Nondiscrete P-groups can be reflexive

We present the first examples of nondiscrete reflexive P-groups (topological groups in which countable intersections of open sets are open) as well as of noncompact reflexive ω-bounded groups (precompact groups in which the closure of every countable set is compact). Our main result implies that every product of discrete Abelian groups equipped with the P-modified topology is reflexive. Taking uncountably many nontrivial factors, we thus answer a question posed by P. Nickolas and solve a problem raised by Ardanza-Trevijano, Chasco, Domínguez, and Tkachenko.New examples of non-reflexive P-groups are also given which are based on a further development of Leptin's technique going back to 1955.     

激光雨滴谱仪光学设计与分析

用来描述降水粒子数浓度随粒子尺度变化函数的雨滴谱,是降水最基本的微物理特征量,利用雨滴谱信息可以更清楚地认识自然降水的发展演变过程。从雨滴在矩形光束中的相对位置出发,理论分析了不同尺寸条件下矩形光束透射强度随粒径的变化,结果显示矩形光束的透过率与雨滴尺寸具有很好的线性关系;数值模拟了不同粒径、不同降落速度下雨滴在矩形光束中的渡越时间。并指出利用测量的雨滴粒子大小和下落时间就可获得降水类型(毛毛雨、普雨、降雪、降霰、冰雹以及混合型降水)、降水强度、降水量和粒子波谱(在体积波谱上的粒子分布)等信息。     

On the Density Property of P𝒮C Fields

Let 𝒮 be a finite set of finite and real local primes of a field K. We prove two results. First, a PAC field over K is already PAC over each nonempty 𝒮‐open subset of K; if K is global, this implies that it is also PAC over each separable Hilbert subset of K. Second, each P𝒮C field inside K_tot,𝒮 has the 𝒮‐density property.     

具有扰动映射族的不动点的普遍存在性

设X为实Banach空间,D是X中非空有界闭凸集,本文证明了D上一类具有全连续扰动的γ-非膨胀映射族或具有强连续扰动的广义压缩映射族M在Baire纲的意义下,几乎所有的映射都具有不动点。     

对矩阵初等变换应用中某些问题的探讨

运用初等变换的正确步骤可以减少计算量,现行用初等变换求向量组的一个极大无关组的两种方法,各有所长,文[5]的批评是不全面的.     

Fresh function spectra

In this paper, we investigate the fresh function spectrum of forcing notions, where a new function on an ordinal is called fresh if all its initial segments are in the ground model. We determine the fresh function spectrum of several forcing notions and discuss the difference between fresh functions and fresh subsets. Furthermore, we consider the question which sets are realizable as the fresh function spectrum of a homogeneous forcing. We show that under GCH all sets with a certain closure property are realizable, while consistently there are sets which are not realizable.