In this paper, we study the boundedness and compactness of composition operator on the Bloch space β（Ω）, Ω is a bounded homogeneous domain. For Ω＝Ｂｎ， we give the necessary and sufficient conditions for a composition operator C to be compact on β（Ｂn） or β0(Bn) .

Let f(x) be a continued fraction with elements a_nx, where coefficients an are positive algebraic numbers. Using the criterion of [1] for any nonzero real algebraic numbers a1,..as, with distinct absolute values the algebraic independence of the values f(a1 ),... , f(as) is proved under certain assumption concerning only with an. For some transcendental numbers the algebraic independence of values is also established

Let A be an n x n irreducible Boolean matrix with period p. In [1], the generalized maximum density index hA(k) is defined. Let DISn,d(k) = {hA(k) | A PMn(d)}, where PMn(d) is the set of all n x n primitive matrices with d nonzero entries exactly. In this paper, we show that Furthermore, we define the norm of A, denoted by (A), the numbers of 1 in A and describe the extremal matrices with minimum norm.

We deal with the quantifier eliminations and corresponding computational complexities for the theory T of groups of prime orders over language We prove that T has the quantifier elimination property and give,an upper bound of the decision problem for theory T.

In this paper, we using the results in Hua Luogeng and Lu Qikeng of harmonic analysis in classical domains for functions theorey of several complex variables, consider harmonic analysis in four kind classical domains for complex Clifford analysis and discuss the existence (uniqueness) of solutions of the two relevant boundary value problems and integral representation of the regular solutions of those problems.

In this paper it is prove that a quadratic system with two foci has at most one limit cycle around one of the two foci, and hence the limit cycles of the quadratic system with two fool must be (0, i)-distribution or (1, i)-distribution (i = 0, 1, 2,...).

The notion of limit molecular lattice is introduced, it is proved that the category of limit molecular lattices is a Cartesian closed category containing the category of topological molecular lattices as a bireflective full subcategory and the category of limit spaces as a reflective and coreflective subcategory, respectively.

The formula of invariants with the operation of insertion and pushing are given on long curves.

The embeding relations between Banach-space-valued martingale spaces and and and the duals of martingale Hardy spaces and Dr(X) with small index are studied, the results obtained here are connected closely with the convexity and smoothness of the Banach space which the martingales take values in.

In this paper, we study a class of non-linear singular PDE in holomorphic functions defined on a high dimensional complex domain. Under certain assumptions, we proved the existence and uniqueness of the local holomorphic solution.

In this paper, we consider a nonlinear degenerate quasilinear parabolic initial boundary value problems of second order. Using results from the theory of pseudomonotone operators, we show that there exists at least one weak solution in a suitable weighted Sobolev space.

The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the asymptotic property of general Dedekind sums, and give an interesting asymptotic formula.

In this paper, 2nth order symmetric differential expressions with real valued coefficients are considered. Some results concerning the discreteness of spectrum of associated operators are obtained. Especially, the necessary and sufficient conditions are given which ensure that the spectrum of differential operators is discrete.

The injectiveness of a mapping from primitive sequences over Z2n to its highest coordinate sequences is known [1]. In this paper,the above fact is generalized to primitive sequences over Galois rings using trace representation, and a restoring algorithm, which output the primitive sequence according to its characteristic polynomial and highest coordinate sequence, is given.

In this paper, we discuss the tournament matrix which can be interpreted as a competition where n participants play each other once in a match that can be end in ties. A player receives two points for each win and one point for each tie. We obtain the number of tournament matrices with special score vectors, and give the lower bound of the number for tournament matrices with strong score vectors and obtain the score vector with this lower bound.

Some sufficient and necessary conditions for sets having the same Hausdorff content and Hausdorff measure are obtained. For the self-similar set satisfying the open set condition, it is proved that its Hausdorff content and Hausdorff measure are equal and a formula, which is convenient for use, of its Hausdorff measure is given. As applications, the Hausdorff measures of uniform Cantor sets are computed in a new way and the upper bound problem of the Hausdorff measure of the Koch curve is also discussed.

In this paper, it is proved that the class number of the number field is even, where are different primes, all congruent to 1 modulo 4.

In this paper, the unique solution of the discontinuous nonlinear Volterra type integral equations in Banach spaces are investigated. In very weakly condition the unique solution of nonlinear Volterra type integral equations can be obtained by the uniformly limit of the iterative sequences is proved. The error estimate of the iterative sequences of approximation solutions is given. And then apply this result to the initial value problem of first order ordinary differential equations. The results obtained here improve and extend recent results.

In this paper a necessary and sufficient condition for the Smash product algebra structure and the crossed coproduct coalgebra structure to form a bialgebra was found. In particular, we also derive a sufficient condition for this new bialgebra to be a Hopf algebra.

