摆动水翼的推力与流场结构数值研究

在一定的Reynolds数范围内,水生动物和微型仿生机械通常采用摆动的方式获得推力,这种摆动可以用行进波来表示,行进波的波长则描述了摆动生物的柔性．该文用浸入边界方法模拟了低Reynolds数情况下,水翼NACA-65-010在水中摆动时的流场．结果表明,水翼摆动产生推力的大小与行进波波长密切相关,随着波长的增大,推力系数减小,推进效率则在一定的波长值达到最大;推力的产生与两种流场结构有关:即反Krmn涡街和涡对,摆动水翼后缘尾迹中形成反Krmn涡街时产生的推力要大于尾迹中形成涡对产生时的推力．     

1:1内共振条件下矩形薄板的全局分叉和多脉冲混沌动力学

首次利用广义Melnikov方法研究了一个四边简支矩形薄板的全局分叉和多脉冲混沌动力学．矩形薄板受面外的横向激励和面内的参数激励．利用von Krmn模型和Galerkin方法得到一个二自由度非线性非自治系统用来描述矩形薄板的横向振动．在1∶1内共振条件下,利用多尺度方法得到一个四维的平均方程．通过坐标变换把平均方程化为标准形式,利用广义Melnikov方法研究该系统的多脉冲混沌动力学,并且解释了矩形薄板模态间的相互作用机理．在不求同宿轨道解析表达式的前提下,提供了一个计算Melnikov函数的方法．进一步得到了系统的阻尼、激励幅值和调谐参数在满足一定的限制条件下,矩形薄板系统会存在多脉冲混沌运动．数值模拟验证了该矩形薄板的确存在小振幅的多脉冲混沌响应．     

给定染色数的无符号Laplace谱半径

设Gkn(k≥2)为n阶的染色数为k的连通图的集合.本文确定了Gkn中具有极大无符号Laplace谱半径的图,即k=2时为完全二部图,k≥3时为Turn图.本文也讨论了Gkn中的具有极小无符号Laplace谱半径的图,对k≤3的情形给出了此类图的刻画.     

微极液体在两个多孔圆盘间的MHD流动及其热传导

两个平行的无限大多孔圆盘,圆盘表面有均匀注入时,数值地研究圆盘间不可压缩导电微极流体,在横向外加磁场作用下的轴对称稳定层流.运用von Krmn的相似变换,将非线性运动的控制方程转化为无量纲形式.使用基于有限差分格式的算法,在相应的边界条件下,求解简化后耦合的常微分方程组.讨论Reynolds数、磁场参数、微极参数和Prandtl数,对流动速度和温度分布的影响.在特殊情况下,所得结果与已有文献的工作有着很好的一致性.研究表明,圆盘表面的传热率随着Rynolds数、磁场参数和Prandtl数的增加而增加;剪切应力随着注入的增加而减少,但它随着外部磁场的加强而增加.和Newton流体相比较,微极流体的剪切应力因素较弱,有利于聚合体加工过程中流动和温度的控制.     

保域上立方幂等矩阵的线性映射

设F是一个特征不为2及3的域，M．(F)记F上n阶全矩阵代数．本文在n≤m时得到了从M．(F)到Mm(F)的保立方幂等矩阵的线性映射的形式．作为应用又确定了保群逆线性映射形式．     

例谈应用导数证明不等式的解题策略

<正>函数与不等式结合的问题,通常应用导数对函数单调性进行判断,转化为函数最值问题,进而求解．下面结合一道函数不等式问题,谈谈应用导数证明不等式的解题策略．题目(2018年海淀期中文科20)已知函数f(x)=(x²-x)lnx．(Ⅰ)求证:1是函数f(x)的极值点;(Ⅱ)设g(x)是函数f(x)的导函数,求证:g(x)>-1．解析第(Ⅰ)问比较基础,证明留给读者自行完成．下文使用五种方法就第(Ⅱ)问的解答进行分析．     

