In this paper,We discuss the general elliptic Mobius groups, elliptic groups andmotive groups in dimension 3 based on the expression of the higher dimensional sense-presservingMobius transformations through 2 ×2clifford matrices and obtain their characteristics.

Let Ω be an homogeneous function of degree zero on R￣n-1,and Ω satisfy the can-cellation. It is proved in this paper that a class of singular integral operators along arbitrarysurfaces are bounded on L￣2(R￣n) provided Ω belongs to certain space generated dy blocks, wherethe kernels of these operators take the form of b(t)Ω(t)/|t|￣n-1, and b is a bounded radial functionon R￣n-1.

In this paper we study the value distribution of in the finite disc,wheref(z)is a non-constant meromorphic function and is a non-zero one .If the disc is infiniteand is slowly growing with respect to f(z),we obtain a theorem which is a generalizationof W.Hennenkemper in 1981.

In this paper,we find that when the Chebyshev nodes are disturbed,if the dis-turbence is then the Hermite-Fejer interpolation process based on the disturbedChebyshev nodes will converges uniformly on [-1,1]for all continuous functions. Besides,theconvergence order is given out in this paper.

Kaplansky density theorem is a foundational and important theorem in the theoryof von Neumann algebra axd C￣* algebra. Many deep results for operator algebra are deducedby tkis tool.The main purpose of this paper is to give a relevent density theorem on Pontrjaginspace.At the samt tume, another result on density for complete regular selfatljoint operators willbe given.

In this paper,we study compact Riemannian manifolds which Ricci curvature ten-sors are parallel,and establish some pinching theorems for square of length of the Riemanniancurvatuer tensor.

Let X be a Banach space,if, for every weak compact and weak separable subsetK of X(K,ω) is metrisablemZ is said subseparable.If,for each sequence in Xkerx is sepqrable,X is said quadi-sepqrable.In the paper,we prove that the two newtype of Banach spaces are more extensive than separable Banach spaces and weakly compactlygenerated Banach spaces,and retaim a lot of properties of sepatable Banach spaces.

In this paper,we discuss the normality of a family of meromorphic functions whichand whose differential polynomials omit a fixed value and generalized results due to Yang Lo,Chen Huaihai, Zhu Xiurong and Gong Xiang Hong.

Let C_u={(x,y,z):u￣2x￣2+y￣2+z￣2≤1},where u ≥ 0.For any positive realnumber α, we define Δ(C_u,α)byThe view-obstruction problem for C_u is to determine the lower bound K(C_u) of those αfor which any half-line x_i=α_it(i=1,2,3),where the α_i (i=1,2,3)are positive real numbers and the parameter t ≥0,intersects Δ(C_u,α).In this paper K(C_u)is determined for all u.

In this paper we shall give the necessary and sufficient conditions of solutions onsome parabolic equations with initial-boundary value.

For any>0, letbe the Hilbert-vaiued stochastic processgoverned by the following random evolution equation where Y(t) is random process.In this paper,we establish the Ventsel-Freidlin type large deviation principle for Consequently, a result in[4] is extended to infinite dimension random fields。

In this paper,mainly a general theorem concerning the unicity of meromorphicfunctions satisfying certain deficient relation and their n-th derivatives sharing two values isobtained.As an immediate consequence, a number of known results can be derived from thetheorem.

Let a >1,b>1 and (α,b)=1,and let h(-αb)be the class number of the imaginaryquadratic field .In this paper,we have proved the following results.Theorem 1. If the positive integers x,y, n and k satisfyαx￣2+by￣2=4k￣2, k>1,x|α,y|b,where symbol x|αmeans that α is divided exactly by each prime factor of x .Them hb)≡0(od 2n),except 5.5￣2+3.1￣2=4.2￣5,3.9￣2+13.1￣2=4.2￣6 and n=3 ,of by￣2=3k+λ(λ=±1).Teorem 2.If the positive integers x,y,n and k satisfyαx￣2+by￣2=k￣n,αb≡2(mod 4),x|α,y|b,then

In the paper, we obtained the structure of the finite groups having three ciasses ofmaximal subgroups of the same order。Thus we solved the problem which was suggested to studyby Professor Shi Wujie on Chinese Mathematical Society Annual Conference On Finite Groupsin 1987.

