Function P-sets and Mining-discovery Theorems of Unknown Information Law

Function P-sets are a set pair which are composed of function internal packetsets S F and function outer packet sets S F or （S F , S F ） are function P-sets. Function P-sets have dynamic characteristics and law characteristics. Based on function P-sets, P-information law discovery theorems which has attribute supplementing-deleting are given. Mining-discovery and mining-discovery theorems of unknown information law are proposed. Function P-sets are a new theory and new method to research dynamic information laws for information systems.     

Chemotaxis-Growth方程的近似惯性流形

The long-time behaviour of solution to chemotaxis-growth system with Neumann condition is considered in this paper.The approximate inertial manifolds of such equations are constructed based on the contraction principle,and the orders of approximations of the manifolds to the global attractor are derived.     

Stabilization of 4-manifolds

The complex surface X obtained by 8 points blown up on CP2 and Barlow’s surface Y are homeomorphic,but not diffeomorphic.Using the Gromov-Witten invariant Ruan showed that the stabilized manifolds X×S2and Y×S2are not deformation equivalent.In this note,we show that the stabilized manifolds X×S1and Y×S1are diffeomorphic and non-deformation equivalent in cosymplectic sense.     

关于UR-环

A ring is said to be UR if every element can be written as the sum of a unit and a regular element. These rings are shown to be a unifying generalization of regular rings, clean rings and （S, 2）-ring~. Some relations of these rings are studied and several properties of clean rings and （S, 2）-rings are extended. PAng extensions of UR-rings are also investigated.     

Interval Valued Intuitionistic （S, T）-fuzzy Hv-submodules

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy Hv-submodules of an Hv-module with respect to a t-norm T and an s-norm S is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated. In particular, the connections between interval valued intuitionistic （S, T）-fuzzy Hv-submodules and interval valued intuitionistic （S, T）-fuzzy submodules are discussed.     

The K°-relation on the Congruence Lattice of a Regular Semigroup with an Inverse Transversal

Let S be a regular semigroup with an inverse transversal S° and C(S) the congruence lattice of S. A relation K° on C(S) is introduced as follows: if ρ, θ∈ C(S), then we say that ρ and θ are K°-related if Ker ρ° = Ker θ° , where ρ° = ρ|S°. Expressions for the least and the greatest congruences in the same K°-class as ρ are provided. A number of equivalent conditions for K° being a congruence are given.     

SUPERFLUOUS AND S-ESSENTIAL HOMOMORPHISMS

Let R be a ring and S a class of R-modules. S-superfluous epimorphisms and S-essential monomorphisms are introduced and studied in this article. As applications, some new characterizations of von Neumann regular rings and perfect rings are given. Finally, these notions are also used to study minimal homomorphisms.     

序半环的序理想

An ordered semiring is a semiring S equipped with a partial order ≤ such that the operations are monotonic and constant 0 is the least element of S.In this paper,several notions,for example,ordered ideal,minimal ideal,and maximal ideal of an ordered semiring,simple ordered semirings,etc.,are introduced.Some properties of them are given and characterizations for minimal ideals are established.Also,the matrix semiring over an ordered semiring is consid-ered.Partial results obtained in this paper are analogous to the corresponding ones on ordered semigroups,and on the matrix semiring over a semiring.     

Commuting dual Toeplitz operators on the harmonic Bergman space

We completely characterize commuting dual Toeplitz operators with bounded harmonic symbols on the harmonic Bergman space of the unit disk. We show that for harmonic ■ and ψ, S■Sψ= SψS■ on(L2h)⊥if and only if ■ and ψ satisfy one of the following conditions:(1) Both ■ and ψ are analytic on D.(2) Both ■ and ψ are anti-analytic on D.(3) There exist complex constants α and β, not both 0, such that ■ = αψ + β.Furthermore, we give the necessary and sufficient conditions for S■Sψ= S■ψ.     

素环中的协中心化广义导子

Let R be a prime ring with center Z and S (?) R. Two mappings D and G of R into itself are called cocentralizing on S if D(x)x-xG(x) ∈ Z for all x ∈ S. The main purpose of this paper is to describe the structure of generalized derivations which are cocentralizing on ideals, left ideals and Lie ideals of a prime ring, respectively. The semiprime case is also considered.     