线性模型下F-检验最优的误差协方差结构

文献中回归参数线性假设的F-检验统计量主要包括基于广义最小二乘估计F- 统计量F(θ),基于最小二乘估计的F-统计量FLSE以及Wu C．F．J．等于1988年提出的调整的F-统计量FA(θ)．其中后两者因形式简单而常常被广泛采用．本文主要研究了FA(θ)和FLSE的最优性,并分别获得了FA(θ)=F(θ)和ELSE=F(θ)的充要条件．最后,我们将所得的结果应用到医药领域的两类重要模型．     

一个不等式的推广及应用

最近文[2]给出了此不等式的一些应用．本文首先给出(2)的一个推广，然后给出推广结果的一些应用．     

对称自正交相似矩阵逆特征值问题的推广

1引言对称自正交相似矩阵在结构力学、土木工程、数值分析等方面有实际应用,不少问题中常会遇到其逆特征值同题,研究它是有应用价值的．记(?)其中E=E_m(m阶单位阵)．容易验证1)T_k(E)·T_k(E)=E_(km)．2)T′_k(E)=T_k(E),其中T′_k(E)表示T_k(E)的转置．3) (?)其中k∈N(自然数)．令(?)当m=1时,T_k(E)就是k阶反序单位矩阵,即文[1]的(1)和(2)．定义1．1设A∈R~(2km×2km)满足SAS′=A,A′=A,则称A为对称自正交相似矩     

关于交换群上的Cayley有向图的正规性

Cayley有向图X=Cay(G,S)叫做正规的,如果G的右正则表示R(G)在X的全自同构群Aut(X)中正规,我们定出了交换群上的小度数的非正规的Cayley有向图, 并给出了一个猜想．应用这个结果,给出了pn(n≤2)个点上的度数不超过3的有向对称图的分类,这里p是一个奇素数．     

微极流体在两个伸展平面之间的不稳定轴对称MHD流动

研究在两个径向伸展的平面之间,微极流体作随时间变化的磁流体动力学(MHD)流动.考虑了高浓度微元(n=0)和低浓度微元(n=0.5)两种情况.使用恰当的变换,将偏微分方程转换为常微分方程.用同伦分析法(HAM),对变换后的方程求解.给出不同参数下,角速度、表面摩擦因数和面应力偶系数的图形结果.     

Three-webs defined by a system of ordinary differential equations

We consider a three-web W(1, n, 1) formed by two n-parametric family of curves and one-parameter family of hypersurfaces on a smooth (n + 1)-dimensional manifold. For such webs, the family of adapted frames is defined and the structure equations are found, and geometric objects arising in the third-order differential neighborhood are investigated. It is showed that every system of ordinary differential equations uniquely defines a three-web W(1, n, 1). Thus, there is a possibility to describe some properties of a system of ordinary differential equations in terms of the corresponding three-web W(1, n, 1). In particular, autonomous systems of ordinary differential equations are characterized.     

Numerical method of solution to loaded nonlocal boundary value problems for ordinary differential equations

A numerical method is suggested for solving systems of nonautonomous loaded linear ordinary differential equations with nonseparated multipoint and integral conditions. The method is based on the convolution of integral conditions into local ones. As a result, the original problem is reduced to an initial value (Cauchy) problem for systems of ordinary differential equations and linear algebraic equations. The approach proposed is used in combination with the linearization method to solve systems of loaded nonlinear ordinary differential equations with nonlocal conditions. An example of a loaded parabolic equation with nonlocal initial and boundary conditions is used to show that the approach can be applied to partial differential equations. Numerous numerical experiments on test problems were performed with the use of the numerical formulas and schemes proposed.     

不确定微分方程的数值解法及其应用研究

不确定微分方程广泛应用于不确定财政、不确定控制、不确定微分博弈等领域。由于一些不确定微分方程解析解难以实现,本文首先研究了不确定微分方程的Euler方法和Runge-Kutta方法两种数值解法,并进行误差分析。通过比较随机领域Black-Scholes模型和不确定领域Liu模型的欧式期权定价公式,验证不确定微分方程描述证券市场的合理性和实用性。     