This paper mainly concerns about the commutation formulas of Lax operators and masters symmetries for KP hierarchy. At first the quickly decaying function space is extended and the condition for operator to be Lax operator is discussed. On the basis of above work, the representation vector of Lax operator is found. Then, by studying the relationship among the Lax operator, Lax flow and the representa- tion vector of Lax operator, a method to calculate the representation vector of the Lie bracket of two Lax operators as well as a method to calculate the commutation of two master symmetries are obtained. At the end of this paper,a formula that can be used to obtain a symmetry from an arbitrary master symmetry is also given.

Taking the valuation lattice to be the unit interval [0, 1] this paper introduced the concepts of truth degree and similarity degree for formulas by means of integrals, and then introduced on the set F consisting of all formulas a kind of pseudo-metric so as to offer a possible framework for approximate reasoning.

This paper gives the propersitions of extension concerning automorphisms and derivations of semiprime rings. These results generalize some results of reference [1]. Then, through the idempotents in the generalized centroid of semiprime rings, topological space is established on the extended module of (1, ) derivations. From the point of view of topology we give the structure theorem concerning the extended module of (1, ) derivations.

In this paper authors use the concepts of cs-networks, sequential-neighbor- hood networks, sequential-open networks and weak bases, discuss the relations among point-regular covers, uniform covers and point-star networks of point-finite covers in spaces, and establish the characterizations of images of metric spaces under some sequence-covering (compact) mappings. In particular, it is shown that the image of metric spaces under sequence-covering (or 1-sequence-covering) compact mappings is equivalent to the space with point-regular cs-networks, which answers a Tanaka's question.

In this paper the authors solve the maximal dissipative extension representation of P dissipative operators in Banach space and get some nice application.

The structure of the set S of shiftable points of wavelet subspaces is researched in this paper. We prove that S = R or S =1\q Z where q ∈ N. The spectral and functional characterizations for the shiftability are given. Furthermore, the nonharmonic wavelet bases is discussed.

Let G be a finite group. The question of how the properties of its minimal subgroups influence the structure of G is of considerable interest for some scholars. In this paper we try to use c-normal condition on minimal subgroups to to characterize the structure of G. Some previously known results are generalized.

In this paper, the numerical range of nonlinear Lipschitz continuous operator is presented. Using it, many insteresting properties of operator, including the invertibility) contractivity and stability are quantitatively studied. The relation of numerical range with spectrum of operator is discussed also.

In this paper, we study composition operators between Hardy spaces on the unit ball in CN. We introduce the η-Carleson measure and use it to give the characterization of the bounded or compact composition operator C■: HP(B) → Hq(B).

We introduce a new definition of convergence of filters on a locale, which is equivalent to topological convergence on spatial lovales and can be applied to any locale. As applications, some characteriztions of compactness and description of Cauchy completeness are obtained.

In this paper we research the Drazin inverse of morphisms in the exact ad- ditive category.The existence and the uniqueness for the core-nilpotent decomposition of morphisms are proved.

By using fixed-point theorem in cones and analysis method, we study existence of positive solutions for a class of singular initial value problem. THe results are better than our main literature [1].

In this paper, we investigate the Toeplitz operators on the weighted Bergman spaces. It is shown that if S is the finite sum of finite product of Toeplitz operators, then S is compact iff the Berezin transform of S vanishes at the boundary of the unit disk.

In the present paper, an iff condition on the compactness of Toeplitz operators on Dirichlet spaces is obtained, in addition, it is proved that a Toeplitz operator with C1- symbol is compact if and only if it equals zero if and only if the boundary value of its symbol equals zero.

This paper establishes the Radon-Nikodym theorems for set-valued measures on Banach spaces, and gives Petits-Aumann integral representations for two kinds of set-valued operators.

In this paper, We study Dirichlet series and random Dirichlet series on the right half-plane. We give a very good coefficient condition; count precision order; study random series with non-uniformly distribution random variables and know that every points it (t ∈ R) is Borel point with no finite exceptional value for random Dirichlet series of infinite order.

The main purpose of this paper is to introduce a general Dedekind sums, and deduce one kind identities for Dirichlet L-functions.

In this paper, it is shown that there is no ε-isometric operator of any infinitely dimensional abstract LP space (0 < p < ∞) into (c) for ε > 0 small enough.

In this paper, we first investigate the number of meromorphic solutions of algebraic differential equation (f')" = R(z,f) with rational coefficients and give examples to show its precise. Secondly, applying Nevanlinna distribution theories, we consider solutions of a typical algebraic differential equation (f')3 = a0(f - τ1)2(f- τ2)2(f-τ3)2. Results in this paper improve others, such as by Gao shi'an [1], Gundersen G. and Laine I[2], He Yuzan and Laine I.[3-5].

In this papers we study a subclass of starlike mappings-quasi-convex map- pings on bounded convex circular domains in Cn. The relations between quasi-convex mappings and starlike mappings or convex mappings are established. Moreover, the growth and covering theorems which are same as convex mappings are given.

In this paper, the permanence and extinction of general nonautonomous Nspecies Lotka-Volterra type competitive systems with pure-delays are studied. Some new criteria are established. The results obtained in [8-10] for nondelayed nonautonomous Lotka-Volterra type competitive systems are improved and extended.