相容连续Domain的不变性

引入了Scott相容连续映射与商相容Domain等概念,研究了Scott相容连续映射保局部基与保waybelow序及保局部基与保紧元之间的关系,证明了相容连续Domain或相容代数Domain在保局部基的Scott相容连续满映射下保持不变.     

一类Domain范畴及其笛卡儿闭子范畴

本文给出一类新的 Ｄｏｍａｉｎ范畴 ＡｌｇＤ■（即以代数 Ｄｏｍａｉｎ为对象,保逼近序的Ｓｃｏｔｔ连续函数为态射的范畴）及其满子范畴ＡｌｇＤ■（即以有底（最小元）的代数Ｄｏｍａｉｎ为对象,保逼近序的Ｓｃｏｔｔ连续函数为态射的范畴）,并且讨论它们的极大的笛卡儿闭的满子范畴．     

连续Domain的遗传性及其不变性

引入Domain子空间的概念,得到Scott开集和闭集都是Domain的子空间。证明连续Domain或代数Domain对开子空间和闭子空间都是可遗传的。证明连续Domain或代数Domain在保Waybelow序的Scott连续映射下保持不变。     

算术半格的闭包空间表示

本文主要讨论算术半格的闭包空间表示。首先通过在给定的闭包空间中增加适当的条件,提出了算术闭包空间的概念,并且给出了算术半格的闭包空间表示。接着提出了算术闭包空间之间的算术逼近映射的概念,并证明了以算术逼近映射作为态射的算术闭包空间范畴和以Scott连续函数作为态射的算术半格范畴之间的范畴等价性。     

关于交半格同态构成的函数空间与FS-交连续Domain

定义了一类序结构—FS-交连续domain,讨论其相关性质并证明:(1)FS-交连续domain关于由Scott连续且保持非空有限交运算的函数构成的函数空间封闭,以(代数)FS-交连续domain为对象、以Scott连续函数为态射的范畴是Cartesian闭范畴;(2)任意分配可乘的有界完备domain是FS-交连续domain,从而紧连续dcpo的Smyth幂domain是FS-交连续domain.这些结果表明,FS-交连续domain是关于保非空有限交的连续映射构成的函数空间封闭的最恰当序结构.     

关于交半格同态构成的函数空间与FS-交连续Domain

定义了一类序结构-FS-交连续domain,讨论其相关性质并证明:(1)FS-交连续domain关于由Scott连续且保持非空有限交运算的函数构成的函数空间封闭,以(代数)FS-交连续domain为对象、以Scott连续函数为态射的范畴是Cartesian闭范畴;(2)任意分配可乘的有界完备domain是FS-交连续domain,从而紧连续dcpo的Smyth幂domain是FS-交连续domain.这些结果表明,FS-交连续domain是关于保非空有限交的连续映射构成的函数空间封闭的最恰当序结构.     

代数的局部完备集范畴和FS-局部dcpo范畴的笛卡儿闭性

本文引入了代数的局部完备集,FS-局部dcpo,局部稳定映射等概念．主要结果是：以局部Scott连续映射为态射的代数的局部完备集范畴,以局部稳定映射为态射的代数的局部完备集范畴以及以局部Scott连续映射为态射的FS-局部dcpo范畴都是笛卡儿闭范畴．     

拟信息基,ω-代数Cpo,和SFP domain

G.Sam b in引入了(代数)信息基的概念,并证明了代数Scott D om a in范畴和信息基范畴是等价的.B.R.C.Bedrega l给出了ω-代数cpo和SFP dom a in的刻划.而G.Q.Zhang通过序结构给出了SFP dom a in的刻划.本文将引入了拟信息基的概念并给出了ω-代数cpo和SFP dom a in的刻划.     

伪Scott拓扑与伪Scott开滤子

讨论抽象基(特别是偏序集带辅助序)上的伪Scott拓扑与伪Scott开滤子集的一些基本性质, 推广了Domain理论中一些熟知的结论,证明了抽象基上的伪Scott拓扑是完全分配格;若在偏序集P上赋予辅助关系＜, 则其上伪Scott开滤子之集是连续domain.     

软泛代数及其整体结构性质

提出了软泛代数概念,将已有的软群、软环等概念统一纳入这一框架中,从整体上研究了软泛代数的序结构性质,证明了固定指标集和T-代数后,相应的软T-代数全体以点式序形成代数格.引入了Scott连续软泛代数概念,证明了从代数紧拓扑空间到给定T-代数的Scott连续软T-代数的全体以点式序形成代数格.     

