An Almost-Everywhere Solution to a Mixed Problem for One Degenerate Linear Evolution System

Siberian Mathematical Journal -     

Solution of Semi-Boundless Mixed Problem for Time-fractional Telegraph Equation

In this paper,we study the semi-boundless mixed problem for time-fractional telegraph equation.We are able to use the integral transform method(the Fourier sin and cos transforms)to obtain the solution.     

Solution of the Mixed Problem for a Third-Order Partial Differential Equation

Mathematical Notes - We consider the initial-boundary value problem for a third-order partial differential equation with highest mixed derivative. An abstract Cauchy problem for a first-order...     

膜盘联轴器非对称弯曲的一种解析解法

考虑到膜盘的内外缘的刚性远较膜面为大,并且非对称弯曲是在高速旋转运动下,而引进了中面等半径圆假设,即膜盘中面上的每个同心圆变形前后半径不变,但同心圆所在的平面各自发生了角度不同的偏转．在此基础上,通过能量变分原理,导出了相应变形的Euler方程．该方程具有首次积分,忽略一些次要项后,可得到变形的解析解．通过对双曲型面的膜盘计算表明,非对称弯曲下的八面体剪应力在径向及厚向上都变化很小,可近似认为不变,但周向上呈明显脉动变化,因此非对称弯曲对膜盘的疲劳寿命有重要影响．     

非齐次偏微分方程混合问题的形式解

通过待定函数法给出了非齐次偏微分方程混合问题的形式解，从数学角度说明了齐次化原理．     

An Improved Solution Procedure for the Scheduling Problem

Given a set of n jobs to be processed on a single machine, the problem is to find an optimal job sequence that hierarchically minimizes a bi-criterion objective function. The primary criterion is the maximum value of a general non-decreasing penalty function of job completion time, while the secondary criterion is total job flow time. An extension of Emmons's result is presented on the basis of which an improved solution procedue is developed to reduce the computational effort to find the optimal solution.     

Classical Solution to the Electropainting Problem

The mathematical modelling of the electrodeposition phenomenon leads to a linear elliptic partial differential equation subject to nonlinear evolutionary mixed boundary conditions. ln this paper, the existence, uniqueness and regularity of classical solution are proved for the electropainting problem when “dissolution current” is zero.     

Existence and Uniqueness of a Weak Solution to the Initial Mixed Boundary-Value Problem for Quasilinear Elliptic-Parabolic Equations

We prove the existence and the uniqueness of a weak solution to the mixed boundary problem for the elliptic-parabolic equation

An Iterative Method for Finding the Least Solution to the Tensor Complementarity Problem

In this paper, we are concerned with finding the least solution to the tensor complementarity problem. When the involved tensor is strongly monotone, we present a way to estimate the nonzero elements of the solution in a successive manner. The procedure for identifying the nonzero elements of the solution gives rise to an iterative method of solving the tensor complementarity problem. In each iteration, we obtain an iterate by solving a lower-dimensional tensor equation. After finitely many iterations, the method terminates with a solution to the problem. Moreover, the sequence generated by the method is monotonically convergent to the least solution to the problem. We then extend this idea for general case and propose a sequential mathematical programming method for finding the least solution to the problem. Since the least solution to the tensor complementarity problem is the sparsest solution to the problem, the method can be regarded as an extension of a recent result by Luo et al. (Optim Lett 11:471–482, 2017). Our limited numerical results show that the method can be used to solve the tensor complementarity problem efficiently.     

非均匀半平面问题的弹性力学解

本文使用非均匀平面弹性力学的基本方程,通过富氏积分变换,求得了应力函数通解。在此基础上对弹性模量E(x)=E_oexp[βx]为指数型的非均匀半平面问题,具体求得了当边界上受任意载荷作用的精确解。最后经退化处理,还得到了有名的Boussnesq解,这说明本文的方法是成功的。     

波动方程Cauchy问题的一种间接求解方法

给出一种化归方法,通过适当的手段巧妙地将求解波动方程初值问题化归为传输方程的初值问题或热传导方程的初值问题.     

A Solution to the Invariant Subspace Problem

In this paper we exhibit a Banach space X, and a continuouslinear operator T: X X, such that X has no nontrivial closedT-invariant subspace.     

A Short Solution to the Busemann-Petty Problem

A unified analytic solution to the Busemann-Petty problem was recently found by Gardner, Koldobsky and Schlumprecht. We give an elementary proof of their formulas for the inverse Radon transform of the radial function of an origin-symmetric star body .     

A Complementary Solution to the Dam Problem

This paper is concerned with the solution of the porous damproblem, as an example of an elliptic free boundary problem.We outline the main methods of solving this problem, togetherwith their drawbacks and then present a new method, a complementaryenergy approach based on a stream function formulation. Thisprovides a more satisfactory calculation of the unknown pointof contact of the free boundary with the dam wall and also adirect estimate of the "discharge" of the dam. Numerical resultsillustrating the accuracy of the method are given for homogeneousand inhomogeneous rectangular dams and an axisymmetric case.     

A Simulation Solution to the PERT Problem

The completion times of a set of paths through a PERT networkare expressed in terms of the multivariate normal distribution.The inverse transformation of the multivariate normal distribution.The inverse transformation of the multivariate normal distributionto the multivariate independent normal distribution is thenused to obtain a random sample of the completion times for theset of paths. Additional paths are introduced progressivelyuntil their contribution becomes insignificant. Economy, interms of computational load, is achieved by the need to generatethe completion times of entire paths only, and by the use ofsimulation variance reduction techniques.     

A Posteriori Error Analysis for Mixed Finite Element Solution of the Two-Dimensional Stationary Stokes Problem

In this paper we present a posteriori error estimator in a suitable norm of mixed finite element solution for two-dimensional stationary Stokes problem. The estimator is optimal in the sense that, up to multiplicative constant, the upper and lower bounds of the error are the same. The constants are independent of the mesh and the true solution of the problem.     

RESEARCH ANNOUNCEMENTS：Morrey Regularity of the Solution to the Diri

To study the local regularity of solutions to second orderelliptic partial differential equations, Morrey in ［1］ introduced somefunction spaces, which are called the Morrey spaces today. Since then, manymathematicians have studied regularities of solutions to some kinds of secondorder elliptic equations in Morrey spaces.     

三人博弈问题的模型和一种解法的修正

简要叙述了三个擂台赛博弈问题,指出解法[1]的错误所在,其一是将无限延伸的博弈树以有限的形式看待,其二是概率计算过程与结果错误,提出一种新的解法,并比较了结果的大小。