ED(i)形图簇的伴随多项式的因式分解及色性分析

令Dm表示三阶完全圈K3的一个顶点与路Pm-2的一个1度点重迭后得到的图；ψD^(i)(k,m），表示把Dm的第i个顶点（第1个顶点是1度点）与星图Sk 1的k度点重迭后得到的图；Erm r-1^D(i)表示把rDm中一个分支的第i个顶点与Sr的r-1度点重迭，同时把其余r-1个分支的第i个顶点分别与Sr的r-1个1度点都依次连一条边后得到的图。我们证明了对于1≤i≤m,r≥2，科簇Erm r-1^D(i) ∪(r-1)K1与Dm∪(r-2)ψD^(i)(1,m)∪ψD^(i)(r,m)两的补图是色等价的。     

The Order of Hypersubstitutions of Type （2, 2）

Hypersubstitutions are mappings which map operation symbols to terms of the corresponding arities. They were introduced as a way of making precise the concept of a hyperidentity and generalizations to M-hyperidentities. A variety in which every identity is satisfied as a hyperidentity is called solid. If every identity is an M-hyperidentity for a subset M of the set of all hypersubstitutions, the variety is called M-solid. There is a Galois connection between monoids of hypersubstitutions and sublattices of the lattice of all varieties of algebras of a given type. Therefore, it is interesting and useful to know how semigroup or monoid properties of monoids of hypersubstitutions transfer under this Galois connection to properties of the corresponding lattices of M-solid varieties. In this paper, we study the order of each hypersubstitution of type （2, 2）, i.e., the order of the cyclic subsemigroup generated by that hypersubstitution of the monoid of all hypersubstitutions of type （2, 2）. The main result is that the order is 1, 2, 3, 4 or infinite.     

On the Factorizations of （mg, mf）-graph

Let G be an (mg, mf)-graph, where g and f are integer-valued functions defined on V(G) and such that 0≤g(x)≤f(x) for each x ∈ V(G). It is proved that(1) If Z ≠ , both g and f may be not even, G has a (g, f)-factorization, where Z = {x ∈ V(G): mf(x)-dG(x)≤t(x) or dG(x)-mg(x)≤ t(x), t(x)= f(x)-g(x)>0}.(2) Let G be an m-regular graph with 2n vertices, m≥n. If (P1, P2,..., Pr) is a partition of m, P1 ≡ m (mod 2), Pi ≡ 0 (mod 2), i = 2,..., r, then the edge set E(G) of G can be parted into r parts E1 , E2,...,Er of E(G) such that G[Ei] is a Pi-factor of G.     

The Existence of Solutions of （k, n - k） Conjugate Boundary Value Problems in Banach Spaces

In this paper,by use of the Schauder fixed-point theorem,the existence of solution of (k,n-k) Conjugate boundary value problems in Banach spaces is investigated.     

On（N,U）-Coherence of Modules and Rings

Let U be a flat right R-module and N an infinite cardinal number.A left R-module M is said to be (N,U)-coherent if every finitely generated submodule of every finitely generated M-projective module in σ[M] is (N,U)-finitely presented in σ[M].It is proved under some additional conditions that a left R-module M is (N,U)-coherent if and only if Л^Ni∈I U is M-flat as a right R-module if and only if the (N,U)-coherent dimension of M is equal to zero.We also give some characterizations of left (N,U)-coherent dimension of rings and show that the left N-coherent dimension of a ring R is the supremum of (N,U)-coherent dimensions of R for all flat right R-modules U.     

The Characterizations of Weighted H^p（w）Spaces on the Certain Groups

ＴｈｅＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｓｏｆＷｅｉｇｈｔｅｄ　Ｈ~ｐ（ｗ）ＳｐａｃｅｓｏｎｔｈｅＣｅｒｔａｉｎＧｒｏｕｐｓＺｏｕＪｉｎ（邹进）（Ｌｅｓｈａｎ，ＴｈｅａｃｈｅｒｓＣｏｌｌｅｇｅ，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：ＴｈｅｗｅｉｇｈｔｅｄＨＰ（?..     

