A Graceful Numbering of A Class of Graphs

The graphs considered here are finite, undirected and simple. The sets ofvertices and edges of a graph G are denoted by V(G) and E(G), respectively.A graph G is called to be numbered if each vertex υ of G is assigned a nonnegative integer φ(υ), and each edge {u,υ} is assigned the absolute value of thedifference of the numbers at its endpoints, i.e.,|φ(u)-φ(υ)|.     

A Construction of Cryptogroups

Abstract In this paper, a cryptogroup is constructed by a band and a family of groups and homomorphisms satisfying some conditions.     

A Generalization of a Theorem of Liao

Let X be a metrizable space and let φ：R× X → X be a continuous flow on X. For any given {φt}-invariant Borel probability measure, this paper presents a {φt}-invariant Borel subset of X satisfying the requirements of the classical ergodic theorem for the contiImous flow （X, {φt}）. The set is more restrictive than the ones in the literature, but it might be more useful and convenient, particularly for non-uniformly hyperbolic systems and skew-product flows.     

A Theory of Isomorphisms of Fuzzy Groups

In this paper, a theory of isomorphisms of fuzzy groups is put forward. First, a new definition of isomorphisms of fuzzy groups is proposed and compared with the corresponding ones given in other related papers. Next, some basic properties of this kind of isomorphisms are roughly examined. Then, as the main results of this paper, two basic isomorphism theorems for fuzzy groups are establised. Finally, presenting applications of these theorems, we point out that for any given t-norm T∈■_(ss)∪■_H∪■_F∪■_Y)/{Min}, every T-fuzzy group is isomorphic to a Prod-fuzzy or T_m-fuzzy group, where ■_(ss), ■_H, ■_F and ■_Y denote the Schweizer-Sklar, Hamacher, Frank and Yager families of t-norms, respectively.     

A generalization of A ∘ A−1 ⩾I

A matrix inequality is obtained, in an elementary way, for the Schur product of two positive definite matrices. The inequality generalizes a well-known result due to Fiedler which asserts that if A is a positive definite matrix, then A ∘ A^-1-I is a positive semidefinite matrix, where ∘ denotes the Schur multiplication.     

A Note of log A ≥log B

In this paper,firstty we shall show some equivalent conditions of A＞B＞0;secondly by using the results of ours we shall show some characterizations of the chaotic order(i.e.,log A≥log B)by norm inequalities.     

A Generalization of Algebraic Lattices

In this paper,we prove two theorems on lattices and operators.Definition Let L be a complete lattice.An element a in L is(＊)-compact if and only 1if whenever a≤VA for A(?)L then a≤VB for some B(?)Awith B is at most countable.L is called(＊)—algebraic lattice if every element in L is a supremum of(＊)—compactelements.(＊)—algebraic lattice is a generalization of algebraic lattice.     

A Construction of Co-H Spaces

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Rectifications of A∞-Algebras

In this article, in the setting of connected DG-modules, we prove that, for any A _∞-algebra (M, {m _i } _i≥1), there is a chain contraction from a DG-algebra A _M onto the DG-module M such that the A _∞-algebra structure induced by perturbation theory on M is precisely the original one. In fact, the mentioned DG-algebra can be considered a rectification of the A _∞-algebra in the sense of (Boardman and Vogt, 1973 Boardman , J. M. , Vogt , R. M. ( 1973 ). Homotopy Invariant Algebraic Structures on Topological Spaces . Lecture Notes in Mathematics . Springer-Verlag , pp. 347 . [Google Scholar]). Appropiate dual results are given for A _∞-coalgebras.     

A proof of Sethares'''' conjecture

Let (?)(z) be holomorphic in the unit disk △ and meromorphic on △. Suppose / is a Teichmuller mapping with complex dilatation In 1968, Sethares conjectured that f is extremal if and only if either (i)(?) has a double pole or (ii)(?) has no pole of order exceeding two on (?)△. The "if" part of the conjecture had been solved by himself. We will give the affirmative answer to the "only if" part of the conjecture. In addition, a more general criterion for extremality of quasiconformal mappings is constructed in this paper, which generalizes the "if" part of Sethares' conjecture and improves the result by Reich and Shapiro in 1990.     

A Kind of Partition Identity

Let σ(n) denote the set of partitions of n, usually denoted by 1~(k_1)2~(k_2)…n~(k_n) with k_1 2k_2 …nk_n. Let φ_i (t) (i=1,…, r) be power series in t (over comp lex field C) with positive radii of convergence and φ_i(0)=1.For every let the power-type generating function     

A Graceful Algorithm of a Class of Trees

Let T be a tree with v vertices. It is said to be graceful if we can label the vertices with numbers 1,2,……,v in such a manner that the differences of any two adjacent vertices will again form the set {1,2,…,v-1}.Ringel conjectured, in1963, that every tree has a such labelling [1]. Ringel's conjecture remains unsettled. In this article, we shall investigate a class of graceful trees. Definition The,T_λ~((n)) is a tree with v_n vertices. Its vertices are v_i(j=0,1,…,n+1);v_(?)(j_o=1,2,…,n;j_1=1,2,…,k_1;……; j=1,2,…,k,≤λ), where λ,n,k_1,     

A generalization of a basic inequality of Telyakovski?

Two classes of numerical sequences are defined by means certain properties of the differences of terms of positive sequences, and their relationship to some newly defined classes and the well-known Sidon-Telyakovski? class is analyzed. It is also verified that if a sequence belongs to the newly defined wider class, then with this sequence in place of the sequence {1/k} an essential inequality established by Telyakovski? can be generalized notably. This new result and the previous generalizations of the original Telyakovski???s theorem are incomparable.     

A matrix generalization of a theorem of SzegŐ

— -B T . , T, T. — T, .., d=1. - . Cere: 0<p< exp logd=inf ¦1–t¦ ^p d, t , t(0)=0., . . . . . , . [1]. , . p=2 . - . p=2 [6, 8]. — p.     

Group of automorphisms of the ring ℤA4

The structure of the group of automorphisms of the integer group ring of the group A₄ is studied in terms of a semidirect product. We show that the Zassenhaus conjecture on the structure of automorphisms of integer group rings of finite groups for the group Aut ?A₄ holds.     

A Class of Singular Integral Operators

Our main tool is the block decomposition of functions defined on∑_(n-1). Definition 1 A function b(x')defined on ∑_(n-1) is called a q-block,1相似文献   

A Note for one of Inequality

In this paper, we find the largest contant C such that sin2 x xtanx > 2x2 cx5tan x 0相似文献   

A family of à n -groups

For each integern≥2 and for each prime powerq, we exhibit a group Γ which acts simply transitively on the set of vertices of the building of type à _n associated with the local field $\mathbb{F}^q ((Y))$ . This generalizes work in [2] and [8] (wheren=2) and in [1] (wheren≤4).     

Nonnegative Rank Factorization of a Nonnegative Matrix A with A A ≥0

In this article we obtain a nonnegative rank factorization of nonnegative matrices A satisfying one or both of the following conditions: (i) AA ? ? 0 (ii) A ? A ? 0, thus providing a new set of conditions that guarantee the existence of a nonnegative least-squares solution of a linear system. Indeed, the characterization of such matrices improves some of the previous known conditions for the existence of a nonnegative least-squares solution of a linear system.