CONVERGENCE AND GROWTH OF MULTIPLE DIRICHLET SERIES

This article investigates the convergence and growth of multiple Dirichlet series. The Valiron formula of Dirichlet series is extended to n-tuple Dirichlet series and an equivalence relation between the order of n-tuple Dirichlet series and its coefficients and exponents is obtained.

A WEIGHTED ESTIMATE OF THE HORMANDER MULTIPLIER ON THE HEISENBERG GROUP

In this article, the anthors prove the weighted boundedness of Hoermander-type multiplier on the Heisenberg group.

ON THE OPERATIONS OF ALGEBROID FUNCTIONS

In this article, we first investigate the operational properties of algebroid functions. Then we prove two uniqueness theorems for algebroid functions.

Incidence Colorings of Powers of Circuits

The incidence chromatic number of G is the least number of colors such that G has an incidence coloring. It is proved that the incidence chromatic number of Cn^p, the p-th power of the circuit graph, is 2p ＋ 1 if and only if n = k（2p ＋ 1）, for other cases： its incidence chromatic number is at most 2p ＋ [r/k] ＋ 2, where n = k（p ＋ 1） ＋ r, k is a positive integer. This upper bound is tight for some cases.

THE PITS PROPERTY OF ENTIRE FUNCTIONS DEFINED BY DIRICHLET SERIES

The value distribution of entire functions defined by Dirichlet series are studied in this present article.It is proved that entire functions defined by Dirichlet series have the pits property,which improve the relative results on lacunary Taylor series obtained by Littlewood J.E.and Offord A.C.

List Extremal Number of Union of Short Cycles

The list extremal number f（G） is defined for a graph G as the smallest integer k such that the join of G with a stable set of size k is not ｜V（G）｜-choosable. In this paper, we find the exact value of f（G）, where G is the union of edge-disjoint cycles of length three, four, five and six. Our results confirm two conjectures posed by S. Gravier, F. Maffray and B. Mohar.

THE PITS PROPERTY OF ENTIRE FUNCTIONS DEFINED BY DIRICHLET SERIES

The value distribution of entire functions defined by Dirichlet series are studied in this present article.It is proved that entire functions defined by Dirichlet series have the pits property,which improve the relative results on lacunary Taylor series obtained by Littlewood J.E.and Offord A.C.

A Class of Antimagic Join Graphs

A labeling f of a graph G is a bijection from its edge set E（G） to the set {1, 2, ..., ｜E（G）｜}, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y. A graph G is antimagic if G has an f which is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than K2 is antimagic. In this paper, we show that if G1 is an n-vertex graph with minimum degree at least r, and G2 is an m-vertex graph with maximum degree at most 2r - 1 （m ≥ n）, then G1 V G2 is antimagic.

The Second Main Theorem Concerning Small Algebroid Functions

In this paper, we firstly give the definition of meromorphic function element and algebroid mapping. We also construct the algebroid function family in which the arithmetic, differential opera- tions are closed. On basis of these works, we firstly prove the Second Main Theorem concerning small algebroid functions for v-valued algebroid functions.

Remarks on g-functions on H^n

In this paper, the authors study some properties of Littlewood-Paley g-functions gψ（f）,Lusin area functions Sψ,α（f） and Littlewood-Paley gψ^＊,λ（f） functions defined on H^n, where α,λ 〉 0 and ψ, f are suitable functions. They are the generalization of the corresponding operators on R^n.