Asymptotic solution of a quasistatic thermoelasticity problem for a slender rod

An asymptotic expansion is constructed for solving a quasistatic thermo-elasticity problem for a slender cylindrical rod in the presence of mass forces and non-linear heat sources. The algorithm for constructing the asymptotic form, based on the method of boundary functions, is fairly simple and convenient for carrying out numerical calculations. A deduction is made on the basis of the asymptotic form constructed on how to select correctly a simplified one-dimensional model so as to obtain a better approximation for the solution of the initial two-dimensional problem. An existence theorem for the solution is proved under certain conditions.     

线性方程组的反问题

给定线性方程组AX= b,易求其通解,设为U0+ k1U1+ …+ krUr ()反过来,当给定()式,怎样构造一个线性方程组以()为通解? 本文称这类问题为线性方程组的反问题,并给出了这类问题的一个解法.     

A variable step-size control algorithm for the weak approximation of stochastic differential equations

In this paper, we propose two local error estimates based on drift and diffusion terms of the stochastic differential equations in order to determine the optimal step-size for the next stage in an adaptive variable step-size algorithm. These local error estimates are based on the weak approximation solution of stochastic differential equations with one-dimensional and multi-dimensional Wiener processes. Numerical experiments are presented to illustrate the effectiveness of this approach in the weak approximation of several standard test problems including SDEs with small noise and scalar and multi-dimensional Wiener processes.     

A mixed collocation–finite difference method for 3D microscopic heat transport problems

Three-dimensional time-dependent initial-boundary value problems of a novel microscopic heat equation are solved by the mixed collocation–finite difference method in and on the boundaries of a particle when the thickness is much smaller than both the length and width. The collocation method on fixed grid size is used to approximate the space operator, whereas the finite difference scheme is used for time discretization. This new mixed method is applied to a novel heat problem in a particle, in order to compute the temperature distribution in and on the particle's surface. The second derivatives of the basis functions for the spectral approximation are derived. Direct substitution of derivatives in the model transforms the differential equation into a linear system of equations that is solved by the specific preconditioned conjugate gradient method. The high-order accuracy and resolution achieved by the proposed method allows one to obtain engineering-accuracy solution on coarse meshes. The consistency, stability and convergence analysis are provided and numerical results are presented.     

Representing Geometric Morphisms Using Power Locale Monads

It is shown that geometric morphisms between elementary toposes can be represented as adjunctions between the corresponding categories of locales. The adjunctions are characterized as those that preserve the order enrichment, commute with the double power locale monad and whose right adjoints preserve finite coproduct. They are also characterized as those adjunctions that preserve the order enrichment and commute with both the lower and the upper power locale monads.     

无失效数据失效概率的Bayes估计

本文对无失效数据(ti,ni)在ti 时刻的失效概率pi= P｛T< ti｝的先验密度的核为(1- pi)k时,给出了pi 的Bayes估计和多层Bayes估计,由此可以得到无失效数据可靠度的估计.最后,结合实际问题进行了计算.     

On Rates of Uniform Convergence of Lower Extreme Generalized Order Statistics

Under a von Mises-type condition the joint distribution of suitable normalized lower extreme generalized order statistics converges w.r.t. the variational distance to the asymptotic joint distribution of lower extreme order statistics. Rates of uniform convergence are established. It turns out that the rates of uniform convergence known for ordinary extremes carry over to lower generalized extremes. Finally, models of Weibull type are concerned, where uniform rates are used in connection with model approximations in order to simplify statistical inference.AMS 2000 Subject Classification. Primary—60G70     

A stable range for quadratic forms over commutative rings

A commutative ring A has quadratic stable range 1 (qsr(A) = 1) if each primitive binary quadratic form over A represents a unit. It is shown that qsr(A) = 1 implies that every primitive quadratic form over A represents a unit, A has stable range 1 and finitely generated constant rank projectives over A are free. A classification of quadratic forms is provided over Bezout domains with characteristic other than 2, quadratic stable range 1, and a strong approximation property for a certain subset of their maximum spectrum. These domains include rings of holomorphic functions on connected noncompact Riemann surfaces. Examples of localizations of rings of algebraic integers are provided to show that the classical concept of stable range does not behave well in either direction under finite integral extensions and that qsr(A) = 1 does not descend from such extensions.     

Poisson Difference Schemes for Hamiltonian Systems on Poisson Manifolds

In this paper a systematical method for the construction of Poisson difference schemes with arbitrary order of accuracy for Hamiltonian systems on Poisson manifolds is considered. The transition of such difference schemes from one time-step to the next is a Poisson map. In addition, these schemes preserve all Casimir functions and, under certain conditions, quadratic first integrals of the original Hamiltonian systems. Especially, the arbitrary order centered schemes preserve all Casimir functions and all quadratic first integrals of the original Hamiltonian systems.