利用场耦合理论研究开放微波谐振腔

利用电磁场的等效原理，将一个开放微波腔等效于一个闭合边界微波腔（即封闭微波腔）和开放边界（即行波吸收边界）两部分，然后利用等效封闭微波腔的本征模式及其与开放边界的耦合，建立了关于开放微波腔模式（即模式场分布、频率、品质因子）的耦合方程组，其中开放边界为行波吸收边界.以X波段六腔渡越振荡管为例进行分析，将该振荡管等效为封闭微波腔和同轴输出结构两部分，用SUPPERFISH获得封闭腔的各个模式场分布及频率，然后根据封闭微波腔与开放边界的耦合，求得六腔渡越振荡管的工作模频率为9.25GHz，品质因子为115.2，与实验测量结果基本符合.     

Maximizing the Product of Two Linear Functions In 0-1 Variables

We study both the continuous and discrete problems of maximizing the product of two linear functions subject to all variables being between 0 and 1. We first give linear and low-order polynomial algorithms for the solution of the continuous problem. In addition, we describe penalties that help to fix variables in the discrete problem. Extensive computational tests demonstrate the effectiveness of these results.     

Relaxation of variational problems in two-dimensional nonlinear elasticity

Consider a plate occupying in a reference configuration a bounded open set Ω ⊂ ℝ ² , and let be its stored-energy function. In this paper we are concerned with relaxation of variational problems of type:

解与HJB方程相关的拟变分不等式的松弛法

本文对关于HJB方程的拟变分不等式提出了松弛算法，也给出了基于上述算法的区域分解方法，并建立了相应的收敛性定理。     

General decay of solutions in one-dimensional porous-elastic system with memory

In this work we consider a one-dimensional porous-elastic system with memory effects. It is well-known that porous-elastic system with a single dissipation mechanism lacks exponential decay. In contrary, we prove that the unique dissipation given by the memory term is strong enough to exponentially stabilize the system, depending on the kernel of the memory term and the wave speeds of the system. In fact, we prove a general decay result, for which exponential and polynomial decay results are special cases. Our result is new and improves previous results in the literature.     

Relaxation oscillations in a slow–fast modified Leslie–Gower model

In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result.     

Dynamics of A Damping Oscillator with Impact and Impulsive Excitation

There exist many types of external excitations that make the damping oscillator with impact have complex dynamics. In this study, both external impulsive excitation and impact are considered to construct a vibro-impact system. The fixed time pulse (impulsive excitation) and the state pulse (impact) lead to the complex and interesting dynamics. The conditions of the existence and stability of four kinds of periodic solutions are investigated, and the bifurcations of period-(1, 0) and period-(1, 1) solutions are analytically studied. Numerical simulations on periodic solutions and bifurcation diagrams are shown by the illustrative example.     

Relaxation oscillations and canard explosion in a predator–prey system of Holling and Leslie types

We give a geometric analysis of relaxation oscillations and canard cycles in a singularly perturbed predator–prey system of Holling and Leslie types. We discuss how the canard cycles are found near the Hopf bifurcation points. The transition from small Hopf-type cycles to large relaxation cycles is also discussed. Moreover, we outline one possibility for the global dynamics. Numerical simulations are also carried out to verify the theoretical results.