Correlation of zeros of automorphic L-functions

We compute the n-level correlation of normalized nontrivial zeros of a product of L-functions:L(s,π1)···L(s,πk), where πj, j=1,...,k, are automorphic cuspidal representations of GLmj(QA). Here the sizes of the groups GLmj(QA) are not necessarily the same. When these L(s,πj) are distinct, we prove that their nontrivial zeros are uncorrelated, as predicted by random matrix theory and verified numerically. When L(s,πj) are not necessarily distinct, our results will lead to a proof that the n-level correlation of normalized nontrivial zeros of the product L-function follows the superposition of Gaussian Unitary Ensemble (GUE) models of individual L-functions and products of lower rank GUEs. The results are unconditional when m1,...,mk 4,but are under Hypothesis H in other cases.     

Lie Bialgebras of a Family of Lie Algebras of Block Type

Lie bialgebra structures on a family of Lie algebras of Block type are shown to be triangular coboundary.     

Isometric Embeddings of Subsets of Boundaries of Teichmüller Spaces of Compact Hyperbolic Riemann Surfaces

It is known that every finitely unbranched holomorphic covering π:S→S of a compact Riemann surface S with genus g≥2 induces an isometric embedding Φπ:Teich(S)→Teich(S).By the mutual relations between Strebel rays in Teich(S)and their embeddings in Teich(S),we show that the 1 st-strata space of the augmented Teichmüller space Teich(S)can be embedded in the augmented Teichmüller space Teich(S)isometrically.Furthermore,we show that Φπ induces an isometric embedding from the set Teich(S)B(∞)consisting of Busemann points in the horofunction boundary of Teich(S)into Teich(S)B(∞)with the detour metric.     

Sums of Squares of Integers

We find a formula for the sum of the first n squares:Sn = 12 22 32 42 … n2.We haveS1 = 1, S2 = 12 22 = 5, S3 = l2 22 32 = 14,S4 = 30, S5 = 55, S6 = 91.and so on. To make things a little simpler, we will also use the sum of the squares of the first zero terms , S0 = 02 = 0. Arranging these values in a table,we find thatSince the third differenes △3Sn are constant,these data values must follow a cubic pattern;that is, the formula for the sum of the squares of the first n integers is a cubic function,     

Some Properties of Two Kinds of Multifunctions

Let X and Y be metrizable topological linear spaces.In this paper,the following results are proved:(1)If X and Y are complete,F;X→Y is a point closed u.s.c.,and symmetric process with ——↑F(X)=Y,then either F(X) is meager in Y,or else F is an open multifunction with F(X)=Y.(2)If X is complete,and F:X→Y is a process with a subclosed graph,then F is l.s.c..We also discuss topological multi-homomorphisms between topological linear spaces.     

Vertices of π-Irreducible Characters of Groups of Odd Order

If G is a group of odd order and χ ∈ Irr(G) lifts an irreducible Brauer character ?, then we associate to χ a canonical pair (Q, δ) up to G-conjugacy, where Q is a vertex of ? and δ ∈ Irr(Q) is a linear character of Q. We show that (Q, δ) is a Navarro vertex for χ. We also discuss examples.     

Stability of Solution of a Class of Quasilinear Elliptic Equations

In this paper, using capacity theory and extension theorem of Lipschitz functions we first discuss the uniqueness of weak solution of nonhomogeneous quasilinear elliptic equationsin space W(θ,p)(Ω), which is bigger than W1,p(Ω). Next, using revise reverse Holder inequality we prove that if ωc is uniformly p-think, then there exists a neighborhood U of p, such that for all t ∈U, the weak solutions of equation corresponding t are bounded uniformly. Finally, we get the stability of weak solutions on exponent p.     

On the Growth of Components of Meromorphic Solutions of Systems of Complex Differential Equations

This paper investigates the problem of the growth of the components of meromorphic solutions of a class of a system of complex algebraic differential equations, and generalized some of N. Toda＇s results concerning the growth of differential equations to the case of systems of differential equations. The paper considers the existence of admissible solutions of the system of differential equations.     

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.     

