两个垂直圆柱在水波中的水动力相互作用

基于线性势流理论研究了两个垂直圆柱在水波中的水动力相互作用．两个圆柱中的一个固定在底部，另一个铰接在底部且可以在入射波方向以小振幅振动．本文研究了绕射波和辐射波，运用加法定理得到了每个圆柱表面速度势的简单的解析表达式，用级数形式显式表示了圆柱上的波浪激励力和力矩及振动圆柱的附加质量和辐射阻尼系数．级数的系数由代数方程组的解决定．给出了一些数值例子以说明诸如间距、圆柱的相对大小、入射角等各种参数对一阶力、定常二阶力、附加质量和辐射阻尼系数以及振动圆柱的响应等的影响．     

奇异值函数的二阶方向导数

本文用一个直接的方法给出了奇异值函数的二阶方向导数公式. 作为应用, 利用这一公式建立了谱范数的上图集合与核范数的上图集合的切锥和二阶切集的具体表达式, 这些表达式在矩阵优化的一阶和二阶最优条件的研究中起着重要作用.     

发展流动与形成流动

本文着重研究振荡状态下的管流问题.从基本的Navier-Stokes方程出发,进行线性化之后采用虚宗量Bessel函数的方法求解,得出了一组描述圆管振荡状态下发展流动的速度分布、压力分布公式.它们较之Atabek等人推导的公式更为简明和易于计算.并且,在相同的条件下简化为形成流动的表达式后,两者的公式完全一致.数值计算还表明,本文公式的理论结果无论是和Atabek等人的理论计算结果比较,还是和他们的实验结果比较,都是相当一致的.     

积商求导公式与微分方程求解

对一些特殊类型的一阶或二阶微分方程,从其结构特点出发,联系积商求导公式,可减少求解步骤并降低计算量.     

关于二层海中的二阶波浪绕射问题*

在本文中,我们用二层海模型,探讨了层化海洋中任意三维物体的二阶波浪绕射问题,给出了多色波场中二阶波浪散射势边值问题的数学提法以及基于一个弱的远场辐射条件下解的表式。同时,利用Green定理,并通过引入一个辅助势函数,我们导出了结构所受二阶波浪荷载的积分表式。结果表明,海水的层化特性对结构物所受之二阶差频波浪荷载可能具有显著的影响。     

多目标规划局部有效解的二阶条件

最优性条件的研究一直是多目标规划理论的一个热点,关于有效解的一阶最优性条件的研究,已有大量的文献涌现.可是关于有效解的二阶条件,其研究结果寥寥无几.分析其原因,恐怕主要有两方面.其一,绝大多数多目标优化方法还是基于先将问题标量化,然后借用线性规划或非线性规划中已有的一些成熟的方法来求解,这些方法中的一部分对二阶条件不作任何要求;其二,二阶条件的讨论需要更多的分析工具和更精致的分析     

二维瞬态热传导问题的无单元Galerkin法分析

采用无单元Galerkin(element-free Galerkin,EFG)法求解具有混合边界条件的二维瞬态热传导问题.首先采用二阶向后微分公式离散热传导方程的时间变量,将该问题转化为与时间无关的混合边值问题;然后采用罚函数法处理Dirichlet边界条件,建立了二维瞬态热传导问题的无单元Galerkin法;最后基于移动最小二乘近似的误差结果,详细推导了无单元Galerkin法求解二维瞬态热传导问题的误差估计公式.给出的数值算例表明计算结果与解析解或已有数值解吻合较好,该方法具有较高的计算精度和较好的收敛性.     

巧用乘法公式解题

乘法公式是《整式的乘除》中的重要内容,在初中代数里有很广泛的应用,在一些竞赛试题中也是常考的热门内容,其题目形式多样,技巧性强,解题时应根据题目的结构特征,选择乘法公式恰当地变形,或是对题目条件进行灵活的处理,化繁为简,或是将题目转化为熟悉的形式,从而达到求解的目的,本文通过一些典型的习题,介绍利用乘法公式处理这些题目的一些常见技巧,帮助大家总结和积累解题的方法.     

多重改良Logistic模型在磷酸电位滴定的离解平衡常数计算中的应用

基于磷酸电位滴定实验常用切线法、一阶微商法及二阶微商内插法等进行实验数据处理并计算磷酸离解平衡常数的烦琐与不准确性,提出一种与实验数据有高度吻合性的多重改良Logistic模型,应用优化求解得最佳函数表达式,解此函数一阶导数极大值点并计算得磷酸滴定半中和点,结合离解平衡常数校正公式最终得出了磷酸的离解平衡常数的各级pKa值,与文献结果相一致.另外,减少部分实验数据后应用模型处理并计算pKa值,所得结论仍具有一致性,从而提高了实验效率。     

高阶导数的一个极限表达式

通过对二阶微分问题的求解与推广,给出求解高阶导数的极限表达式．这也是差分法的一个推广．     

The existence of a generalized fourier transform for a solution as a radiation condition for a class of problems generalizing oscillation excitation problems in regular waveguides

For a second-order inhomogeneous differential equation defined on the real axis and such that its right-hand side and solutions are functions in a Hilbert space, it is shown that the existence of a generalized Fourier transform of the solution is a correct radiation condition if the right-hand side is sufficiently smooth and compactly supported.     