A Kind of Generalization of the Curve Type Node Configuration in R^S（S 〉 2）

A kind of generalization of the Curve Type Node Configuration is given in this paper,and it is called the generalized node configuration CTNCB in RS(S＞2).The related multivariate polynomial interpolation problem is discussed.It is proved that the CTNCB is an appropriate node configuration for the polynomial space PSn (S＞2).And the expressions of the multivariate Vandermonde determinants that are related to the Odd Curve Type Node Configuration in R2 are also obtained.     

E~(G(i))类图簇的伴随多项式的因式分解及色性分析

设Sn+1是n+1个顶点的星图,G是任意的p阶连通图.ΨG(i)(n,p)表示把Sn+1的n度点与G的第i(1 i p)个顶点重迭后得到的图;ErG(p+i)(r-1)表示把rG的r-1个分支的第i个顶点依次与Sr的r-1个1度点邻接,同时把剩下的一个图G的第i个顶点与Sr的r-1度点重迭后得到的图.我们通过讨论图簇ErG(p+i)(r-1)∪(r-1)K1的伴随多项式的因式分解,证明了它的补图的色等价图的结构性质.     

SG类图簇的伴随多项式的因式分解及色性分析

设G是任意的P阶连通图，V(G)={V1，V2，…，Vp}，Sn 1是具有度序列(n，1，1，…，1)的．n 1阶星图．令(ψ)^G(i）(n，P)表示图G的第i个顶点与Sn 1的n度点重迭后得到的图；Srp 1^G（i）表示rG的每个分支的第i个顶点依次与Sr 1的r个1度点重迭后得到的图，这里n≥1，P≥2，1≤i≤P．我们通过研究图的伴随多项式的因式分解，证明了两个图簇Srp 1^G(i）U（r-1)K1与(r-1)GUψG(i)(r,P)的补图是色等价的，但它们均不是色唯一的，从而推广了张秉儒证明的文[14]中的定理1。     

G_(v_i)~*型图的伴随多项式的因式分解及其色性分析

通过研究图的伴随多项式的因式分解 ,给出了证明非色唯一图的一种新的途径 ,并且得到了色等价图簇的结构特征 .     

图的伴随多项式基于挖补定理的因式分解及其色性分析

通过研究H_t~Γ及H_t~L类图簇的伴随多项式的因式分解,证明了两类图的补图的色等价图的结构性质和非色唯一性.     

S~s一类图簇的伴随多项式的因式分解及色性分析

通过研究图的伴随多项式的因式分解 ,给出了证明非色唯一图的一种新方法 ,并且得到了色等价图的一些结构特性 .     

若干图簇的伴随多项式的因式分解及色性分析

我们通过研究图的伴随多项式的因式分解,给出了证明非色唯一图的一种新方法,同时得到若干图簇的色等价图的结构定理.     

两类图簇的伴随多项式的因式分解及色性

令Sk 1表示k 1阶星图,φ^*(2k,n)表示2Sk 1的两个k度点分别与路Pn的两个1度点重迭后得到的图．对于1≤i≤2k n=1,用Srq 2^*(i)表示rφ^*(2k,n)的每个分支的第i个顶点依次与Sr 1的r个1度点重迭后得到的新图；Гpq 1^*(i)表示pφ^*(2k,n)的每个分支的第i个顶点及其对称点依次与S2p 1的2p个1度点配对且重迭后得到的新图．我们通过研究这两类新图与一定数目的孤立点组成的并图的伴随多项式的因式分解，证明了上述并图的补图的色等价图的结构定理．     

图的伴随多项式的两个因式分解定理及其应用

设G是m阶连通图,P_m是m个顶点的路.令S_km+1^G(i)表示把kG的每一个分支的第i(1≤i≤m)个顶点依次与星图S_k+1的k个1度顶点重迭后得到的图;令G_i1^S*(q,km)表示q阶图G的顶点V_i1与S_km+1^p(1)的k度顶点重迭后得到的图     

S~(GS*)类图簇的伴随多项式的因式分解及其色性

通过研究SGS*类图簇的伴随多项式的因式分解,证明了这类图簇的补图的色等价图的结构特征.