分次环的分次根

给出了建立分次环根的一般方法．作为其应用，建立了分次环的分次Brown—McCoy根，并给出了Brown—McCoy半单分次环的结构定理．     

用MATLAB求解二元理想体系的泡露点问题

通过MATLAB工程计算软件，采用步长法、二分法、迭代法和黄金分割法等多种方法．求解了二元理想体系的泡露点问题．结果表明，几种计算值都能与手算值吻合地很好．相对误差远远小于1％，完全满足工程要求；用MATLAB内部函数Solve计算最为便捷．     

特征为2的素环的Lie理想上中心化自同构

Let R be a prime ring with an automorphism σ≠1, an identity map. Let L be a noncentral Lie ideal of R such that [x^σ,x] E Z for all x ∈ L, where Z is the center of R. Then L is contained in the center of R, unless char(R)=2 and dimc RC = 4.     

A refinement of the Zipf-Mandelbrot law and the lacunarity in an ideal gas

The Zipf-Mandelbrot formula for occurrence frequencies is refined and is applied to an ideal gas. This refinement essentially affects the value of the prefactor c₂ and consequently the value of the lacunarity. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 3, pp. 511–512, June, 2006.     

Linear rank and corank preserving maps on (H) and an application to *-semigroup isomorphisms of operator ideals

We characterize linear rank-k nonincreasing, rank-k preserving, and corank-k preserving maps on B(H), the algebra of all bounded linear operators on the Hilbert space H. This unifies and extends finite-dimensional results and results on linear rank-1 non-increasing and rank-1 preserving maps in the infinite-dimensional case. We conclude with an application to *-semigroup isomorphisms of operator ideals.     

准-Groebner基的计算

本文通过定义S－多项式，给出了系数环是整环的多项式中理想的准－Groebner基的一个算法，并据此给出了计算该理想极大无关变元组和维数的一种方法。     

Induced characters, Mackey analysis and primitive ideal spaces of nilpotent discrete groups

Let G be a nilpotent discrete group and Prim(C^*(G)) the primitive ideal space of the group C^*-algebra C^*(G). If G is either finitely generated or has absolutely idempotent characters, we are able to describe the hull-kernel topology on Prim(C^*(G)) in terms of a topology on a parametrizing space of subgroup-character pairs. For that purpose, we introduce and study induced traces and develop a Mackey machine for characters. We heavily exploit the fact that the groups under consideration have the property that every faithful character vanishes outside the finite conjugacy class subgroup.     

麦克斯韦等面积法则在范氏气体中的应用

对与范德瓦耳斯气体状态方程有关的几个问题作了进一步分析,给出了一种证明麦克斯韦等面积法则的方法,并指出了有关文献的不妥之处.     

所有双理想都是素双理想的半群

设S为一个半群,B是S的一个双理想(即B是S的一个满足条件BSBB的子半群)．如果对S的任意双理想C,D都有CDB蕴涵CB或DB,我们就称B为S的一个素双理想．如果K是一个N-覆盖的纯LR-带,我们就称K为一条拟链．本文证明了半群S的所有双理想都是素双理想的充分必要条件是S是一个幂等元形成拟链的纯整群并半群．     

Evaluations of initial ideals and Castelnuovo-Mumford regularity

This paper characterizes the Castelnuovo-Mumford regularity by evaluating the initial ideal with respect to the reverse lexicographic order.