模糊化弱拓扑和模糊化预拓扑

在模糊化拓扑空间基础上,放宽了模糊化拓扑结构的公理体系,引入模糊化弱拓扑和模糊化预拓扑的概念,并且讨论了它们构成的范畴和模糊化拓扑空间范畴的关系.结果表明,模糊化拓扑空间范畴既是模糊化弱拓扑空间范畴的双余反射满子范畴,又是模糊化预拓扑空间范畴的双余反射满子范畴.     

拓扑系统的紧性和分离性

考察拓扑系统的两种紧性——空间式紧和locale式紧,给出紧性的若干刻画,讨论了两种紧性的相互关系,证明了拓扑系统的两种紧性都是拓扑空间紧性的良好推广,说明了紧拓扑系统的闭子拓扑系统、有限和系统以及积系统仍是紧拓扑系统。最后在拓扑系统中考察了紧性加强分离性的问题,得到了紧,(强)T2拓扑系统为(强)T3,(强)T4拓扑系统等结论,并用理想收敛刻画了拓扑系统的强T2分离性。     

极小正则 LF 拓扑空间

本文引入极小正则LF拓扑空间的概念,给出了构造弱于已知正则LF拓扑的正则LF拓扑的一般方法.此外,得出了正则LF拓扑成为极小正则LF拓扑的条件.     

极小正则LF拓扑空间

本文引入极小正则ＬＦ拓扑空间的概念，给出了构造弱于已知正则ＬＦ拓扑的正则ＬＦ拓扑的一般方法此外，得出了正则ＬＦ拓扑成为极小正则ＬＦ拓扑的条件     

L-fuzzifying拓扑空间范畴和可延L-fuzzy拓扑空间范畴的Galois联络

在完全分配格的格值环境下,提供了L-fuzzifying拓扑结构和可延L-fuzzy拓扑结构相互转化的方法。还进一步研究了L-fuzzifying拓扑空间范畴和可延L-fuzzy拓扑空间范畴之间的关系。文中结果表明,L-fuzzifying拓扑空间范畴和可延L-fuzzy拓扑空间范畴之间存在Galois联络。     

测度拓扑和连续偏序集的刻画

研究偏序集上的测度拓扑以及与其它内蕴拓扑间的关系,利用测度拓扑刻画了偏序集的连续性.构造了反例说明存在完全分配格,其上的测度拓扑不是连续格从而不是局部紧拓扑.     

诱导的I-fuzzy拓扑生成序空间

本文研究了模糊拓扑生成序空间与其诱导的I-fuzzy拓扑生成序空间之间的关系.利用三种Lowen映射内在关联的方法,引入了三种I-fuzzy拓扑生成序空间,建立了诱导的I-fuzzy拓扑生成序空间理论.获得了诱导的I-fuzzy拓扑与诱导的I-fuzzy拓扑生成序之间的从属关系.     

半连续格上的半Scott拓扑与半Lawson拓扑

在完备格上引入了半Scott拓扑与半Lawson拓扑,讨论了半连续格和强连续格上半Scott拓扑与半Lawson拓扑的一些基本性质。     

乘积拓扑动力系统的转移不变集

研究一般拓扑动力系统的复杂性是很困难的,拓扑共轭、拓扑半共轭、嵌入映射和转移不变集都可以不同程度保持动力系统的复杂性.通过研究拓扑动力系统与符号动力系统拓扑共轭,找到了拓扑动力(子)系统存在转移不变集的条件,同时证明了拓扑动力系统存在转移不变集与乘积拓扑动力系统存在转移不变集的关系,通过研究相对简单、直观的符号动力系统,间接的反应一般拓扑动力(子)系统与其乘积拓扑动力系统的动力性状.     

关于函数空间Y~X上三个特殊拓扑间关系的讨论

本文对函数空间上的一致收敛拓扑、紧收敛拓扑及 Cauchy收敛拓扑之间的关系进行了讨论 ,给出了这三个拓扑间两两等价的充要条件     

Asymptotic analysis of the differences between the Stokes-Darcy system with different interface conditions and the Stokes-Brinkman system

We consider the coupling of the Stokes and Darcy systems with different choices for the interface conditions. We show that, comparing results with those for the Stokes-Brinkman equations, the solutions of Stokes-Darcy equations with the Beavers-Joseph interface condition in the one-dimensional and quasi-two-dimensional (periodic) cases are more accurate than are those obtained using the Beavers-Joseph-Saffman-Jones interface condition and that both of these are more accurate than solutions obtained using a zero tangential velocity interface condition. The zero tangential velocity interface condition is in turn more accurate than the free-slip interface boundary condition. We also prove that the summation of the quasi-two-dimensional solutions converge so that the conclusions are also valid for the two-dimensional case.     

On the number of roots of self-inversive polynomials on the complex unit circle

We present a sufficient condition for a self-inversive polynomial to have a fixed number of roots on the complex unit circle. We also prove that these roots are simple when that condition is satisfied. This generalizes the condition found by Lakatos and Losonczi for all the roots of a self-inversive polynomial to lie on the complex unit circle.     

On the Positivity of the Stochastic Heat Equation

We study the positivity preserving properties of the heat equation with a white noise potential and random initial condition. Moreover, we find a generalized Feynman--Kac formula for the solution of the problem using methods from the white noise analysis. The initial condition can anticipate the driving white noise. We show that the solution is positive, when the random initial condition is positive. For the case of a time-dependent white noise potential, we give a special representation of the solution together with regularity results.     

重复造林情况下最优伐木时间的经济决策模型

本文根据林木生长的特点及投资理论 ,建立了重复造林条件情况下最优伐木时间的经济决策模型 ,模型分析表明 ,一期造林情况下最优伐木时间迟于无限期重复造林情况下最优伐木时间     

Necessary condition for the existence of the S matrix outside the scope of perturbation theory

Using the Maslov—Shvedov complex-germ method due to Maslov—Shvedov, we obtain a necessary condition for the existence of the quantum-field S matrix outside the scope of perturbation theory in the leading order of semiclassical approximation. This condition consists in that the tangent symplectic transformation to the evolution operator of the nonlinear classical field equation is realized by a unitary transformation of Fock space. It follows from the results of the book of Maslov and Shvedov that this condition always holds.     

On the solvability of the systems of equations arising in implicit Runge-Kutta methods

In this paper we present a new condition under which the systems of equations arising in the application of an implicit Runge-Kutta method to a stiff initial value problem, has unique solutions. We show that our condition is weaker than related conditions presented previously. It is proved that the Lobatto IIIC methods fulfil the new condition.     

关于多元函数最佳逼近精确阶的Timan问题

关于找一个充分必要条件使Ω^k(f,1/σ)L_p(Rⁿ)=O(A_σ(f)L_p(Rⁿ)),σ→∞,成立的Timan问题被解决.这个条件是Q^k(f,δ)L_p(Rⁿ)=O(Ω^k+1(f,δ)L_p(Rⁿ)),δ→0.     

利用分块矩阵对两个结论的进一步推广

利用分块矩阵的知识,将高等代数中两道在文献[3]中已推广的结论作了进一步的推广证明,使对原有习题成立的充分条件加强到充要条件.并用新方法给出了证明.     

关于满足弱开集条件的自相似测度的局部维数的注记

对于自相似集合,已知开集条件与强开集条件是等价的,我们讨论了强开集条件的基些性质,并给出了自似测度局部维数研究的一个应用。