Some results on pointwise second-order necessary conditions for stochastic optimal controls

The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms. When the control region is convex, a pointwise second-order necessary condition for stochastic singular optimal controls in the classical sense is established; while when the control region is allowed to be nonconvex, we obtain a pointwise second-order necessary condition for stochastic singular optimal controls in the sense of Pontryagin-type maximum principle. It is found that, quite different from the first-order necessary conditions, the correction part of the solution to the second-order adjoint equation appears in the pointwise second-order necessary conditions whenever the diffusion term depends on the control variable, even if the control region is convex.     

SINE TRANSFORM PRECONDITIONERS FOR SECOND-ORDER PARTIAL DIFFERENTIAL EQUATIONS

In this paper, we are concerned with the numerical solution of second-order partial differential equations. We analyse the use of the Sine Transform precondilioners for the solution of linear systems arising from the discretization of p.d.e. via the preconditioned conjugate gradient method. For the second-order partial differential equations with Dirichlel boundary conditions, we prove that the condition number of the preconditioned system is O(1) while the condition number of the original system is O(m 2) Here m is the number of interior gridpoints in each direction. Such condition number produces a linear convergence rale.     

Problems of the theory of generalized Newtonian fluids with dissipative potential of subquadratic growth

Two-dimensional boundary-value problems describing a slow stationary flow of Newtonian fluid are considered in the case where the dissipative potential is of power growth close to 2. The regularity of this problem is investigated under the condition that the dissipative potential depends only on the module of the strain velocity tensor. The integrability of the second-order derivatives of the solution is established near a plane part of the boundary. The Hölder continuity of the strain velocity tensor is also proved. Bibliography: 8 titles.     

Convergence of Rothe scheme for a class of dynamic variational inequalities involving Clarke subdifferential

In the first part of the paper we deal with a second-order evolution variational inequality involving a multivalued term generated by a Clarke subdifferential of a locally Lipschitz potential. For this problem we construct a time-semidiscrete approximation, known as the Rothe scheme. We study a sequence of solutions of the semidiscrete approximate problems and provide its weak convergence to a limit element that is a solution of the original problem. Next, we show that the solution is unique and the convergence is strong. In the second part of the paper, we consider a dynamic visco-elastic problem of contact mechanics. We assume that the contact process is governed by a normal damped response condition with a unilateral constraint and the body is non-clamped. The mechanical problem in its weak formulation reduces to a variational–hemivariational inequality that can be solved by finding a solution of a corresponding abstract problem related to one studied in the first part of the paper. Hence, we apply obtained existence result to provide the weak solvability of contact problem.     

薄层流中的一类三阶奇摄动边值问题的渐近分析

本文研究薄层流中出现的一类三阶奇摄动数学模型．本文不采用研究其渐近等价的二阶奇摄动微分方程的方法,而利用边界层函数法,直接讨论该数学模型的渐近解,并严格地证明了解的存在唯一性和其渐近解的一致有效性．本文的结果不仅去掉了以往方法所必须的位势条件,纠正了某个不适定的假设,而且推广了以往的结果．     

Dynamic contact problem for viscoelastic piezoelectric materials with normal damped response and friction

In this paper, we deal with a class of inequality problems for dynamic frictional contact between a piezoelectric body and a foundation. The model consists of a system of the hemivariational inequality of hyperbolic type for the displacement, the time dependent elliptic equation for the electric potential. The contact is modeled by a general normal damped response condition and a friction law, which are nonmonotone, possibly multivalued and have the subdifferential form. The existence of a weak solution to the model is proved by embedding the problem into a class of second-order evolution inclusions and by applying a surjectivity result for multivalued operators.     

Explosion time of second-order Ito processes

In this paper a sufficient condition is given for the existence of the global solution as is a sufficient condition for the non-existence of the global solution of the second-order stochastic differential equation with the random disturbance of the so-called white noise.     

Log-Sigmoid nonlinear Lagrange method for nonlinear optimization problems over second-order cones

This paper analyzes the rate of local convergence of the Log-Sigmoid nonlinear Lagrange method for nonconvex nonlinear second-order cone programming. Under the componentwise strict complementarity condition, the constraint nondegeneracy condition and the second-order sufficient condition, we show that the sequence of iteration points generated by the proposed method locally converges to a local solution when the penalty parameter is less than a threshold and the error bound of solution is proportional to the penalty parameter. Finally, we report numerical results to show the efficiency of the method.