一般约束极大极小问题的一个有效的近似解法

一般约束极大极小问题的一个有效的近似解法唐焕文，张立卫，王云诚（大连理工大学应用数学系，辽宁，１１６０２４）．摘要＊从共扼的观点出发，导出了极大熵函数，给出了处理一般约束极大极小问题的一个有效的近似方法—极大熵方法，并在较弱的条件下，证明了算法的收敛...     

Rn上带奇异性的非线性双调和方程的正整解

该文以Schauder-Tychonoff不动点定理为工具,建立了一类Rⁿ上带奇异性的非线性双调和方程 Δ²u=f(|x|, u,| u|)u^-β (x ∈ Rⁿ, n ≥ 3, β > 0) 正的径向对称整体解的存在性定理,并给出了解的有关性质,所得的结果丰富和发展了文献[1--5]的结果.     

Exact and limiting distributions of the number of successions in a random permutation

Traditionally the distributions of the number of patterns and successions in a random permutation ofn integers 1,2, ..., andn were studied by combinatorial analysis. In this short article, a simple way based on finite Markov chain imbedding technique is used to obtain the exact distribution of successions on a permutation. This approach also gives a direct proof that the limiting distribution of successions is a Poisson distribution with parameter =1. Furthermore, a direct application of the main result, it also yields the waiting time distribution of a succession.This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant NSERC A-9216, and National Science Council of Republic of China under Grant 85-2121-M-259-003.     

Nonlinear Diffusion with Absorption

We consider the nonlinear diffusion-absorption problem in L¹() u - div a(, Du) + j (, u) f on , u = 0 on where is an arbitrary open set in ^N. Conditions for the existence of a strong solution are presented and the existence of a natural generalized solution in the general case is established. We study the dependence of the generalized solution on the absorption term j and characterize generalized solutions which are essentially bounded.     

一类n阶线性微分方程解的复振荡

本文研究了齐次方程ｆ（ｎ）＋∑ｊ＝１＾ｎ－２ｂｊｆ（ｊ）＋ｅ＾ｚｆ＝０的复振荡问题,其中ｂｊ（ｊ＝１,２,．．．,ｎ－２）是复常数,如果上面方程存在非平凡解,其零点的密指量等价于０（ｅ＾ｒ）时,我们得到了方程的非平凡解ｆ的一般表达式及系数ｂｊ（ｊ＝１,２,．．．,ｎ－２）之间的关系。     

约束非光滑极小化的随机拟次梯度法

用随机拟次梯度法处理非随机非光滑问题是极小化领域的新方法．本文利用Ｌａｇｒａｎｇｅ对偶理论把一般混合约束问题归化为非约束凸规划问题，并用随机次梯度法求解后者，相应的算法有合理的停机准则，并在适当条件下几乎处处收敛．     

On the domain dependence of solutions to the two-phase Stefan problem

We prove that solutions to the two-phase Stefan problem defined on a sequence of spatial domains _n ^N converge to a solution of the same problem on a domain where is the limit of _n in the sense of Mosco. The corresponding free boundaries converge in the sense of Lebesgue measure on ^N.     

单调有界数列必有极限定理的一个直接证明及其作用

利用实数十进制无限小数表示直接构造性地给出"单调有界数列必有极限"定理的一种简洁的新证明,并且从新视角揭示数学分析中的实数完备性和高等数学中的数列极限存在准则.