Nonlinear Double-well Schrödinger Equations in the Semiclassical Limit

We consider time-dependent Schrödinger equations with a double well potential and an external nonlinear, both local and non-local, perturbation. In the semiclassical limit, the finite dimensional eigenspace associated to the lowest eigenvalues of the linear operator is almost invariant for times of the order of the beating period and the dominant term of the wavefunction is given by means of the solutions of a finite dimensional dynamical system. In the case of local nonlinear perturbation, we assume the spatial dimension d=1 or d=2.     

The Complete Biorthogonal Expansion Theorem and Its Application to a Class of Rectangular Plate Equations

In this paper, we first establish the separable $Hamiltonian$ system of rectangular cantilever thin plate bending problems by choosing proper dual vectors. Then using the characteristics of off-diagonal infinite-dimensional $Hamiltonian$ operator matrix, we derive the biorthogonal relationships of the eigenfunction systems and based on it we further obtain the complete biorthogonal expansion theorem. Finally, applying this theorem we obtain the general solutions of rectangular cantilever thin plate bending problems with two opposite edges slidingly supported.     

基于UGC大数据挖掘的大群体两阶段风险性应急决策方法

针对在重大突发事件应急决策大数据环境下决策者偏好的不确定性及偏离群体一致性导致的风险,提出一种基于UGC大数据挖掘的大群体两阶段风险性应急决策方法。首先,通过数据挖掘和自然语言处理方法从UGC中获取公众对事件的偏好信息并构建应急决策属性体系,利用TF-IDF方法结合专家评估信息确定属性权重;其次,建立一个意见开放式的两阶段决策流程,提出依据决策者意见的可靠度和准确度量化决策风险,利用聚类方法得到相应的成员权重,并使用TOPSIS法对决策方案进行排序。最后通过天津港“8·12”重大爆炸事故的案例分析和对比验证了所提出方法的可行性和有效性。     

Critical point approaches to Gradient-Type systems on the Sierpi\'{n}ski Gasket

We investigate the existence of multiple solutions for parametric quasi-linear systems of the gradient-type on the Sierpi\''{n}ski gasket. We give some new criteria to guarantee that the systems have at least three weak solutions by using a variational method and some critical points theorems due to Ricceri. We extend and improve some recent results. Finally, we give two examples to illustrate the main results.     

Limit cycles for two classes of planar polynomial differential systems with uniform isochronous centers

In this article, we study the maximum number of limit cycles for two classes of planar polynomial differential systems with uniform isochronous centers. Using the first-order averaging method, we analyze how many limit cycles can bifurcate from the period solutions surrounding the centers of the considered systems when they are perturbed inside the class of homogeneous polynomial differential systems of the same degree. We show that the maximum number of limit cycles, $m$ and $m+1$, that can bifurcate from the period solutions surrounding the centers for the two classes of differential systems of degree $2m$ and degree $2m+1$, respectively. Both of the bounds can be reached for all $m$.     

联保贷款中的策略性违约规避机制设计

针对联保贷款的策略性违约问题,通过对其产生原因的分析以及对现有文献中解决措施的探讨,设计了一个弹性联保贷款合约。该合约的特点在于,随着企业愿意承担的连带责任的增加,企业可获得的期望收益也随之增加,旨在从正面激励企业主动为同伴承担还款责任,达到规避策略性违约的目的。通过数值分析验证了该弹性合约的特性以及适用范围。并进一步在两企业模式基础上进行拓展,讨论了多于两企业的情况下该弹性合约的适用条件。     

非线性离散微分方程的双曲函数法求解

本文推广了双曲函数方法用于求解非线性离散系统。求解离散的(2+1)维Toda系统和离散的mKdV系统，成功地得到了离散钟型孤立子、离散冲击波型孤立子及一些新的精确行波解。     

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.