二阶线性时滞微分方程的广义振动性

本文主要研究了二阶线性时滞微分方程的广义振动性和广义非振动性,给出了方程广义振动和广义非振动的一些判定定理,同时给出了一类方程广义非振动的充要条件.     

二阶非线性泛函微分方程解的振动性质

研究了一类二阶非线性泛函微分方程解的振动性以及非振动解的有界性.在一定条件下,建立了几个新的振动性和有界性定理,其结果推广和改进了已有的一些结果.     

圆环膜自由振动的数学模型及其若干声学特性

本文研究了圆环膜的横向自由振动.利用该振动的数学模型,得到了其形式解以及固有频率和节线的计算公式.该结果可用于涉及圆环膜振动的领域,也可以用于某些乐器.     

悬索桥竖向自由振动的传递矩阵解

该文将传递矩阵方法引入悬索桥竖向自由振动求解.首先,提出了悬索桥竖向自由振动微分方程的求解方法,由此求解方法可直接得到结构自由振动解析式.在此基础上,得出了悬索桥竖向自由振动分析的传递矩阵.应用此方法,该文研究了等截面悬索桥及变截面悬索桥竖向自由振动问题.研究结果表明,传递矩阵法能高效地进行悬索桥竖向自由振动分析,并对变截面问题的处理有独特的优势.研究工作对悬索桥在方案设计阶段的动力学分析有一定的参考价值和借鉴意义.     

脉冲中立型时滞抛物方程的振动性

本文研究了一类脉冲中立型时滞抛物方程解的振动性及强振动性,获得了此类脉冲中立型时滞抛物方程解振动和强振动的代数判据.     

三阶非线性泛函微分方程振动的比较准则

本文利用比较法,与一阶时滞微分方程的振动性相比较,研究一类三阶非线性泛函微分方程的振动性,建立该类方程振动的新比较振动准则.本文结果推广和改进了最近文献中的一些新结果.     

快速多极方法的概念性介绍

本文对快速多极方法作一概念性的非严格的描述, 该方法用来评估具有源分布的卷曲核函数.我们分别考虑了非振动核情形以及振动核情形. 对于非振动核情形, 我们概述了由Greengard 和Rokhlin 提出的经典快速多极方法的主要思想. 对于振动核情形, 我们介绍了最近由Engquist 和Ying所发展的定向快速多极方法.     

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.     

研究分子振动光谱的Fermi共振代数模型

提出了一种描述多原子分子振动能谱的Fermi共振U( 2 )代数模型 .在这一模型中 ,用U( 2 )代数描述键的振动 ,并考虑了伸缩振动和弯曲振动间的Fermi共振相互作用 .成功地把这一模型应用到H₂ O和AsH₃ 的最新观测的振动谱 ,并与其他模型的结果进行了比较 .计算结果表明代数模型能以较小的标准偏差描述分子的振动谱     

微曲输流管道振动固有频率分析与仿真北大核心CSCD

首次建立了基于Timoshenko梁理论的微曲输流管道横向振动的动力学模型,并分析了流体流动影响下微曲管道横向自由振动的固有特征.采用广义Hamilton原理,导出了考虑流体影响的微曲管道横向振动的控制方程,通过Galerkin截断对控制方程离散化,再由广义本征值问题得到管道横向振动的固有频率,并研究了液体流速和弯曲幅度对管道横向固有振动特征的影响.发展了基于等效刚度和等效阻尼方法的考虑流体影响的微曲管道振动分析的有限元仿真计算方法,并通过有限元软件实现数值仿真,验证了Galerkin截断的分析结果以及所建立的Timoshenko微曲管道动力学模型的有效性.研究表明,流体的流速以及管道的弯曲幅度对管道横向振动固有频率均有显著影响.     

New type of fixed point result of F-contraction with applications

The purpose of this paper is to prove theorem which generalize the corresponding results of Rhoades [B. E. Rhoades, Two New Fixed Point Theorems, Gen. Math. Notes, 2015, 27(2), 123--132]. This paper is to introduce the notion of dynamic process for generalized $F-$contraction mappings and to obtain coincidence and common fixed point results for such process. It is worth mentioning that our results do not rely on the commonly used range inclusion condition. We provide some examples to support our results. As an application of our results, we obtain the existence and uniqueness of solutions of dynamic programming and integral equations. Our results provide extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature.     

