For Ideal Fluids,Eulerian and Lagrangian Instabilities are Equivalent

No Abstract.  .     

Finiteness Conditions and Relative Singularity Categories

Acta Mathematica Sinica, English Series - We introduce the n-pure projective (resp., injective) dimension of complexes in n-pure derived categories, and give some criteria for computing these...     

Rewriting Systems and Geometric Three-Manifolds

The fundamental groups of most (conjecturally, all) closed three-manifolds with uniform geometries have finite complete rewriting systems. The fundamental groups of a large class of amalgams of circle bundles also have finite complete rewriting systems. The general case remains open.     

Residuated Structures,Concentric Sums and Finiteness Conditions

This article is motivated by a concern with finiteness conditions on varieties of residuated structures—particularly residuated meet semilattice-ordered commutative monoids. A “concentric sum” construction is developed and is used to prove, among other results, a local finiteness theorem for a class that encompasses all n-potent hoops and all idempotent subdirect products of residuated chains. This in turn implies that a range of residuated lattice-based varieties have the finite embeddability property, whence their quasi-equational theories are decidable. Applications to substructural logics are discussed.     

Properties of Integers and Finiteness Conditions for Semigroups

Let h and k be integers greater than 1; we prove that the following statements are equivalent: 1) the direct product of h copies of the additive semigroup of non-negative integers is not k-repetitive; 2) if the direct product of h finitely generated semigroups is k-repetitive, then one of them is finite. Using this and some results of Dekking and Pleasants on infinite words, we prove that certain repetitivity properties are finiteness conditions for finitely generated semigroups.     

Homological Finiteness Conditions for Groups,Monoids, and Algebras

Let ? be an additive category and 𝒞 a full subcategory with split idempotents, and closed under isomorphic images and finite direct sums. We give conditions on ? and 𝒞 implying that ? embeds into an abelian category, so that the objects of 𝒞 turn into injective objects. This construction generalizes the embedding of exactly definable categories into locally coherent categories, while the dual construction generalizes the embedding of finitely accessible categories into Grothendieck categories with a family of finitely generated projective generators. As applications, we characterize exactly definable categories through intrinsic properties and study those locally coherent categories whose fp-injective objects form a Grothendieck category.     

混沌与SS混沌不等价

构造了是混沌但不是SS混沌的极小子转移,从而证明对于限制在测度中心上的紧系统而言,混沌一般地不等价于SS混沌.     

发展型p-Laplace方程(组)解的整体有限性

本文主要在多维空间中讨论一类发展型p-Laplace方程及方程组的初边值问题.这类问题在非牛顿渗流方程的理论研究中有着重要的意义.作者通过上、下解的方法证明了发展型p-Laplace方程解的整体有限性;同时利用两个关于常微分方程的比较原理,给出了相应的方程组解的整体有限性结果.     

Rewriting Systems and the Complete Growth Series for Triangular Coxeter Groups

In this paper, a complete finite rewriting system is constructed for Coxeter groups of the form $$W = \left\langle {a,b,c|a^2 = b^2 = c^2 = (ab)^p = (bc)^q = (ca)^r = 1} \right\rangle $$ with respect to the system of generators $S = \{ a,b,c\} $ , where $p,q,r \in \mathbb{Z}$ , $p,q,r \geqslant 2$ , and $1/p + 1/q + 1/r < 1$ . Rewriting systems of this kind can be used to evaluate the complete growth series of a group.     

Dynamical and Topological Methods in the Theory of Geodesically Equivalent Metrics

We suggest a new, more global, approach to the study of geodesically equivalent metrics which is based on application of the theory of integrable geodesic flows. Bibliography: 17 titles.     

带有限性条件Abel群的自同态环和自同构群

给出了带极大或极小条件的Abel群A的自同构群以及自同态环的相伴Lie环是可解或幂零的充要条件.同时也给出了群A=Q_(π1)⊕Q_(π2)⊕…⊕Q_(πr)的自同构群是可解或幂零的充要条件,以及群A的自同态环的相伴Lie环是可解或幂零的充要条件.     

拓扑系统的紧性和分离性

考察拓扑系统的两种紧性——空间式紧和locale式紧,给出紧性的若干刻画,讨论了两种紧性的相互关系,证明了拓扑系统的两种紧性都是拓扑空间紧性的良好推广,说明了紧拓扑系统的闭子拓扑系统、有限和系统以及积系统仍是紧拓扑系统。最后在拓扑系统中考察了紧性加强分离性的问题,得到了紧,(强)T2拓扑系统为(强)T3,(强)T4拓扑系统等结论,并用理想收敛刻画了拓扑系统的强T2分离性。     

Weak Factorization Systems and Topological Functors

Weak factorization systems, important in homotopy theory, are related to injective objects in comma-categories. Our main result is that full functors and topological functors form a weak factorization system in the category of small categories, and that this is not cofibrantly generated. We also present a weak factorization system on the category of posets which is not cofibrantly generated. No such weak factorization systems were known until recently. This answers an open problem posed by M. Hovey.     

John区域的等价条件

讨论了单位圆盘D内的局部单叶的解析函数,在其Schwarz导数满足条件│Sf(z)│≤2a[1+(1-α)│z│2](1-│z│2)-2(1≤α≤2)时的映射性质,得到了f(D)为John区域的两个等价命题.并给出了f(D)为John区域的一个必要条件.     

Finiteness Conditions for Hochschild Homology Algebra and Free Loop Space Cohomology Algebra

We prove that over a characteristic zero field, in most cases, neither the Hochschild homology algebra of a commutative algebra, nor the free loop space cohomology algebra of a topological space, is finitely generated.     

新型拓扑KKM定理与等价形式及其应用

在不具线性结构拓扑空间—广义区间空间—中得到了新型拓扑KKM定理及其几个等价形式.作为应用,本文研究了广义区间空间中一类抽象形式变分不等式解的存在性问题.     

关于Hille-Yosida条件的等价刻画

本文得到了算子半群理论中的Ｈｉｌｅ－Ｙｏｓｉｄａ条件［１－５］的等价刻画，同时对Ａｒｅａｄｔ与Ｋｅｌｅｒｍａｎｎ的结果［４］作了相应的改进．     

关于二个方程同解的条件及其应用

探讨ｆ［ｎ］（ｘ）＝ｘ与ｆ（ｘ）＝ｘ同解的条件，分析一维离散动力系统的周期和混沌问题、并举例说明同解条件在解方程中的应用。