具有势函数的弱f-稳态映射的若干结果

本文研究了与拉回度量有关广义泛函Φ_f,H.利用应力能量张量的方法,得到具有势函数的弱f-稳态映射的一些刘维尔型定理.     

格的TL-模糊理想

本文研究了格的TL-模糊理想. 利用生成TL-模糊理想, 证明了一个模格的全体T_M-模糊理想形成一个完备的模格. 此外, 利用L-模糊集的投影和截影, 获得了将直积格的TL-模糊理想表示成分量格的TL-模糊理想的L-直积的一个充分必要条件. 所得结果进一步推广和发展了格的模糊理想的理论.     

(α,β)-γ开集与(α,β)-γ-Ti空间

本文首先给出(α,β)-γ开集定义,获得了(α,β)-γ开集性质;然后引入了(α,β)-γ-T_i空间和(α,β)-γ-T_i^*空间概念(i=0,1/2,1,2,5/2),并得到它们更广泛的拓扑性质.     

辫子T-范畴的构造

本文首先引入了一类新的范畴_AYD_G^H, 这个范畴是一簇范畴{_AYD^H(α,β)}_(α,β)∈G的非交并, 获得了范畴{_AYD^H(α,β)}_(α,β)∈G是一个辫子T-范畴当且仅当(A,H,Q)是一个G-偶结构, 推广了2005年Panaite和Staic的主要结论. 最后, 当H是有限维时, 构造了一个拟三角T-余代数{A#H^*(α,β)}_(α,β)∈G, 它的表示范畴与{_AYD^H(α,β)}_(α,β)∈G是同构的.     

QK空间的插值序列

本文研究了Q_K空间的插值问题.利用复分析和调和分析的方法,获得了单位圆盘上的一个序列{z_n}是Q_K∩H^∞空间的插值序列的一个充分必要条件,推广了Q_p空间的部分结果.     

离散时间观测下的α-赋权分数桥的参数估计

本文研究了赋权分数桥dX_t=-α(X_t)/(T-t)dt+dB_t^a,b,0≤t < T,中未知参数α>0的参数估计问题,其中B^a,b是参数为a>-1,|b|<1,|b|≤a+1的赋权分数布朗运动.假设对随机过程X_t进行离散观测t_i=i△_n,i=0,…,n,且T_n=n△_n.本文构造了α的最小二乘估计α_n,证明了当n→∞时,α_n依概率收敛到α.     

环Fp+vFp上互补对偶常循环码

本文研究了环F_p+vF_p上互补对偶（1-2v）-常循环码.利用环F_p+vF_p上（1-2v）-常循环码的分解式C=vC_1-v ⊕（1-v）C_v,得到了环F_p+vF_p上互补对偶（1-2v）-常循环码的生成多项式.然后借助从F_p+vF_p到F_p²的Gray映射,证明了环F_p+vF_p上互补对偶（1-2v）-常循环码的Gray像是F_p的互补对偶循环码.     

不含有5-圈和k4平面图的森林分解

本文研究了不含有5-圈和K₄的平面图的森林分解问题.利用权转移法,证明了任意不含有5-圈和K₄的平面图能分解成三个森林,且其中有一个森林的最大度不超过2,这一结果推广了文献[2,3]中的结论.     

具有左中心幂等元的U-富足半群

本文研究了具有左中心幂等元的U-富足半群的半格分解.利用半格分解,证明了半群S为具有左中心幂等元的U-富足半群,当且仅当S为直积M_α×Λ_α的强半格,其中M_α是幂幺半群,Λ_α是右零带.这一结果为具有左中心幂等元的U-富足半群结构的建立奠定了基础.     

二部图中求正交于星的(g, f)-染色的一个多项式算法

令G是一个具有顶点集V(G)和边集 E(G)的二部图, 且令g和f是定义在 V(G)上的两个非负整数值函数,使得对每个顶点x∈V(G)都有g(x)≤f(x). G的一个(g,f)-染色是一个推广的边染色,它满足在每个顶点x每一种颜色至少出现g(x)次且至多出现f(x)次. 给出了求二部图中满足某些约束条件且具有最小颜色数的(g,f)-染色的一个多项式算法并证明了此结果是最好的可能.     

Inequalities involving independence domination, f-domination, connected and total f-domination numbers

Let f be an integer-valued function defined on the vertex set V(G) of a graph G. A subset D of V(G) is an f-dominating set if each vertex x outside D is adjacent to at least f(x) vertices in D. The minimum number of vertices in an f-dominating set is defined to be the f-domination number, denoted by _f (G). In a similar way one can define the connected and total f-domination numbers _c,f (G) and _t,f (G). If f(x) = 1 for all vertices x, then these are the ordinary domination number, connected domination number and total domination number of G, respectively. In this paper we prove some inequalities involving _f (G), _c,f (G), _t,f (G) and the independence domination number i(G). In particular, several known results are generalized.     