In tkis paper. we consider certain first order delay differential equations of neutraltype. and obtian several classes of sufficient conditions for the oscillation of all of its solutions. As corollaries to our resnlts. the corresponding theorems in[1] ,[2],[3]are improved.

This paper construct some couplings for non-degenerate diffusion processes on acompact connected manifold.By a stochastic analysis method we prove that these couplingsare successful. moreover. the first moment of the coupling time is finite. Finially.the rate ofconvergence in total variation norm is also studied.

In a general case of the application of the Melnikov function only the first orderforms are used.This paper deduces the formula of the second order Melnikov function. Thesecond order criterion. Which can be used to analyse the relative positions of the stable manifoldand unstable manifold of the hyperbolic saddle.is given and is successfully used in studing ofthe toral van der Pol equations.

The distributfon of αn￣k modulo one is discussed. and proved there are infinitelymany natural numbers n satisfy for.

By the use of Vaughan′s method,an explicit upper bound for linear trigonometricalsums with primes is given in this paper.

In this paper, the(0,1)-heat form of B￣n is constructed.As an application of the(0,1)-heat form of B￣n,the integral reprentation of the solution of the-equation on B￣n is given。

This paper study the problem for the chaxacteriztions of the minus partial order ofmorphism set in a category, its main results are: 1. prove fourteen characterizations of the minuspartial order in a general category ; 2. the results that using inclusion relation of (1)-inverse,(1,2)-inverse and parallel sum characterized the minus partial order of a complex matrix by category; 3.give the inverse example for proposition 1(ix) of [5], then negate the Hartwig's this characterization.

In this paper we investigate the relationship between a module and a comodule. LetA be a algebra and M be a right A-module,we show that M°={f ∈M￣*; there be some idealI of A such that f(MI)= 0 and dim A/I finite}is a right A°-comodule. We use the result togive a H-module algebra A,with its dual there be some ideal I of A such thatF(I)=0 and dim A/I finite } is not a H°-comodule coalgebra.

A class of l-groups is called a sub-product class,if it is closed under taking convexl-subgroups and forming completely subdirect products.Let U be a sub-product class and G beis called a sub-product radical of G.In this paper we proved that a sub-product class U is determined by the sub-product radical mapping G→U(G).And we also proved that in thethe meet is determined by the sub-product radical mapping G→whilethe join is determined by the sub-product radical mapping G→ this is beautiful result.

Let R be a G-graded ring,HG, be a subgroup of G; By constructing two Moritacontexts, we give some sufficient and necessary conditions for R{H}to be Morita equivalent toR_H, and for R#G￣* to be equivalent to R_H#H￣*.

In this paper, the(0,1)-heat form of B￣n is constructed.As an application of the(0,1)-heat form of B￣n,the integral reprentation of the solution of the-equation on B￣n is given。

This paper studies the average sum of partial quotients of a class of the finitecontinued frartions.A accurate asymptotic formula is given out. It improves upon a well-knownresult due H. Yao and D.Knuth.

In this paper, using the first standard imbedding of CP￣m into an (m￣2 + 2m)-dimentional Euclide an space, we define a Gauss map for a submanifold in CP￣m. We obtainsome conditions which ensure that the Gauss map is harmonic or relatively affine.

In the theory of the universal phenomenon obtained in the numerical research aboutinterval maps and circle maps,a key role is played by the renormalization group hinctionalequations and their solutions.This paper studies the functional equations connecting the twomaps The existence of its infinite C￣∞ solutions is shown by constructing method.The scope ofparameter is larger than D in[9]. Finaly, some further problems which need to be studied areposed.

