Hanoi塔问题的一个公式解

Hanoi塔问题自提出以来已有一百多年的历史.其间,这一问题吸引了许多的研究者.正如H.A.Simon所指出的,Hanoi塔问题对于认知科学就象大肠杆菌对现代基因学那样,是一个无价的研究标本.事实上,它已成为组合数学,人工智能,计算机科学以及规划等中的递归问题的典型例子,并由此产生了各种各样成熟的算法.回顾这些结果,我们提出一个基本问题能否对Hanoi塔问题给出一个公式解?本文就此给出了一个肯定的回答.在我们的研究中,图论将是一个有力的工具     

关于Petrich和Reilly的一个问题

本文研究了M.Petrich和N.R.Reilly的一个公开问题:即整体关系的下运算是否为一个完全同态.利用Clifford半群上的同余刻画,得到了该运算不是一个∩-同态.从而解决了上述公开问题.     

一类两个边界带特征参数的不连续四阶微分算子的自共轭性

本文研究了一类具有特殊转移条件且两个边界条件中带有特征参数的四阶微分算子的自共轭性问题.建立了一个与其相关的新的空间H,将上述问题的研究转化为对此空间中一个线性算子A的研究.     

关于H.Fujimoto一个结果的改进

本文研究了权分担一个公共值集的亚纯函数唯一性问题.利用值分布理论,获得了一个唯一性定理,所获结论改进了H.Fujimoto的一个结果.     

2016年全国研究生数学建模竞赛E题赛题点评

首先阐明了2016年全国研究生数学建模竞赛E题"粮食最低收购价政策问题研究"的研究背景和问题研究的实际意义.接着,针对每一个问题,从研究思路、研究方法、研究结论等方面均作了详细的叙述.最后,对学生论文中出现的问题、难点以及创新性等方面做了点评.     

从问题研究入手 立足问题解决

在解析几何复习课上,同学们与我一道从一个简单的题目入手,进行问题研究,得出一般性结论,既解决了问题,同时也向同学们展示了一个问题发现、研究、解决的过程,有效地提高了课堂效率.     

区间AHP权重计算的目标规划法

本文对区间 AHP的权重计算问题进行了研究 ,给出了几种新的权重计算方法 .每种方法求解一个线性目标规划问题得到各方案的区间权重 .文章最后给出了一个算例 .     

一个非线性方程转向点问题

本文讨论了一个非线性方程的转向点问题 .研究了转向点的所处位置 ,以及问题解的渐近性态 .     

带约束导数值域的L逼近

1972年J.A.Roulier和G.D.Taylor研究了带约束导数值域的一致逼近,在文章最后,他们提出了一个未解决的问题,就是关于带约束导数值域的L逼近问题.本文研究了这个问题,得到与[1]平行的结果.这个结果同时也推广了 R.A.Lorentz的工作. 第一节给出存在定理,第二节证明若干特征定理,第三节给出一个唯一性定理.     

非光滑非线性互补问题的牛顿法

研究了非光滑的非线性互补问题. 首先将非光滑的非线性互补问题转化为一个非光滑方程组,然后用牛顿法求解这个非光滑方程组. 在该牛顿法中,每次迭代只需一个原始函数B-微分中的一个元素. 最后证明了该牛顿法的超线性收敛性.     

The optimal solution of multi-kernel regularization learning

In regularized kernel methods, the solution of a learning problem is found by minimizing a functional consisting of a empirical risk and a regularization term. In this paper, we study the existence of optimal solution of multi-kernel regularization learning. First, we ameliorate a previous conclusion about this problem given by Micchelli and Pontil, and prove that the optimal solution exists whenever the kernel set is a compact set. Second, we consider this problem for Gaussian kernels with variance σ∈(0,∞), and give some conditions under which the optimal solution exists.     

Modelling and control of natural convection in canned foods

In this paper we study mathematically an industrial problemrelated to sterilization processes involving heat transfer bynatural convection. We give results of existence and regularityfor the solution of this problem. We recast the whole problemas an optimal control problem with pointwise constraints onthe state and the control in order to ensure the reduction ofmicroorganism concentration and the retention of nutrients,and to save energy. Finally, we give results on existence ofthe optimal solution and optimality conditions for its characterization.     

An inverse optimal problem in discrete-time stochastic control

In this paper, we study an inverse optimal problem in discrete-time stochastic control. We give necessary and sufficient conditions for a solution to a system of stochastic difference equations to be the solution of a certain optimal control problem. Our results extend to the stochastic case the work of Dechert. In particular, we present a stochastic version of an important principle in welfare economics.     

A result on scalarization

In this short paper, we give a result on scalarization of multiobjective optimization. Any local weakly efficient solution of a multiobjective programming problem is a locally optimal solution of the corresponding weighted optimization problem if and only if one of the three conditions proposed in this paper is satisfied.     

Optimal consumption of the finite time horizon Ramsey problem

In this paper, we study the stochastic Ramsey problem related to an economic growth model with the CES production function in a finite time horizon. By changing variables, the Hamilton-Jacobi-Bellman equation associated with this optimization problem is transformed. By the viscosity solution technique, we show the existence of a classical solution of the transformed Hamilton-Jacobi-Bellman equation, and then give an optimal consumption policy of the original problem.     

单纯形法解装卸工问题

本文提出装卸工问题,对一种特殊情况下的装卸工问题用单纯形方法求得了它的最优解和最优值.     

A simple characterization of solution sets of convex programs

By means of elementary arguments we first show that the gradient of the objective function of a convex program is constant on the solution set of the problem. Furthermore the solution set lies in an affine subspace orthogonal to this constant gradient, and is in fact in the intersection of this affine subspace with the feasible region. As a consequence we give a simple polyhedral characterization of the solution set of a convex quadratic program and that of a monotone linear complementarity problem. For these two problems we can also characterize a priori the boundedness of their solution sets without knowing any solution point. Finally we give an extension to non-smooth convex optimization by showing that the intersection of the subdifferentials of the objective function on the solution set is non-empty and equals the constant subdifferential of the objective function on the relative interior of the optimal solution set. In addition, the solution set lies in the intersection with the feasible region of an affine subspace orthogonal to some subgradient of the objective function at a relative interior point of the optimal solution set.     

A variational technique for optimal boundary control in a hyperbolic problem

We investigate the problem of controlling the boundary functions in a one dimensional hyperbolic problem by minimizing the functional including the final state. After proving the existence and uniqueness of the solution to the given optimal control problem, we get the Frechet differential of the functional and give the necessary condition to the optimal solution in the form of the variational inequality via the solution of the adjoint problem. We constitute a minimizing sequence by the method of projection of the gradient and prove its convergence to the optimal solution.     

双指数跳扩散过程的最优停止问题

美式期权定价问题是金融数学的热点问题,一般要用最优停止理论。本文给出了双指数跳扩散过程的最优停止问题的解析解。     

Generalized Reflected BSDE and an Obstacle Problem for PDEs with a Nonlinear Neumann Boundary Condition

Abstract

In this article, we derive the existence and uniqueness of the solution for a class of generalized reflected backward stochastic differential equation involving the integral with respect to a continuous process, which is the local time of the diffusion on the boundary, in using the penalization method. We also give a characterization of the solution as the value function of an optimal stopping time problem. Then we give a probabilistic formula for the viscosity solution of an obstacle problem for PDEs with a nonlinear Neumann boundary condition.