Positive Derivations on Archimedean Almost f-Rings

It is shown by P. Colville, G. Davis and K. Keimel that if R is an Archimedean f-ring then a positive group endomorphism D on R is a derivation if and only if the range of D is contained in N(R) and the kernel of D contains R ², where N(R) is the set of all nilpotent elements in R and R ² is the set of all products uv in R. The main objective of this paper is to establish the result corresponding to the Colville–Davis–Keimel theorem in the almost f-ring case. The result obtained in this regard is that if D is a positive derivation in an Archimedean almost f-ring, then the range of D is contained in N(R) and the kernel of D contains R ³, where R ³ is the set of all products uvw in R. Examples are produced showing that, contrary to the f-ring case, the converse is in general false and the third power is the best possible.     

<Emphasis Type="Italic">f</Emphasis>-Colorings of some graphs of <Emphasis Type="Italic">f</Emphasis>-class 1

An f-coloring of a graph G is an edge-coloring of G such that each color appears at each vertex v V（G） at most f（v） times. The minimum number of colors needed to f-color G is called the f-chromatic index of G and is denoted by X′f（G）. Any simple graph G has the f-chromatic index equal to △f（G） or △f（G） ＋ 1, where △f（G） =max v V（G）{[d（v）/f（v）]}. If X′f（G） = △f（G）, then G is of f-class 1; otherwise G is of f-class 2. In this paper, a class of graphs of f-class 1 are obtained by a constructive proof. As a result, f-colorings of these graphs with △f（G） colors are given.     

Orthogonal factorizations of digraphs

Let G be a digraph with vertex set V(G) and arc set E(G) and let g = (g ⁻, g ⁺) and ƒ = (ƒ ⁻, ƒ ⁺) be pairs of positive integer-valued functions defined on V(G) such that g ⁻(x) ⩽ ƒ ⁻(x) and g ⁺(x) ⩽ ƒ ⁺(x) for each x ∈ V(G). A (g, ƒ)-factor of G is a spanning subdigraph H of G such that g ⁻(x) ⩽ id _H (x) ⩽ ƒ ⁻(x) and g ⁺(x) ⩽ od _H (x) ⩽ ƒ ⁺(x) for each x ∈ V(H); a (g, ƒ)-factorization of G is a partition of E(G) into arc-disjoint (g, ƒ)-factors. Let = {F ₁, F ₂,…, F _m} and H be a factorization and a subdigraph of G, respectively. is called k-orthogonal to H if each F _i , 1 ⩽ i ⩽ m, has exactly k arcs in common with H. In this paper it is proved that every (mg+m−1,mƒ−m+1)-digraph has a (g, f)-factorization k-orthogonal to any given subdigraph with km arcs if k ⩽ min{g ⁻(x), g ⁺(x)} for any x ∈ V(G) and that every (mg, mf)-digraph has a (g, f)-factorization orthogonal to any given directed m-star if 0 ⩽ g(x) ⩽ f(x) for any x ∈ V(G). The results in this paper are in some sense best possible.      

Maps Interchanging f-Structures and their Harmonicity

We study some remarkable classes of metric f-structures on differentiable manifolds (namely, almost Hermitian, almost contact, almost S-structures and K-structures). We state and prove the necessary condition(s) for the existence of maps commuting such structures. The paper contains several new results, of geometric significance, on CR-integrable manifolds and the harmonicity of such maps.     

Subgroups and Hulls of Specker Lattice-Ordered Groups

In this article, it will be shown that every -subgroup of a Specker -group has singular elements and that the class of -groups that are -subgroups of Specker -group form a torsion class. Methods of adjoining units and bases to Specker -groups are then studied with respect to the generalized Boolean algebra of singular elements, as is the strongly projectable hull of a Specker -group.     

A Characterization of Graphs without Even Factors

In this paper, we first reduce the problem of finding a minimum parity (g,f)-factor of a graph G into the problem of finding a minimum perfect matching in a weighted simple graph G*. Using the structure of G*, a necessary and sufficient condition for the existence of an even factor is derived. This paper was accomplished while the second author was visiting the Center for Combinatorics, Nankai University. The research is supported by NSFC     

Structural Remarks on Bipartite Graphs with Unique f-Factors

In this note we will derive some structural results for a bipartite graph G with a unique f-factor. Two necessary conditions will be that G is saturated, meaning that the addition of any edge leads to a second f-factor, and that f_A, f_B≥1. Here f_A and f_B are defined as the minimum of f over the vertices in the two partite sets A and B of G, respectively. Our main result states that G has at least f_A + f_B vertices for which d_G (v) = f(v) holds.     

<Emphasis Type="Italic">f</Emphasis>-Vectors of barycentric subdivisions

For a simplicial complex or more generally Boolean cell complex Δ we study the behavior of the f- and h-vector under barycentric subdivision. We show that if Δ has a non-negative h-vector then the h-polynomial of its barycentric subdivision has only simple and real zeros. As a consequence this implies a strong version of the Charney–Davis conjecture for spheres that are the subdivision of a Boolean cell complex or the subdivision of the boundary complex of a simple polytope. For a general (d − 1)-dimensional simplicial complex Δ the h-polynomial of its n-th iterated subdivision shows convergent behavior. More precisely, we show that among the zeros of this h-polynomial there is one converging to infinity and the other d − 1 converge to a set of d − 1 real numbers which only depends on d. F. Brenti and V. Welker are partially supported by EU Research Training Network “Algebraic Combinatorics in Europe”, grant HPRN-CT-2001-00272 and the program on “Algebraic Combinatorics” at the Mittag-Leffler Institut in Spring 2005.