Dynamic fracture analysis of an annular interfacial crack between dissimilar magnetoelectroelastic layers

Transient response of an annular interfacial crack between dissimilar magnetoelectroelastic layers under impacts is investigated. On the crack surface, magnetoelectrically impermeable boundary condition is adopted. Using Laplace and Hankel transform techniques, the mixed boundary value problem is reduced to a system of singular integral equations. The integral equations are further reduced to a system of algebraic equations with the aid of Jacobi polynomials. The dynamic field intensity factor and dynamic energy release rate are determined. Numerical results reveal the effects of electric or magnetic loadings and material parameters of composite on crack propagation and growth.     

Supercritical superprocesses: Proper normalization and non-degenerate strong limit

Suppose that X = {X_t, t≥0; P_μ} is a supercritical superprocess in a locally compact separable metric space E. Let φ0 be a positive eigenfunction corresponding to the first eigenvalue λ_0 of the generator of the mean semigroup of X. Then Mt := e~(-λ_0t)〈φ0,X_t〉 is a positive martingale. Let M_∞ be the limit of M_t. It is known(see Liu et al.(2009)) that M_∞ is non-degenerate if and only if the L log L condition is satisfied. In this paper we are mainly interested in the case when the L log L condition is not satisfied. We prove that, under some conditions, there exist a positive function γ_t on [0,∞) and a non-degenerate random variable W such that for any finite nonzero Borel measure μ on E,lim/t→∞γ_t〈φ0,X_t〉=W, a.s.-P_μ~.We also give the almost sure limit of γ_t〈f, X_t〉for a class of general test functions f.     

What are the Factors that Determine the Number of People Coming to China?

This paper studies the factors that affect people coming to China. We select the spending of United States and South Korea, GDP, railway transportation capacity of China as observations. Based on the data from 1988 to 2015, we use the ordinary least squares analysis regression model and present a most reasonable regression equation. It is found that South Korea’s spending is negative to the number of visitors, whereas the spending of US is positive. On comparing the effect of other variables, the growth of railway transportation capacity and the overseas travel expenses of South Korea or United States, have almost no significant impact on the number of people coming to China. However, as China economic growth increasing rapidly, more and more people are willing to come.     

A Consumption Behavior Model with Advertising And Word-of-Mouth Effect

It is widely-held belief that people’s consumption behavior is partly determined by advertising and word-of-mouth effect especially in monopolistic competitive market. Owing to this, we propose a mathematical model to interpret consumer behavior under the advertising and word-of-mouth effects, which is divided into continuous and discrete types for dynamic behavior analysis. Our research indicates the continuous model undergoes fold bifurcation, Hopf bifurcation, and degenerate fold-Hopf bifurcation; the discrete model undergoes flip bifurcation and Neimark-Sacker bifurcation. Moreover, bifurcation diagrams are given by using MATLAB to illustrate the model. Based on the theory of Hopf bifurcation or Flip bifurcation, the system undergoes supercritical Hopf bifurcation or Flip bifurcation under certain conditions. This lead to both advertising impacts periodically on consumer behavior, and a short-term reduction cause no effect the public¡s recognition of the brand, which can guide precision advertising investment.     

A preconditioned general two-step modulus-based matrix splitting iteration method for linear complementarity problems of H+-matrices

Numerical Algorithms - In this paper, we present a preconditioned general two-step modulus-based iteration method to solve a class of linear complementarity problems. Its convergence theory is...     

半直线上的独立随机环境中可逗留的随机游动

主要研究了在随机环境独立的情况下,右半直线上随机环境中可逗留的随机游动的常返性和非常返性.     

Estimation of partially specified spatial panel data models with random-effects

In this article, we study estimation of a partially specified spatial panel data linear regression with random-effects. Under the conditions of exogenous spatial weighting matrix and exogenous regressors, we give an instrumental variable estimation. Under certain sufficient assumptions, we show that the proposed estimator for the finite dimensional parameter is root-N consistent and asymptotically normally distributed and the proposed estimator for the unknown function is consistent and asymptotically distributed. Consistent estimators for the asymptotic variance-covariance matrices of both the parametric and unknown components are provided. The Monte Carlo simulation results verify our theory and suggest that the approach has some practical value.     

Existence Results for Fractional Order Semilinear Integro-Differential Evolution Equations with Infinite Delay

This paper is concerned with existence results of mild solutions for fractional order semilinear integro-differential evolution equations (FSIDEEs) and semilinear neutral integro-differential evolution equations (FSNIDEEs in short) with infinite delay in α-norm. Our tools include the Banach contraction principle, the nonlinear alternative of Leray–Schauder type and the Krasnoselskii–Schaefer type fixed point theorem.     

Robust adaptive synchronization of uncertain complex networks with multiple time‐varying coupled delays

In this article, the synchronization problem of uncertain complex networks with multiple coupled time‐varying delays is studied. The synchronization criterion is deduced for complex dynamical networks with multiple different time‐varying coupling delays and uncertainties, based on Lyapunov stability theory and robust adaptive principle. By designing suitable robust adaptive synchronization controllers that have strong robustness against the uncertainties in coupling matrices, the all nodes states of complex networks globally asymptotically synchronize to a desired synchronization state. The numerical simulations are given to show the feasibility and effectiveness of theoretical results. © 2014 Wiley Periodicals, Inc. Complexity 20: 62–73, 2015     

Equality of the homogeneous and the Gabor wave front set

We prove that Hörmander’s global wave front set and Nakamura’s homogeneous wave front set of a tempered distribution coincide. In addition, we construct a tempered distribution with a given wave front set, and we develop a pseudodifferential calculus adapted to Nakamura’s homogeneous wave front set.