P—adic超越连分数

本文借助于Ｔｈｕｅ－Ｓｉｅｇｅｌ－Ｒｏｔｈ定理的Ｐ－ａｄｉｃ类似，Ｐ－ａｄｉｃ代数数的有理逼近定理以及Ｐ－ａｄｉｃ简单连分数的一些性质给出了Ｐ－ａｄｉｃ数是超越数的两个充分条件。     

某些多元线性正算子的加权逼近

本文首先给出了在Ｌｐ逼近意义下某些线性正算子加Ｊａｃｏｂｉ权逼近时的特征定理，作为应用，我们给出了多元Ｂａｓｋａｋｏｖ型算子、多元Ｓｚａｓｚ－Ｍｉｒａｋｊａｎ型算子和多元Ｂｅｔａ算子加权逼近时的特征刻划．     

多元Bernstein-Durrmeyer算子L~p逼近的Steckin-Marchaud型不等式

本文给出多元 Ｂｅｒｎｓｔｅｉｎ－Ｄｕｒｒｍｅyｅｒ算子 ＬＰ逼近的 Ｓｔｅｃｋｉｎ－Ｍａｒｃｈａｕｄ型不等式,从该不等式得到多元Ｂernstein-Ｄurrmeyer算子Ｌp对逼近的特征刻划定理．     

一类高阶多维非线性伪双曲方程

本文研究了一类高阶多维非线性伪双曲方程，通过先验估计结合Ｓｏｂｏｌｅｖ嵌入定理及Ｌｃａｒｙ－Ｓｃｈａｕｄｅｒ不动点定现证明了初边值问题整体广义解的存在性和唯一性。     

3—Sasakian流形的3—C—全实子流形

引入并研究了３－Ｓａｓａｋｉａｎ流形的３－Ｃ－全实子流形，借助了第二基本形式的长度，给出了单位球面Ｓ＾４ｍ＋３－Ｃ－全实子流形的一个Ｐｉｎｃｈｉｎｇ定理。     

局部凸空间中的不动点定理

证明了局部凸空间中非凸集上的上半连续凝集值映射的一个Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ型不动点定理,并推广了一些已知的不动点定理。     

PSL（2，F）的一个嵌入定理及其应用

设Ｆ是任意域，Ｇ代表ＳＬ（２，Ｆ）或ＰＳＬ（２，Ｆ）．本文的主要结果是：设Ｋ是Ｆ的子域，则Ｇ中同构于ＳＬ（２，Ｋ）或ＰＳＬ（２，Ｋ）的子群在Ｇ的自同构的作用下彼此共轭，利用这一结果，本文明确确定了A₁^[1]型的仿射Ｋａｃ－Ｍｏｏｄｙ群的一类极大正规子群．     

一类非线性泛函边值问题的可解性

本文考虑非线性泛函边值问题，利用Ｂｏｒｓｕｋ定理与Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ不动点定理，得到了上述边值问题的若干可解性结果。     

稀疏素数值中的Waring—Goldbach问题

本文研究了Ｗａｒｉｎｇ－Ｇｏｌｄｂａｃｈ问题与Ｐｉａｔｅｓｋｉ－Ｓｈａｐｉｒｏ素数定理的混合问题，从而进一步深化了华罗庚教授的经典结果。     

一个无穷矩阵收敛定理及其应用

本文在最一般情况下获得了一个无穷矩阵收敛定理．作为应用，我们研究了求和理论中著名的Ｓｃｈｕｒ求和法，并且也改进了Ｓｔｉｌｅｓ型Ｏｒｌｉｃｚ Ｐｅｔｉｓ定理．     

关于可约布尔矩阵幂敛指数的一个Brualdi─Ross型上界

本文证明了可约布尔矩阵幂敛指数的一个Ｂｒｕａｌｄｉ－Ｒｏｓｓ型上界，并给出了幂敛指数达到此上界的矩阵的完全刻划．     

A Relaxation of a Min-Cut Problem in an Anisotropic Continuous Network

Strang [18] introduced optimization problems on a Euclidean domain which are closely related with problems in mechanics and noted that the problems are regarded as continuous versions of famous max-flow and min-cut problems. In [15] we generalized the problems and called the generalized problems max-flow and min-cut problems of Strang's type. In this paper we formulate a relaxed version of the min-cut problem of Strang's type and prove the existence of optimal solutions under some suitable conditions. The conditions are essential. In fact, there is an example of the relaxed version which has no optimal solutions if the conditions are not fulfilled. We give such an example in the final section. Accepted 8 October 1998     

直觉主义类型论中π和Σ规则的研究

本文研究直觉主义类型论中π和Σ规则，对于类型（πｘ∈Ａ）Ｂ（ｘ），我们给出新的消去和相等规则使新规则的式样与其他类型的规则相同，然而不使用高阶交元和常元，我们证明新规则等价于旧规则，对于类型（Σｘ∈Ａ）Ｂ（ｘ），我们利用投影运算给出新规则，而且证明它们等价于旧规则。     

Solutions with internal jump for an autonomous elliptic system of FitzHugh–Nagumo type

Systems of elliptic partial differential equations which are coupled in a noncooperative way, such as the FitzHugh–Nagumo type studied in this paper, in general do not satisfy order preserving properties. This not only results in technical complications but also yields a richer solution structure. We prove the existence of multiple nontrivial solutions. In particular we show that there exists a solution with boundary layer type behaviour, and we will give evidence that this autonomous system for a certain range of parameters has a solution with both a boundary and an internal layer. The analysis uses results from bifurcation theory, variational methods, as well as some pointwise a priori estimates. The final section contains some numerically obtained results.     

Remarks on Martin-Löf's partial type theory

In this paper we discuss Martin-Löf's partial type theory, that is type theory with general recursion, and in particular the consequences of the presence of a fixed point operator. We model Martin-Löf's logical framework domain-theoretically in the category of conditional upper semi lattices and parametrizations thereof. An interpretation of a type of sets in the logical framework, which defines partial type theory with one universe, is finally described.During the preparation of this paper, the first author was supported by the Swedish Natural Science Research Council as a PhD-student in mathematical logic.     

二项式型自反多项式

In this paper, we define the self-inverse sequences related to sequences of polynomials of binomial type, and give some interesting results of these sequences. Moreover, we study the self-inverse sequences related to the Laguerre polynomials.     

Deterministic and Stochastic Control of Navier—Stokes Equation with Linear, Monotone, and Hyperviscosities

This paper deals with the optimal control of space—time statistical behavior of turbulent fields. We provide a unified treatment of optimal control problems for the deterministic and stochastic Navier—Stokes equation with linear and nonlinear constitutive relations. Tonelli type ordinary controls as well as Young type chattering controls are analyzed. For the deterministic case with monotone viscosity we use the Minty—Browder technique to prove the existence of optimal controls. For the stochastic case with monotone viscosity, we combine the Minty—Browder technique with the martingale problem formulation of Stroock and Varadhan to establish existence of optimal controls. The deterministic models given in this paper also cover some simple eddy viscosity type turbulence closure models. Accepted 7 June 1999     

Semicontinuous lattices

In this paper we introduce and study a new type of lattices, semicontinuous lattices, by using semiprime ideals. Such lattices have many properties similar to that of continuous lattices, and are closely related to the theory of continuous lattices. Received November 3, 1995; accepted in final form March 13, 1997.     

拓扑量子场理论与相交指标

该文构造了一新的上同调型拓扑量子场理论并证明了其配分函数是相交指标 (crossingindex)     

Extremal problems on the Hua domain of the first type

In this paper we study some extremal problems between the Hua domain of the first type and the unit ball.