可分解半群的Morita等价

设S,R是可分解半群.记US-FAct={sM∈S-Act|SM=M且SHoms(S,M)≌M],给出了范畴US-FAct与UR-FAct等价的刻划;S分别强Morita等价于一个夹层半群、局部单位半群、幺半群和群的条件;S是完全单半群当且仅当S强Morita等价于一个群且对任何指标集I,S SHoms(S,i∈I S)→i∈I S,s t·f→(st)f,是同构.     

Pseudo-Anosov Mapping Classes and Their Representations by Products of Two Dehn Twists

Let S be a Riemann surface of analytically finite type （p, n） with 3p-3＋n 〉 0. Let a ∈ S and S = S - {a}. In this article, the author studies those pseudo-Anosov maps on S that are isotopic to the identity on S and can be represented by products of Dehn twists. It is also proved that for any pseudo-Anosov map f of S isotopic to the identity on S, there are infinitely many pseudo-Anosov maps F on S - {b} = S - {a, b}, where b is a point on S, such that F is isotopic to f on S as b is filled in.     

乘法半群为左正规纯正群的半环

研究了加法半群为半格,乘法半群为左正规纯正群的半环．证明了此类半环（S,＋,．）可以嵌入到半格（S,＋）的自同态半环中．构造S的一个特定的偏序关系,得到了（S,·）上的自然偏序与所构造偏序相等的等价条件．     

拓扑分子格的S紧性和S次紧性

利用半开元等半拓扑概念在拓扑分子格中引入S紧性与S次紧性，给出了它们的刻画，推广了文[1]中的紧性与次紧性，证明了拓扑分子格的S紧性，S次紧性，STi分离性(i=-1，0，1，2)与STi^*分离性(i=0，1，2)为半拓扑性质。     

线性流形上两类矩阵反问题的最小二乘解

给定广义自反矩阵R,S,即R=R=R-1,S=S=S-1,若复矩阵X满足条件RXS=X（或RXS=X）,则称其为（R,S）-对称矩阵（或（R,S）-斜对称矩阵）.分别讨论了线性流形上（R,S）-对称矩阵和（R,S）-斜对称矩阵约束下矩阵方程MZN=E的最小二乘问题,得到了通解表达式.     

纯正半群上的强同余及其格

给出了纯正半群S的强同余格上同余T的一些判别性质,证明了S上所有基础强同余所构成的集合FCP（S）是CP（S）的完备子格,最后讨论了由纯正半群的正规子半群决定的交完备子格的结构及由“求核”运算确定的（交完备格）同余K的若干性质,还顺带讨论了群同余格.     

某些半环上Green关系的刻划

假设S是乘法半群为完全正则半群的半环.给出了S上的Green关系H,L和D是S上的半环同余的等价刻划,并利用幂等元的方法证明了在一定条件下D是S上的同余当且仅当L,R是S上的同余.     

右连续上鞅的提升及其应用

本文首先给出了一个右连续上鞅的ＳＤ提升，在引进Ｓ－上鞅和强Ｓ－上鞅概念之后，研究了一一致可积上鞅与Ｓ－上鞅，类上鞅与强Ｓ－上鞅之间的关系，并得到了Ｓ－上鞅与强Ｓ－上鞅的许多性质，作为其直接结果，给出了类上鞅的Ｄｏｏｂ－ＭＮｅｙｅｒ分解。     

Arithmetical and semihereditary semigroup rings

In this paper conditions on the commutative ring R (with identity) and the commutative semigroup ring S (with identity) are found which characterize those semigroup rings R[S] which are reduced or have weak global dimension at most one. Likewise, those semigroup rings R[S] which are semihereditary are completely determined in terms of R and S.     

Automorphic and endomorphic reducibility and primitive endomorphisms of free metabelian groups

Let S be the free metabelian group of rank 2. In this paper we prove the following results:(i) Given a pair of elements g, h of S, there exists an algorithm to decide whether or not g is an automorphic image of h; (ii) If g, h are in the commutator subgroup S′ of S such that each is an endomorphic image of the other then g , h are automorphic; (iii) If an endomorphism of S maps primitive elements of S to primitive elements of S then it defines an automorphism of S. We also include an example to show that, in (ii) above,the requirement that g,h are in S ? can not be relaxed.