On the vibrations of lumped parameter systems governed by differential-algebraic equations

In this paper, we consider the vibratory motions of lumped parameter systems wherein the components of the system cannot be described by constitutive expressions for the force in terms of appropriate kinematical quantities. Such physical systems reduce to a system of differential-algebraic equations, which invariably need to be solved numerically. To illustrate the issues with clarity, we consider a simple system in which the dashpot is assumed to contain a “Bingham” fluid for which one cannot describe the force in the dashpot as a function of the velocity. On the other hand, one can express the velocity as a function of the force.     

Kerr度规的解析推导

通过直接求解Emst方程,给出了Kerr度规的解析推导。     

A methodology for character recognition and revision of the linear equations solving procedure

Linear equations are valuable for real-world modeling phenomena involving at least one variable. However, verifying if the procedure followed by a human for solving a linear equation was done correctly is still a complicated matter. In this paper, we propose a methodology for the automatic character recognition and revision of the solving procedure of linear equations with one unknown. First, a camera is used to acquire an image of the handwritten solving procedure. Then, the image is pre-processed, and each character and equation lines are segmented. Subsequently, a convolutional neural network (CNN) is used to conduct the character recognition stage. Finally, a comparison rule is applied to revise the solving procedure. The character recognition was verified on a 2800 image data set (2100 for training and 700 for testing), including the ten digits and four symbols: ×, +, -, /. The revision procedure was tested on a data set with 140 handwritten equations (125 for training and 15 for testing). The results revealed that we recognized handwritten characters with an accuracy of 99%, which is similar to the state-of-the-art. Moreover, our proposal revised the solving procedure with an efficiency of 86.66%.     

混合单调算子方程组解的存在唯一性

利用非线性泛函分析中的锥与半序理论和单调迭代技巧,讨论几类混合单调算子方程组解的存在性和唯一性,对每类算子方程组都给出了几种迭代序列,并研究了各种迭代序列收敛于算子方程组解的误差估计．所得结果改进和拓展了混合单调算子方程的某些相应结果,在非线性泛函分析理论中具有重要意义     

一类相轨线方程

本文论述了一类二阶系统的相轨线方程满足一定条件时,对应的曲线是封闭曲线。给出根据相轨线方程判断微分方程组存在周期解的方法。     

Banach空间的非线性微分方程与积分微分方程

本文在实Banach空间E中考虑非线性微分方程的Cauchy问题：及非线性Volterra型积分微分方程的初值问题其中：利用较α—Lipschitz非紧性条件弱的一般非紧性条件及NONCH不动点定理证明了问题（Ⅰ）及（Ⅱ）的解的存在性。对于Cauchy问题（Ⅰ）,本文降低了文[4]冲关于f一致连续性要求。对于（Ⅱ）,放宽了文[2]中的非紧性条件。     

方棋盘上两个互补棋盘棋子多项式之间的关系探析

分析了方棋盘上禁位排列数问题,给出了完整方棋盘的棋子多项式,得出了几枚棋子在互补棋盘上禁位排列数的相互表示,并找到一对存在相互正交关系的组合数列．     

Numerical simulation and experimental investigation of 3-D separated flow field around a blunt body

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关于卡斯猜想的推广形式

研究了亻路卡斯猜想的推广形式,获得了幂和丢番图方程Ｓ２（ｘ）＝ｙｎ有正整数解的充要条件,证明了当ｎ＝３,５和ｎ≥４为偶数时,该方程仅有平凡解（ｘ,ｙ）＝（１,１）．     

中立型泛函微分方程的(A,B,D) —方法(英文)

本文构造了求解volterra中立型泛函徽分方程初值问题的一般多值方法-(A,B,D)方法、讨论了它的存在性和唯一性.