The immune system, animal behavior and risk management

Some guiding principles in risk management are derived from the immune system and animal behavior.     

Bifurcation and synchronization of synaptically coupled FHN models with time delay

This paper presents an investigation of dynamics of the coupled nonidentical FHN models with synaptic connection, which can exhibit rich bifurcation behavior with variation of the coupling strength. With the time delay being introduced, the coupled neurons may display a transition from the original chaotic motions to periodic ones, which is accompanied by complex bifurcation scenario. At the same time, synchronization of the coupled neurons is studied in terms of their mean frequencies. We also find that the small time delay can induce new period windows with the coupling strength increasing. Moreover, it is found that synchronization of the coupled neurons can be achieved in some parameter ranges and related to their bifurcation transition. Bifurcation diagrams are obtained numerically or analytically from the mathematical model and the parameter regions of different behavior are clarified.     

Solution of Davey-Stewartson equations by homotopy perturbation method

In this paper, we extend the homotopy perturbation method to solve the Davey-Stewartson equations. The homotopy perturbation method is employed to compute an approximation to the solution of the equations. Computation the absolute errors between the exact solutions of the Davey-Stewartson equations and the HPM solutions are presented. Some plots are given to show the simplicity the method. The article is published in the original.     

The method of Kantorovich majorants to nonlinear singular integral equation with shift

The paper is concerned with the applicability of the method of Kantorovich majorants to nonlinear singular integral equation with shift. The result is illustrated in the generalized Hölder space.     

Rotational and voids effect on the reflection of P waves from stress-free surface of an elastic half-space under magnetic field and initial stress without energy dissipation

The influence of rotation, magnetic field, voids and initial stress on the reflection of P waves in thermoelasticity without energy dissipation are studied. The basic governing equations for isotropic and homogeneous thermoelastic half-space with voids, rotation, are based on Green and Naghdi (GN) theory under the effect of initial stress, where there is an initial magnetic field parallel to the plane boundary of the half-space. The solution of the problem in xz-plane indicates the existence of four plane waves; $P_1\text{;}{P}_2\text{;}{P}_3$ and $P_4$ and an SV waves. The relevant boundary conditions at stress-free insulated surface are satisfied by appropriate solutions in the half-space to obtain the reflection coefficients for the incidence of P waves. The numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effect of the rotation, magnetic field, initial stress and voids parameters.     

THE CORNER LAYER SOLUTION TO ROBIN PROBLEM FOR REACTION DIFFUSION EQUATION

A class of Robin boundary value problem for reaction diffusion equation is considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of the corner layer solution to the initial boundary value problem are studied.     

Oscillation of third-order nonlinear functional differential equations with mixed arguments

The objective of this paper is to offer sufficient conditions for the oscillation of all solutions and other asymptotic properties of the third-order nonlinear functional differential equation $$\left[a(t)\left[x''(t)\right]^{\gamma}\right]' =q(t)f \left(x\left[\tau(t)\right]\right)+p(t)h \left(x\left[\sigma(t)\right]\right)$$ with mixed arguments, where both cases ∫^∞ a ^?1/γ (s)?ds=∞ and ∫^∞ a ^?1/γ (s)?ds<∞ are dealt with. We deduce properties of the studied equations via new comparison theorems. Our results essentially improve and complement earlier ones. We also repair one interesting result of Grace et al.     

二阶非线性扰动偏微方程的振荡解（英）

Conditions are given on the hunctions f, g, h,p and q which imply that allcontinuable solutions of are abounded as well as oscillatory on the interval [t₀,∞), t₀> 0.     

任意随机变量序列关于随机选择的一类强偏差定理

本文通过引进极限相对对数似然比,利用限制似然比给出了样本空间的一个子集,得到了任意实值随机变量序列关于随机选择的一类用不等式表示的强极限定理.并作为推论得到了任意整值随机变量序列的m元序组的强偏差定理.     

RESPONSE OF MICROPOLAR THERMOELASTIC SOLID WITH VOIDS DUE TO VARIOUS SOURCES UNDER GREEN NAGHDI THEORY

Green-Naghdi (G-N) theory of thermoelasticity is employed to study the deformation of micropolar thermoelastic solid with voids considering the influence of varions sources acting on the plane surface....