Differential equations on variable time scales

We introduce a class of differential equations on variable   time scales with a transition condition between two consecutive parts of the scale. Conditions for existence and uniqueness of solutions are obtained. Periodicity, boundedness and stability of solutions are considered. The method of investigation is by means of two successive reductions: B$B$-equivalence of the system [E. Akalín, M.U. Akhmet, The principles of B-smooth discontinuous flows, Computers and Mathematics with Applications 49 (2005) 981–995; M.U. Akhmet, Perturbations and Hopf bifurcation of the planar discontinuous dynamical system, Nonlinear Analysis 60 (2005) 163–178; M.U. Akhmet, N.A. Perestyuk, The comparison method for differential equations with impulse action, Differential Equations 26 (9) (1990) 1079–1086] on a variable time scale to a system on a time scale, a reduction to an impulsive differential equation [M.U. Akhmet, Perturbations and Hopf bifurcation of the planar discontinuous dynamical system, Nonlinear Analysis 60 (2005) 163–178; M.U. Akhmet, M. Turan, The differential equations on time scales through impulsive differential equations, Nonlinear Analysis 65 (2006) 2043–2060]. Appropriate examples are constructed to illustrate the theory.     

Theory of Differential Inequalities for Two-Point Boundary Value Problems and their Applications to Three-Point B.V.Ps Associated with n th Order Non-Linear System of Differential Equations

This paper presents a theory of differential inequalities for two-point boundary value problems (B.V.Ps) associated with the system of n th order non-linear differential equations. Using these inequalities as a tool we establish the existence and uniqueness of solutions to three-point B.V.Ps associated with the system of n th order non-linear differential equations by using the idea of matching solutions.     

扩充偏微分方程(组)守恒律和对称的辅助方程方法及微分形式吴方法的应用

首先,我们给出了引入伴随方程(组)扩充原方程(组)的策略使给定偏微分方程(组)的扩充方程组具有对应泛瓯即,成为Lagrange系统的方法,以此为基础提出了作为偏微分方程(组)传统守恒律和对称概念的一种推广-偏微分方程(组)扩充守恒律和扩充对称的概念;其次,以得到的Lagrange系统为基础给定了确定原方程(组)扩充守恒律和扩充对称的方法,从而达到扩充给定偏微分方程(组)的首恒律和对称的目的;第三,提出了适用于一般形式微分方程(组)的计算固有守恒律的方法;第四,实现以上算法过程中,我们先把计算(扩充)守恒律和对称问题均归结为求解超定线性齐次偏微分方程组(确定方程组)的问题.然后,对此关键问题我们提出了用微分形式吴方法处理的有效算法;最后,作为方法的应用我们计算确定了非线性电报方程组在内的五个发展方程(组)的新守恒律和对称,同时也说明了方法的有效性.     

热交换多孔圆盘间三阶流体的MHD轴对称流动

在两个具有热交换可渗透的多孔圆盘之间,研究三阶流体的磁流体动力学(MHD)流动.通过适当变换,将偏微分的控制方程转换为常微分方程.采用同伦分析法(HAM)求解转换后的方程.定义了均方残余误差的表达式,并选择了最佳的、收敛的控制参数值.检测了无量纲参数变化时的无量纲速度和温度场.列表显示表面摩擦因数和Nusselt数,并分析了无量纲参数的影响.     

Complex Lie symmetries for scalar second-order ordinary differential equations

A scalar complex ordinary differential equation can be considered as two coupled real partial differential equations, along with the constraint of the Cauchy–Riemann equations, which constitute a system of four equations for two unknown real functions of two real variables. It is shown that the resulting system possesses those real Lie symmetries that are obtained by splitting each complex Lie symmetry of the given complex ordinary differential equation. Further, if we restrict the complex function to be of a single real variable, then the complex ordinary differential equation yields a coupled system of two ordinary differential equations and their invariance can be obtained in a non-trivial way from the invariance of the restricted complex differential equation. Also, the use of a complex Lie symmetry reduces the order of the complex ordinary differential equation (restricted complex ordinary differential equation) by one, which in turn yields a reduction in the order by one of the system of partial differential equations (system of ordinary differential equations). In this paper, for simplicity, we investigate the case of scalar second-order ordinary differential equations. As a consequence, we obtain an extension of the Lie table for second-order equations with two symmetries.