Finite groups of matrices over group rings

We investigate certain finite subgroups of , where is a finite nilpotent group. Such a group gives rise to a -module; we study the characters of these modules to limit the structure of . We also exhibit some exotic subgroups .

     

ICF靶用空心玻璃微球耐压性能测试

 利用自行研制的空心微球耐外压装置和充气装置，测试了目前激光惯性约束聚变实验打靶使用的空心玻璃微球耐内压能力和耐外压能力。空心玻璃微球采用液滴法制备，直径为180～250 mm、壁厚为0.8~4.0 mm。理论计算表明，当微球纵横比超过90时，耐外压能力与球壳材料的杨氏模量有关，由此测量得到的空心玻璃微球杨氏模量为55~75 GPa。玻璃微球的耐内压能力主要与球壳材料的抗拉强度有关，实验测量得到的玻璃微球抗拉强度为90~140 MPa。     

A conservative unstructured scheme for rapidly varied flows

This article introduces a new semi‐implicit, staggered finite volume scheme on unstructured meshes for the modelling of rapidly varied shallow water flows. Rapidly varied flows occur in the inundation of dry land during flooding situations. They typically involve bores and hydraulic jumps after obstacles such as road banks. Near such sudden flow transitions, the grid resolution is often low compared with the gradients of the bathymetry. Locally the hydrostatic pressure assumption may become invalid. In these situations, it is crucial to apply the correct conservation properties to obtain accurate results. An important feature of this scheme is therefore its ability to conserve momentum locally or, by choice, preserve constant energy head along a streamline. This is achieved using a special interpolation method and control volumes for momentum. The efficiency of inundation calculations with locally very high velocities, and in the case of unstructured meshes locally very small grid distances, is severely hampered by the Courant condition. This article provides a solution in the form of a locally implicit time integration for the advective terms that allows for an explicit calculation in most of the domain, while maintaining unconditional stability by implicit calculations only where necessary. The complex geometry of flooded urban areas asks for the flexibility of unstructured meshes. The efficient calculation of the pressure gradient in this, and other semi‐implicit staggered schemes, requires, however, an orthogonality condition to be put on the grid. In this article a simple method is introduced to generate unstructured hybrid meshes that fulfil this requirement. Copyright © 2008 John Wiley & Sons, Ltd.     

Extending modules relative to a torsion theory

An R-module M is said to be an extending module if every closed submodule of M is a direct summand. In this paper we introduce and investigate the concept of a type 2 τ-extending module, where τ is a hereditary torsion theory on Mod-R. An R-module M is called type 2 τ-extending if every type 2 τ-closed submodule of M is a direct summand of M. If τ _I is the torsion theory on Mod-R corresponding to an idempotent ideal I of R and M is a type 2 τ _I -extending R-module, then the question of whether or not M/MI is an extending R/I-module is investigated. In particular, for the Goldie torsion theory τ _G we give an example of a module that is type 2 τ _G -extending but not extending.     

JavaStatSoft: design patterns and features

JavaStatSoft, implemented using Java, is an open-source software for performing statistics. The current features of JavaStatSoft are described. Several well-known patterns the software used are introduced. In addition, based on these patterns and the experience in developing the software, a new framework, referred to as Data Analysis Module, is proposed to help programmers develop a user-friendly software for data analysis.     

Schreier rewriting beyond the classical setting Dedicated to our teacher Alfred Lvovich Shmelkin on his 70th birthday

Using actions of free monoids and free associative algebras, we establish some Schreier-type formulas involving ranks of actions and ranks of subactions in free actions or Grassmann-type relations for the ranks of intersections of subactions of free actions. The coset action of the free group is used to establish a generalization of the Schreier formula in the case of subgroups of infinite index. We also study and apply large modules over free associative and free group algebras.     

On locally convex hypersurfaces in Hadamard manifolds

Locally convex compact hypersurfaces immersed in a hollow simply connected Riemannian space of nonpositive sectional curvature are considered. They are proved to be convex hypersurfaces homeomorphic to the sphere. A similar result for immersed hypersurfaces with nonpositive definite second quadratic form of rank no smaller than one is obtained. Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 498–507, April, 2000.     

Track Extensions of Categories and Cohomology

We introduce the notion of n-fold track extensions of a category C by a natural system D and prove that such extensions represent classes in the cohomology of C with coefficients in D introduced by Baues–Wirsching. This generalizes a result of Huebschmann on the cohomology of groups.     

赋$\beta$-范空间中的最佳逼近问题

本文讨论赋$\beta$-范空间中的最佳逼近问题.以[1]引进的共轭锥为工具,借助[2]中关于$\beta$-次半范的Hahn-Banach延拓定理,第二节给出赋$\beta$-范空间的闭子空间中最佳逼近元的特征,第三节得到赋$\beta$-范空间中任何凸子集或子空间均为半Chebyshev集的充要条件是空间本身严格凸,文章最后证明了严格凸的赋$\beta$-范空间中任何有限维子空间都是Chebyshev集.     

Densely continuous forms, pointwise topology and cardinal functions

We consider the space D(X, Y) of densely continuous forms introduced by Hammer and McCoy [5] and investigated also by Holá [6]. We show some additional properties of D(X, Y) and investigate the subspace D*(X) of locally bounded real-valued densely continuous forms equipped with the topology of pointwise convergence τ- _p . The largest part of the paper is devoted to the study of various cardinal functions for (D*(X), τ _p ), in particular: character, pseudocharacter, weight, density, cellularity, diagonal degree, π-weight, π-character, netweight etc. This work was supported by Science and Technology Assistance Agency under the contract No. APVT-51-006904. The authors would like to thank Ľubica Holá for suggestions and comments.