Oscillation of Solutions of Linear Differential Equations

This paper is devoted to studying the growth problem, the zeros and fixed points distribution of the solutions of linear differential equations f″＋e^-zf′＋Q（z）f=F（z）,whereQ（z）≡h（z）e^cz and c∈R.     

The Semimodularity of Cardinal Power of Posets

LetX,Ybeanyposets,Y'denotethecardinalpowerwithbaseYandexponentX.Fortherelatedconceptslsymbolsorterminologies,seeF1],[2jor[3].lnL1],someexamplesaregaven,whichshowthatthesemimodularityofX,YandYxareindepentent.AndaquestionisaskedthatwhenthecardinalpowerYxwithbaseYandexpo-nentXissemimodular.Wenowanswerthequestioninthispaper.LemmaLetX,Ybeanyposets,f,geyx,thenthefollowingconditionsareequivalent:(l)fiscoveredbyg(denotedbyf,g);(2)Thereexists'anelementxoeX,suchthatf(x,),g(x,),andf(x)=g(x)(foran…     

Moments of the maximum of normed partial sums of ρ^--mixing random variables

Let {Xn,n ≥ 1} be a sequence of identically distributed ρ^--mixing random variables and set Sn =∑i^n=1 Xi,n ≥ 1,the suffcient and necessary conditions for the existence of moments of supn≥1 ｜Sn/n^1/r｜^p（0 〈 r 〈 2,p 〉 0） are given,which are the same as that in the independent case.     

Extension of a Theorem of Carleson-Duren

1. Introduction A theorem of Carleson,as generalized by Duren characterizes those positive measure μ on the unit disc U={z∈C:|z|<1} for which the H~p norm domiates the L~q(μ) norm of elements of H~p. Later on, Hasting proved an analogous results with H~p replaced by A~p, the Bergman space of fuctions f     

Estimates of groups of deviations of Faber sums and strong summability of faber series on classes of ψ-integrals

We establish upper bounds for a group of *-deviations of Faber sums on the classes of -integrals in a complex plane introduced by Stepanets.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 4, pp. 451–461, April, 2004.     

New Estimates for the Rate of Convergence of the Method of Subspace Corrections

We discuss estimates for the rate of convergence of the method of successive subspace corrections in terms of condition number estimate for the method of parallel subspace corrections. We provide upper bounds and in a special case, a lower bound for preconditioners defined via the method of successive subspace corrections.     

The Degree of Unsolvability of Models

The purpose of this paper is to describe the complexity of models by theirdegrees of unsolvability,J.Richter defined the degree of a structure to be deg ()=sup{deg(),deg(R_i),i=1,…,n},Where is a model for afinite language L={R_i,i=1,…,n}and the universe of is a subset of ω. Shepointed out that, according to her definition, there can be models which areisomorphic but their degrees are different.Also,her discussions are restricted tofinite languages and models whose universes are subsets of ω.     

Some Kinds of Bargaining Equilibria of Multi-objective Games

To solve the choice of multi-objective game's equilibria,we construct general bargaining games called self-bargaining games,and define their individual welfare functions with three appropriate axioms.According to the individual welfare functions,we transform the multi–objective game into a single-objective game and define its bargaining equilibrium,which is a Nash equilibrium of the single-objective game.And then,based on certain continuity and concavity of the multi-objective game's payoff function,we proof the bargaining equilibrium still exists and is also a weakly Pareto-Nash equilibrium.Moreover,we analyze several special bargaining equilibria,and compare them in a few examples.     

Dynamics of Polynomial Automorphisms of C~N

ＤｙｎａｍｉｃｓｏｆＰｏｌｙｎｏｍｉａｌＡｕｔｏｍｏｒｐｈｉｓｍｓｏｆＣ~Ｎ￥ＺｈａｎｇＷｅｎｊｕｎ（ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ，Ｋａｉｆｅｎｇ，Ｐ．Ｒ．Ｃｈｉａｎ，４７５００１）Ａｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｉｓａｓｓｉｇｎｅｄｔｏｄｉｓ?..     

Higher moment of coefficients of Dedekind zeta function

Let be a non-normal cubic extension over Q.We study the higher moment of the coefficients aK3(n)of Dedckind zeta function over sum of two squares∑n21+n22≤xa1K3(n21+n22),where 2≤l≤8 and n1,n2,l∈Z.