流动致振引出的非线性四阶微分方程周期解的存在性研究

流动引起的振动问题是力学上比较著名的问题。本文应用一些不动点的基本原理研究了这一问题，并给出了周期解存在性条件和尾流振动方程周期解存在的参数范围；另外，在周期解的稳定性及渐近表达方面也做了一些工作，获得一些结果．     

时滞Logistic方程与不等式解的振动性与渐近性

本文研究了时滞Ｌｏｇｉｓｔｉｃ方程与不等式关于方程平衡占的振动与非振动解的渐近性问题，得到了一些新的充分条件。本文的结果推广并改进了若干已知的定理。     

具有摄动边界薄膜振动Robin问题的可解性研究

研究了一个具有摄动边界薄膜振动的R ob in问题,利用参数变形法及问题的可解性条件,得到了该问题非退化的振动频率与振动模态.     

二阶泛函微分方程的振动性质

在本文中，我们研究了一类较广泛的二阶非线性泛函微分方程的振动性质。文中指出，在一定条件下，方程的非振动解仅有两类，而且给出了每一类非振动解存在的必要条件，同时也建立了方程振动的若干充分判据。     

一阶多时滞半线性差分方程解的振动性

本文讨论了一阶多时滞半线性和中立型差分方程解的振动性，在一定的条件下，获得了其解有振动性的一些充分条件。     

高阶泛函数方程的振动性质

本文借助于Ｌｅｂｅｓｇｕｅ测度等工具研究了一类高阶非线性泛函微分方程的振动性质。文中指出，在一定条件下，方程的排振动解仅有两类，而且给出了每一类振动解存在的必要条件，同时也建立了方程振动的若干充分判据。     

一类时滞双曲方程的振动准则

本文考虑一类滞量为连续分布型的双曲偏泛函微分方程解的振动性质，给出了这类方程在三类边值条件下解的振动准则．     

一类一阶非线性中立型微分方程的振动性

讨论了一类一阶非线性中立型微分方程的振动性问题,得到了其具有振动解的“sharp”条件.     

静水压力下压电弹性圆柱振动的主动控制

对静水压力下压电弹性层合壳的振动控制进行了研究。首先利用Hamiltion原理推导出压电弹性层合壳的非线性动力基本方程，进一步得到了静水压力作用下封闭压电弹性层合壳的动力方程。对两端简支条件下的压电弹性圆柱壳的振动问题进行了求解，并基于速度反馈控制法得到了带压电感测层／激励层的层合圆柱壳的主动控制模型，相应的数值结果表明在载荷的情况下，压电层上施加合适大小，方向的电压可以改变圆柱壳的静变形。对于系统的动力响应问题，速度反馈的增益越大，越能抑制系统在共振区的振动，验证了该控制模型抑制结构振动的有效性。     

一类具有欧拉形式的中立型微分方程的振动性

研究具有欧拉形式的无界时滞中立型微分方程解的振动性，给出了方程振动的几个充分条件。     

General necessary conditions for infinite horizon fractional variational problems

We consider infinite horizon fractional variational problems, where the fractional derivative is defined in the sense of Caputo. Necessary optimality conditions for higher-order variational problems and optimal control problems are obtained. Transversality conditions are obtained in the case state functions are free at the initial time.     

高阶微分积分方程的单调迭代法及其应用

首先利用上下解方法以及微分不等式理论给出了n阶微分积分方程的初值问题解的存在性及其单调迭代法,然后将所得结果应用到n阶微分方程的两点边值问题,得到了n阶非线性两点边值问题解的存在性及其单调迭代法,所得结果推广了已有的结果．     

On certain optimization methods with finite-step inner algorithms for convex finite-dimensional problems with inequality constraints

Numerical methods are proposed for solving finite-dimensional convex problems with inequality constraints satisfying the Slater condition. A method based on solving the dual to the original regularized problem is proposed and justified for problems having a strictly uniformly convex sum of the objective function and the constraint functions. Conditions for the convergence of this method are derived, and convergence rate estimates are obtained for convergence with respect to the functional, convergence with respect to the argument to the set of optimizers, and convergence to the g-normal solution. For more general convex finite-dimensional minimization problems with inequality constraints, two methods with finite-step inner algorithms are proposed. The methods are based on the projected gradient and conditional gradient algorithms. The paper is focused on finite-dimensional problems obtained by approximating infinite-dimensional problems, in particular, optimal control problems for systems with lumped or distributed parameters.     

一类四阶变系数振动问题的复合解

以一类斜拉索模型为背景,讨论了一类四阶变系数振动问题.用匹配法导出了方程的复合解,从而较简捷地得出了一类斜拉索的振幅的渐近表达式,并为解决相关类型的变系数问题提供了一种有效的方法.     

线性流形上次反对称矩阵逆特征值问题的最小二乘解

讨论了线性流形上次反对称矩阵逆特征值问题的最小二乘问题及其最佳逼近，给出了这些问题解的通式；并就这些问题的特殊情况进行了讨论，得到了一些结果。     

Causal transport plans and their Monge–Kantorovich problems

This paper investigates causal optimal transport problems. Within this framework, primal attainments and dual formulations are obtained under standard hypothesis, for the related variational problems. Causal transport plans are intrinsically related to martingales by a preserving property. Specific concretizations yield primal problems equivalent to several classical problems of stochastic control, and of stochastic calculus; trivial filtrations yield usual problems of optimal transport.     

Static condensation,partial orthogonalization of basis functions,and ILU preconditioning in the hp-FEM

Static condensation of internal degrees of freedom, partial orthogonalization of basis functions, and ILU preconditioning are techniques used to facilitate the solution of discrete problems obtained in the hp-FEM. This paper shows that for symmetric linear (not necessarily positive-definite) problems, under mild technical assumptions, these three techniques are completely equivalent. In fact, the same matrices can be obtained by the same arithmetic operations. The study can be extended to nonsymmetric problems naturally.     

An unified numerical approach of steady convection between two parallel plates

This paper considers the problem of laminar forced convection between two parallel plates. We present an unified numerical approach for some problems related to this case: the problem of viscous dissipation with Dirichlet and Neumann boundary conditions and the Graetz problem. The solutions of these problems are obtained by a series expansion of the complete eigenfunctions system of some Sturm-Liouville problems. The eigenfunctions and eigenvalues of this Sturm-Liouville problem are obtained by using Galerkin’s method. Numerical examples are given for viscous fluids with various Brinkman numbers.     

Solving the sum-of-ratios problems by a harmony search algorithm

The sum-of-ratios problems have numerous applications in economy and engineering. The sum-of-ratios problems are considered to be difficult, as these functions are highly nonconvex and multimodal. In this study, we propose a harmony search algorithm for solving a sum-of-ratios problem. Numerical examples are also presented to demonstrate the effectiveness and robustness of the proposed method. In all cases, the solutions obtained using this method are superior to those obtained from other methods.     

A method of convolution of Fourier expansions as applied to solving boundary value problems with intersecting interface lines

An efficient method of construction of solutions to a set of boundary value problems with additional interface conditions, more complicated boundary conditions, and so on on the basis of known solutions to classical boundary value problems is proposed. The method is based on the representation of solutions to classical and more complicated problems in the form of expansions into Fourier series with subsequent reduction of one series to the other. As a result, formulas directly expressing solutions to more complicated problems in terms of solutions to classical problems are obtained. On the basis of the well-known solution to the Dirichlet problem on a half plane, solutions to boundary value problems with interface conditions (including generalized conditions of the type of a crack and a screen) on intersecting straight lines for boundary conditions of the first and the third kind are obtained.