In this paper, our main result is as follows.Theorem Suppose thatλ_1,…,λ_q are non-zero real numbers not all in rational ratio, and k=4,5…,11.Then,for 0<σ<σ_k,the inequality has infinitely many solutions in integers. Where K is any real number,

Let G be a graph and g,j be two integer-valued hinctions defined on the vertexset of G and (g,f)-factor of a graph G is a spanning subgraph F of G such thatfor each vertex x of F Inthis paper some sumcient conditions for a graphto be (g,f)-factorable and a necessary and sufficient condition for a grah to be a (g,f)-deleted guaph are given Some applications of these conditions are discussed .

In this paper we give an asympotic estimate for the lifetunes of conditfoned diffusionprocesses in bounded Lipschitz domains D. From this we obtain the spectral conditions for thefiniteness or infiniteness of gauge and conditional gauge, gauge theorem and conditional gaugetheorem are obtained here too.

In this paper,some aufficient conditions of existence of periodic orbits of the typeBC* L￣∞in unimodal functions with kneading sequences BC are given. Then the existence ofeventually periodic orbits in a general ununodal function f discussed. It is proved that if ak-th eventually n-periodic admissible sequence AB￣∞ satisfies certain requirements then f hasa k-th eventually n-periodic orbit of type AB￣∞ For an ext ensive class of unimodal functions,the condition of the main theorem in Part II.3 of Ref. [1] is weakened and simplified adn its conslusion is strengthened.For general continuous functions,the conalusion of Theorem 2 in Ref.[8] is also replenished.

In this paper we give a computation formula for orthogonal groups of the sum oftwo quadric modules over commutative rings.For the quadric modules over polynomial ring,wegive a local-golbal theorem for some subgroups of the quardic modules.

In this paper we characterize the spectrum of strongly continuous cosine functions, defined in L￣P(Ω)(1

<∞)spaces,in terms of properties of the infinitesimal generaror.

Consider the heteroscedastic regression,model y_i=x_iβ+g(t_i)+σ_ie_i forand i=1,2,…,n. Here the design points (x_i,t_i,u_i)are known and nonrandom,g and f areunknown functions, and e_i is an unobserued disturbahce. The family of nonparametric estimatesand including all known estimates is proposed,also proposed is a class of new nearestneighbor estimates of g and f.The least squares estimator β_n and the weighted least squaresestimator are obtained. Some asymptotically efficient estimates are also obtained.

In this paper, by using three iterative method combinatively, we proved the equation has nonzero solutions when s takes the least possible value 37,andgave out an upper bound for the solutions. This improves J.Pitman’s result in the number ofvariables.

The admissibility of a linear estimator is characterized in the linear models （Ｙ，Ｘβ，σ２Ｖ，Ｖ≥０） where considered regression parameter varies in a incomplete ellipsoia (β：（β－β０）’Ｎ（β－ β Ｐ０）≤σ２，Ｎ ≥ ０ The results shown that the admissibility of linear estimator among the class of all linear estimators is independent on β0, but the admissibility of homogeneous linear estimator among the class of all homogeneous linear estimators is dependent oil β0.

Let Ki be the positive integers and k1 < k2 <... < kl. We have determned the groups J6,k2,...,kl (ki are even and k2 >=12). In this paper, we determine the groups J6,10,k3,...,kl J6,8,k3,...,kl (k3 > 10), J6,8,10,k4...,kl (ki are even).

When considering the stability of a differential equation with time lag, one often has to solve the distribute. problem of the roots of a trancedental equation. For the case of the trancendental equation with two parameters, the problem above has been solved completely. For a sort of trancendental equation with three parameters, Bellman and Cooke get a conclusion for partial case: a > 0, b >= 0 in [3]. But it is analytical and inconvenience in application. In this paper, the conditions under which the roots of such equation are in the left half plane, are given in whole parametric space (a, b, c). Furthermore, the roughly shape of the stable region is pointed by figure. The results in this paper are convenient to use, especially in the bifurcation theory.

In this paper we prove that there exists a Ricci condition such that a 2-dimensional Riemannian manifold can be realized as a spacelike maximal surface in L3, and show that the spacelike surface in L3 whose mean curvature vector h satisfies △ｈ＝λｈ for some λ∈Ｒ is a hyperboloid or a cylinder up to a Lorentz motion in L3.