CLASSIFICATIONS OF (2,1)-STABLE AND (1,2)-STABLE UNFOLDINGS OF MAP GERMS WITH CODIMENTION≤3

1IntroductionConsideringthecoarseuessoftheequivalencerelationonunfoldingsusedinThom'scel-ebratedlistofsevenelementarycatastrophesWassermanndeveloped(r,s)-stableunfoldingtheoryinhispaper[4]andgavetheclassificationsof(1,3)-,(3,1)-stableunfoldings.Andclassificationof(2,2)-stableunfoldingswasgivenin[51.Forthecompletenessof(r,s)-stableunfoldingtheoryanditsapplicationinbifllrcationproblemundertheframeworkof(r,s)-equiv-alenceweclassify(2,1)-stableand(1,2)-stableunfoldingsofmaPgermswithcodimentions53…     

Multi-linear variable separation approach to nonlinear systems

The multi-linear variable separation approach is reviewed in this article. The method has been recently established and successfully solved a large number of nonlinear systems. One of the most exciting findings is that the basic multi-linear variable separation solution can be expressed by a universal formula including two (1+1)-dimensional functions, and at least one is arbitrary for integrable systems. Furthermore, the method has been extended in two different ways so as to enroll more low dimensional functions in the solution.      

含两组状态变量等变分歧问题开折的唯一性和稳定性

基于奇点理论中光滑映射芽的接触等价,讨论多参数等变分歧问题关于接触等价的开折的唯一性和稳定性.将这种等变分歧问题的状态变量分为两组,其中一组的诸状态变量可以独立地变化,而属于另一组的诸状态变量在变化过程中依赖于前一组中的诸状态变量.得出了在接触等价下,满足一定条件的等变分歧问题的万有开折是唯一的,并且给出了一定条件下等变分歧问题开折稳定的一个充要条件.     

Kripke submodels and universal sentences

We define two notions for intuitionistic predicate logic: that of a submodel of a Kripke model, and that of a universal sentence. We then prove a corresponding preservation theorem. If a Kripke model is viewed as a functor from a small category to the category of all classical models with (homo)morphisms between them, then we define a submodel of a Kripke model to be a restriction of the original Kripke model to a subcategory of its domain, where every node in the subcategory is mapped to a classical submodel of the corresponding classical model in the range of the original Kripke model. We call a sentence universal if it is built inductively from atoms (including ? and ⊥) using ∧, ∨, ?, and →, with the restriction that antecedents of → must be atomic. We prove that an intuitionistic theory is axiomatized by universal sentences if and only if it is preserved under Kripke submodels. We also prove the following analogue of a classical model‐consistency theorem: The universal fragment of a theory Γ is contained in the universal fragment of a theory Δ if and only if every rooted Kripke model of Δ is strongly equivalent to a submodel of a rooted Kripke model of Γ. Our notions of Kripke submodel and universal sentence are natural in the sense that in the presence of the rule of excluded middle, they collapse to the classical notions of submodel and universal sentence. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

李超代数与Frobenius代数

利用限制李超代数的新定义,给出了李超代数的p-包络的一些相关结果,并将李代数中表示理论的一些结果推广到李超代数上,进而研究了限制李超代数与Frobenius代数的关系．     

Using Fox Derivatives in Treating Groups of the Form F/[R′, F]

For a factor group with respect to periodic part of a group of the form F/[R′, F], an embedding in the matrix group is defined. The criteria for a matrix to belong to an image of this group and for elements to be conjugate are specified. Some statements having a direct bearing on groups of the form in question are proved. Application of the results obtained allows us to refine the answer in [7] to a question by O. Chapuis concerning the universal classification of ∀-free soluble groups with two generators. Supported by RFBR grant No. 02-01-00293 and by FP “Universities of Russia” grant No. UR.04.01.227. __________ Translated from Algebra i Logika, Vol. 45, No. 1, pp. 114–125, January–February, 2006.     

球共振声学法测量普适气体常数

设计和建立了高精度的球共振声学法气体音速测量装置,分析了实际的球共鸣器的结构对共振频率的影响,并给予了相应的修正.测量了温度为29315K,压力在02MPa—08MPa范围内氩气的音速,并根据音速数据确定了普适气体常数.实验温度、压力和普适气体常数的不确定度分别为±14mK,±2kPa和±00036%.最终确定的普适气体常数R为831439±000030J·mol-1·K-1. 关键词： 普适气体常数 音速 球共振器 声学法     

Frames with Transitive Structures

A classical result in the theory of uniform spaces is that any topological space with a base of clopen sets admits a uniformity with a transitive base and the uniform topology of such a space has a base of clopen sets. This paper presents a pointfree generalization of this, both to uniform and quasi-uniform frames, together with various properties concerning total boundedness, compactifications and completions.     

矩阵系统扰动后的稳定性问题

本文证明：若矩阵系统是广义各态历经的，则系统是稳定的；若矩阵系统是善真的，则系统是条件稳定的。