Steady solution of solitary wave and linear shear current interaction

The steady solution of a solitary wave propagating in the presence of a linear shear background current is investigated by the Green–Naghdi (GN) equations. The steady solution is obtained by use of the Newton–Raphson method. Three aspects are investigated; they are the wave speed, wave profile and velocity field. The converged GN results are compared with results from the literature. It is found that for the opposing-current case of the solitary wave with a small amplitude, the results of the GN equations match results from the literature well, while for the solitary wave with a large amplitude, results from the literature are seen to be not as accurate. In the following-current case, though the amplitude of the solitary wave is small, the GN results are shown to be accurate. The velocity along the water column at the wave crest and the velocity field for different cases are calculated by the GN equations. The results of the GN equations show obvious differences when compared with the results obtained by superposing the no-current results and linear shear current linearly. We find that for the same current strength, the vortex is stronger for the steep solitary-wave case than that for the small solitary-wave case.     

温度梯度对温度脉动空间关联的影响

本文给出有温度梯度时,温度脉动的空间关联函数的实验结果.同时也给出没有温度梯度时的结果.这些结果很好地表明了当没有温度梯度时,温度脉动场是各向同性的;而当有温度梯度存在时,温度脉动场具有明显的各向异性.温度脉动场沿温度梯度β方向的空间关联函数明显地大于垂直于β方向的关联.另外实验结果与D.W.Dunn和W.H.Rcid的理论结果一致.     

Nonlinear iteration method for proximal split feasibility problems

The purpose of this paper is to introduce iterative algorithm which is a combination of hybrid viscosity approximation method and the hybrid steepest‐descent method for solving proximal split feasibility problems and obtain the strong convergence of the sequences generated by the iterative scheme under certain weaker conditions in Hilbert spaces. Our results improve many recent results on the topic in the literature. Several numerical experiments are presented to illustrate the effectiveness of our proposed algorithm, and these numerical results show that our result is computationally easier and faster than previously known results on proximal split feasibility problem.     

A mixed integer linear programming formulation of the maximum betweenness problem

This paper considers the maximum betweenness problem. A new mixed integer linear programming (MILP) formulation is presented and validity of this formulation is given. Experimental results are performed on randomly generated instances from the literature. The results of CPLEX solver, based on the proposed MILP formulation, are compared with results obtained by total enumeration technique. The results show that CPLEX optimally solves instances of up to 30 elements and 60 triples in a short period of time.     

提示信息特征对秘书问题决策影响的仿真实验研究

针对具有提示信息的秘书问题,首先分析了提示信息特征变化对决策结果的可能影响.然后在此基础上,提出了在最大值标杆策略下研究提示信息的变化特征对决策结果的影响,接着阐述了仿真试验的理论假设和设计,通过仿真试验考察了提示信息的不同变化对仿真结果的影响;最后给出了对仿真结果的分析和探讨,仿真结果验证了理论假设的判断.     

On nonlinear multiple objective fractional programming involving semilocally type-I univex functions

The aim of this paper is to obtain sufficient optimality conditions for a nonlinear multiple objective fractional programming problem involving semilocally type-I univex and related functions. Furthermore, a general dual is formulated and duality results are proved under the assumptions of generalized semilocally type-I univex and related functions. Our results generalize several known results in the literature.     

Dominant eigenvalue problem for positive integral operators and its solution by Monte Carlo method

In this paper, a method of numerical solution to the dominant eigenvalue problem for positive integral operators is presented. This method is based on results of the theory of positive operators developed by Krein and Rutman. The problem is solved by Monte Carlo method constructing random variables in such a way that differences between results obtained and the exact ones would be arbitrarily small. Some numerical results are shown.     

一类Genocchi数与Riemann Zeta函数多重求和的计算公式

本文利用计算技巧建立Genocchi数Gn与Riemann Zeta函数ζ(2n)多重求和的一般结果,推广王大明,张祥德^[5]的结果。     

关于N-弱鞅和弱鞅不等式的一个注记

$N$-弱鞅($N$-demimartingales)是由Christofides引进的.Christofides指出均值为零的负相协(negatively associated)随机变量序列的部分和序列是$N$-弱鞅. 然而, 相关文献中引理2.1的证明有错误, 这就影响了其文后的结果引理2.2、定理2.1等. 在这篇注记中,修正了相关文献中的引理2.1, 作为应用, 推广了鞅和下鞅的一些结果.