapping function, a new type of mapping functions is obtained. There are two parameters, namely A and k, in the new mapping functions (see Eq. (13)). By choosing and , it leads to the mapping function in Henrick et al., i.e.; the mapped WENO method by Henrick et al. actually belongs to the family of our improved mapped WENO schemes. Furthermore, we show that, when the new mapping function is applied to any th order WENO scheme for proper choice of k, it can achieve the optimal order of accuracy near critical points. Note that, if only one mapping is used, the mapped WENO method by Henrick et al., whose order is higher than five, can not achieve the optimal order of accuracy in some cases. Through extensive numerical tests, we draw the conclusion that, the mapping function proposed by Henrick et al. is not the best choice for the parameter A. A new mapping function is then selected and provides an improved mapped WENO method with less dissipation and higher resolution. [Copyright &y& Elsevier]

• The evolution of cooperation hypothesized that emotion can influence one's own willingness to change strategies is investigated. • Distinct from the traditional evolutionary model, our model hypothesized that individuals are divided into two categories, namely, non-competitive individuals and competitive individuals, and their emotion is considered quantifiable and cumulative. • The existence of non-competitive individuals has a significant positive effect on the survival of cooperators, but the presence of competitive individuals also makes non-competitive individuals much less effective in promoting cooperation. • The emotional cumulative length plays a key role in promoting overall cooperation, but surprisingly, the cooperation rate of competitive individuals peaks at an intermediate value of emotional cumulative length. Emotion emerges along with individuals' interactions, and numerous experimental studies have shown that emotion plays an important role in individual decision making. However, how emotion affects the evolution of cooperation in structured population is largely unknown. Here we introduce emotion into network reciprocity, where emotion is considered quantifiable and cumulative, and then divide individuals into two types, namely non-competitive individuals whose social value orientation is mutually beneficial and competitive individuals whose social value orientation is maximizing outcomes for the self. Here, we explore the effects of the proportion of non-competitive individuals and emotional cumulative length on the evolution of cooperation. Simulation results show that the existence of non-competitive individuals promotes cooperation in the system. Furthermore, we also find that emotional cumulative length plays a key role in promoting overall cooperation, but surprisingly, the cooperation rate of competitive individuals peaks at an intermediate value of emotional cumulative length. [ABSTRACT FROM AUTHOR]