Energy decay result in a Timoshenko‐type system of thermoelasticity of type III with weak damping

We investigate in this paper a thermoelastic system where the oscillations are defined by the Timoshenko model and the heat conduction is given by Green and Naghdi theories. We introduce 2 new stability numbers κ₁ , κ₂, and we prove a general decay result, from which the exponential and polynomial decays are only special cases.     

Bogdanov-Takens bifurcation in a delayed Michaelis-Menten type ratio-dependent predator-prey system with prey harvesting

In this paper, we study a delayed Michaelis-Menten Type ratio-dependent predator-prey model with prey harvesting. By considering the characteristic equation associated with the nonhyperbolic equilibrium, the critical value of the parameters for the Bogdanov-Takens bifurcation is obtained. The conditions for the characteristic equation having negative real parts are discussed. Using the normal form theory of Bogdanov-Takens bifurcation for retarded functional differential equations, the corresponding normal form restricted to the associated two-dimensional center manifold is calculated and the versal unfolding is considered. The parameter conditions for saddle-node bifurcation, Hopf bifurcation and homoclinic bifurcation are obtained. Numerical simulations are given to support the analytical results.     

Energy decay rates for solutions of the wave equations with nonlinear damping in exterior domain

In this paper we study the behaviors of the energy of solutions of the wave equations with localized nonlinear damping in exterior domains.     

Convergence to nonlinear diffusion waves for solutions of Euler equations with time-depending damping

In this paper, we are concerned with the asymptotic behavior of solutions to the system of Euler equations with time-depending damping, in particular, include the constant coefficient damping. We rigorously prove that the solutions time-asymptotically converge to the diffusion wave whose profile is self-similar solution to the corresponding parabolic equation, which justifies Darcy's law. Compared with previous results about Euler equations with constant coefficient damping obtained by Hsiao and Liu (1992) [2], and Nishihara (1996) [9], we obtain a general result when the initial perturbation belongs to the same space, i.e. $H^3(\mathbb{R})\times H^2(\mathbb{R})$. Our proof is based on the classical energy method.     

相位阻尼信道条件下量子斗鸡博弈模型均衡解分析

利用量子博弈的相关理论,以噪音强度和记忆强度为参量,建立了相位阻尼信道条件下的量子斗鸡博弈模型,求出了模型的量子纳什均衡解,讨论了两参量对均衡解稳定性的影响,得出在无记忆相位阻尼信道条件下,当噪音强度小于阈值0.24时,纳什均衡仍然为帕累托最优解,当噪音强度大于0.24时,均衡解演变为另2个均衡解,不再是帕累托最优;在有记忆相位阻尼信道条件下,当噪音强度小于0.24,且记忆强度大于0.5时,均衡解是稳定的.特殊地,当信道是完全记忆时,均衡解的稳定性与噪音强度无关.     

Periodic Solutions for a Damped Rayleigh Beam Model with Time Delay

Vibrations of a beam can be described as an Euler-Bernoulli beam,or as a Rayleigh beam or as a Timoshenko beam. In this paper, we establish the existence of periodic solutions in time for a damped Rayleigh beam model with time delay, which is treated as a bifurcation parameter. The main proof is based on a Lyapunov-Schmidt reduction together with the classical implicit function theorem. Moreover, we give a sufficient condition for a direction of bifurcation.     

Optimal convergence rates to nonlinear diffusion waves for the compressible Euler-Poisson system with damping

In this work, we study the 1-D isentropic bipolar hydrodynamic model. This model takes the form of compressible Euler-Poisson system with nonlinear damping added to the momentum equations. Under some smallness conditions, the solutions to the Cauchy problem of the system globally exist and convergence to the nonlinear diffusion waves, which are the corresponding solutions of nonlinear parabolic equations given by the Darcy's law with a specified initial data. The optimal convergence rates are obtained by Green function method when the initial perturbation is in L¹-space.     

Mining Pareto-optimal modules for delayed product differentiation

This paper presents a framework for finding optimal modules in a delayed product differentiation scenario. Historical product sales data is utilized to estimate demand probability and customer preferences. Then this information is used by a multiple-objective optimization model to form modules. An evolutionary computation approach is applied to solve the optimization model and find the Pareto-optimal solutions. An industrial case study illustrates the ideas presented in the paper. The mean number of assembly operations and expected pre-assembly costs are the two competing objectives that are optimized in the case study. The mean number of assembly operations can be significantly reduced while incurring relatively small increases in the expected pre-assembly cost.     

偶阶半线性阻尼泛函微分方程的振动性

本文讨论了偶阶半线性阻尼泛函微分方程解的振动性质.利用广义Riccati变换和不等式技巧得到了所述方程的一切解均为振动的若干新的振动准则,推广和改进了一些文献中的结果.