On the Validity of Thompson's Conjecture for Finite Simple Groups

In this article, we prove a conjecture of J. G. Thompson for the finite simple group ² D _n (q). More precisely, we show that every finite group G with the property Z(G) = 1 and N(G) = N(² D _n (q)) is necessarily isomorphic to ² D _n (q). Note that N(G) is the set of lengths of conjugacy classes of G.     

Random Amalgamation of Simple Theories

Let T₁ and T₂ be two simple complete theories in disjoint languages. We prove that there is a simple complete theory which extends T₁ ∪ T₂ if T₂ has a certain condition.     

Simple algebras of Weyl type

Over a fieldF of arbitrary characteristic, we define the associative and the Lie algebras of Weyl type on the same vector spaceA[D] =A⊗F[D] from any pair of a commutative associative algebra,A with an identity element and the polynomial algebraF[D] of a commutative derivation subalgebraD ofA We prove thatA[D], as a Lie algebra (modulo its center) or as an associative algebra, is simple if and only ifA isD-simple andA[D] acts faithfully onA. Thus we obtain a lot of simple algebras. Su, Y., Zhao, K., Second cohornology group of generalized Witt type Lie algebras and certain representations, submitted to publication     

Boundary integrability of nonlinear sigma models

We describe recent work on the classical integrability of the principal chiral model and general sigma models with boundaries in (compact) symmetric spaces.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 322–328, February, 2005.     

关于简单MCD图

设G是阶为n的简单图，若G中没有两个等长圈且具有最大可能的边数，则称G为简单MCD图。本文通过引进路分解概念给出了两个关于图中圈数的结果并应用它们证明了下述定理：若G是简单MCD图，则G不是2连通可平面图且对所有整数n，除七个例外，G不是阶为n的含有同胚于K4的2连通图。     

单的非负有序关联半群

一个负有序关联半群(S,≤,.,*)称为单的关联半群,如果S的所有滤子是{1}和S本身.对负有序关联半群是单的关联半群进行了刻画,给出了一个负的关联半群是单的关联半群的等价条件.     

某些Lie单群的传递性

设D为有限线性空间，且T G Aut（T），其中T是非交换单群，并且同构于^2B2（g），Cn（g）（n≥3），^3D4（g），E7（q），E8（q），F4（q），^2F4（q），G2（q），^2G2（q）。假设D不是射影平面，G线传递作用在D上，则T点传递。     

Simple Signed Steiner Triple Systems

Let X be a v‐set, be a set of 3‐subsets (triples) of X, and be a partition of with . The pair is called a simple signed Steiner triple system, denoted by ST, if the number of occurrences of every 2‐subset of X in triples is one more than the number of occurrences in triples . In this paper, we prove that exists if and only if , , and , where and for , . © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 332–343, 2012     

Groups with exactly two supercharacter theories

In this paper, we classify those finite groups with exactly two supercharacter theories. We show that the solvable groups with two supercharacter theories are ?₃ and S₃. We also show that the only nonsolvable group with two supercharacter theories is Sp(6,2).     

简单波的解析解

Riemann于1860年给出了简单波的一般解,可是欲将其中所含的一个任意函数的具体形式按边界条件或初始条件求出来,却难以实现,因而对具体问题就难以深入探讨.本文按拟线性偏微分方程的几何理论,十分方便地给出了由边界条件或初始条件所确定的简单波解析解,并用这些解讨论了有关流动的性质,且得到了若干新颖的结果     

Local collection and end-extensions of models of compositional truth

We introduce a principle of local collection for compositional truth predicates and show that it is arithmetically conservative over the classically compositional theory of truth. This axiom states that upon restriction to formulae of any syntactic complexity, the resulting predicate satisfies full collection. In particular, arguments using collection for the truth predicate applied to sentences occurring in any given (code of a) proof do not suffice to show that the conclusion of that proof is true, in stark contrast to the case of the induction scheme.We analyse various further results concerning end-extensions of models of compositional truth and the collection scheme for the compositional truth predicate.     

Effectively and Noneffectively Nowhere Simple Sets

R. Shore proved that every recursively enumerable (r. e.) set can be split into two (disjoint) nowhere simple sets. Splitting theorems play an important role in recursion theory since they provide information about the lattice ? of all r. e. sets. Nowhere simple sets were further studied by D. Miller and J. Remmel, and we generalize some of their results. We characterize r. e. sets which can be split into two (non) effectively nowhere simple sets, and r. e. sets which can be split into two r. e. non-nowhere simple sets. We show that every r. e. set is either the disjoint union of two effectively nowhere simple sets or two noneffectively nowhere simple sets. We characterize r. e. sets whose every nontrivial splitting is into nowhere simple sets, and r. e. sets whose every nontrivial splitting is into effectively nowhere simple sets. R. Shore proved that for every effectively nowhere simple set A, the lattice L* (A) is effectively isomorphic to ?*, and that there is a nowhere simple set A such that L*(A) is not effectively isomorphic to ?*. We prove that every nonzero r. e. Turing degree contains a noneffectively nowhere simple set A with the lattice L*(A) effectively isomorphic to ?*. Mathematics Subject Classification: 03D25, 03D10.     

Indecomposable Sylow 2-Subgroups of Simple Groups

Let S be a Sylow 2-subgroup of a finite simple group and let S=S₁×S₂××S_k be the direct product and each component S_i, i=1,2,...,k is indecomposable. In this article, we prove that each S_i is also a Sylow 2-subgroup of some simple group. Mathematics Subject Classifications (2000) 20E32, 20D20.     

关于内7-闭单群的结构

研究内ｐ－闭群的结构是一个很活跃的课题．对于ｐ＝２，３，５的内ｐ－闭群的结构已经被确定（见［１，２，３］）．本文确定内７－闭单群的结构     

On Thompson's Conjecture of A 10

In this short article, we prove the Thompson's Conjecture is true for the alternating group A ₁₀, where A ₁₀ has exactly one connected prime graph component.     

Simple transitive 2-representations of left cell 2-subcategories of projective functors for star algebras

In this article, we study simple transitive 2-representations of certain 2-subcategories of the 2-category of projective functors over a star algebra. We show that in the simplest case, which is associated to the Dynkin type A₂, simple transitive 2-representations are classified by cell 2-representations. In the general case we conjecture that there exist many simple transitive 2-representations which are not cell 2-representations and provide some evidence for our conjecture.