分次Armendariz环与P.P.环

引进分次Armendariz环的概念,讨论了分次环R= n∈2Rn及由它导出的非分次环R,R0,及R[x]之间关于Armendariz环性质的关系,并推广了[8]的结论,得到在R= n∈ZRn是Z-型正分次环的前提下,若R是分次Armendariz,分次正规环,则R是P．P环（Bear环）当且仅当R是分次P．P．环（分环Baer环）。     

关于P.Crawleg和R.P.Dilworth的公开问题

本文讨论了P.Crawleg和R.P.Dilworth提出的一个公开问题,研究了偏序集的带有固定点的保序映射,并且给出了若干充分或必要条件,使得一个偏序集的每一个保序映射都至少有一个固定点。     

Solution to a Problem of J.P.Hutchinson and P.B.Trow

Use of the Pigeonhole Principle to solve the following problem was discussed in several books, for example [1,2]. Suppose a player (e. g., tennis or chess) practices on d consecutive days, playing at least one game a day and a total of no more than b games where d相似文献   

P. L. Chebyshev的概率新思想溯源

切贝舍夫是俄国十九世纪最伟大的数学家之一,他第一个主张概率论的极限定理应该严格的证明,并尽可能精确地确定偏离极限的估计量,这在方法论上引起了很大变化.其创立的切贝舍夫不等式和切贝舍夫大数定律是概率论极限理论的基础,从而使概率论成为严密数学分支.切贝舍夫的概率思想是在一定数学文化背景产生的,尤其是法国数学文化对其发展的形成有着深刻影响.     

美国1982年微积分A.P.考试题

美国的中学生,可以选读微积分,经过A.P.考试(Advanced Placement Examination),及格者可由大学承认,得到相当于大学已经学习一年微积分的学分.选读微积分的人数,据一个学区统计,约占高中毕业生人数的10%.在更大范围内可能低于此数.现将1982年5月间访美时带回的A.P.试题译出介绍如下,以供参考. 试题有两部分,一部分是选择题,1~1/2)小时(略),下面是另一部分计算题,1(1/2)小时.     

Analytic solutions of P.D.E’s

The purpose of this paper is to explain the celebrated results by Cattabriga-De Giorgi [5], [6] on partial differential equations with constant coefficients in the space of real analytic functions. These results caught the mathematical world by surprise in the early 70’s, when solvability on convex domains was supposed to be very likely due to the enormous development of Functional Analysis. Now, 30 years later, we have a much easier understanding of them. In particular non-existence of solutions for inR _x1,y1,x2 ³ is explained in terms of complex analysis, by the absence of a fundamental system of neighborhoods ofR _x1,y1,x2 ³ in C _z1,z2 ² . On the other hand, existence of solutions inR ², the other main result of [6], also became elementary. It is a case of analytic solvability for all operators whose principal part is a product of a hyperbolic and an elliptic term. I dedicate this paper to the memory of Lamberto Cattabriga for his masterful example in Mathematics and life. To the memory of Lamberto Cattabriga     

On Weakly P.P. Rings

We introduce, in this paper, the right weakly p.p. rings as the generalization of right p.p. rings. It is shown that many properties of the right p.p. rings can be extended onto the right weakly p.p. rings. Relative examples are constructed. As applications, we also characterize the regular rings and the semisimple rings in terms of the right weakly p.p. rings.     

Mangum,P.I.

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway —a mathematical journal, or what? ” Or you may ask, “Where am I? ” Or even “Who am I? ” This sense of disorientation is at its most acute when you open to Colin Adams ’s column. Relax. Breathe regularly. It ’s mathematical, it ’s a humor column, and it may even be harmless.     

The generalization of some theorems of P. P. Korovkin on positive operators

We introduce a class of linear operators, containing the positive operators, in which P. P. Korovkin's theorem on the conditions and order of convergence of positive operators hold. We consider also the class of linear operators, convergent to the derivative, in which similar theorems hold.Translated from Matematicheskie Zametki, Vol. 13, No. 6, pp. 785–794, June, 1973.