In this paper the dimension of spline spaces on an arbitrary simplicial complex in R￣nis discussed.It is proved that when k≥(3μ+1)2￣(n-2)+1,to derive the dimension of spline spacesof degree k and smooth order μ on an arbitrary simplicial complex Δ,one need only to obtainthe dimensions of spline spaces of degree 2￣(n-i-1)μ and smooth order μ on each i-incident regionR(σ)respectively,where i-simplex σ∈Δ and R(σ)means the simplicial complex of conforming by all the simplices in Δ which contain σ.

By means of the potential theory and techniques of complex dynamical system, wedescribe conmpletely the continuity of Julia sets of polynomials in the parameter space.

Let G(n,m)be a real Grassmann manifold of alI n-dimensional subspaces in R￣n+mFor two points p,q in G(n,m),we first find the equivalent condition that p,q are not conjugatealong any geodesic,then we prove that the geodesics connecting p and q are countable。we canalso obtain the indexformula λ(k_1…,k_n), which is the index ofthe geodesic numbered (ki,…,k_n)。Finally, according to Morse Theory,we can conclude that the space of the picecwise smooth pathsconnecting p and q is homotopic to a countable CW-complex if where the dimension ofthe ceIl numbered(k_1,…,k_n)is λ(k_1…,k_n)。

In this paper,we give a counter-example concerning the integral representation inBanach spaces.precisely,we show that there exists a complex Banach space X with the analyticRadon-Nikodym property,there exists a J-convex subset C of X and a point x ∈ C, suchthat there exists no Jensen measure on X with barvcenter x supported on the set of all Jensenboundary points of C.

In this paper we study the relation between the weighted sharp function andthe weighted maximal function M_uf. First,we give an inequality for their nonincreasing,rear-rangement functions and with respect to measure wdx .Then.for the comparable measures wdx udx we prove that there exist aconstant C.which independs on f and p(1≤p≤+∞),such that .when

In this paper,by use of the Clifford matrix expression of the higher dimensional sense-preserving Mobius transformations,we get a classificatory theorem of higher dimensionalMobius subgroups,prove the existence of minimal system of pure loxodromic generators,andobtain a discrete criterion.

In the present paper,We define a new category of integrable modules over aKac-Moody algebra. A criterian is given to judge an integrable module is in this category or not.Forany integrable module,the imaginary and real weight are defined.In some cases,the imaginaryand real weiglit are calculated explicitly.In addition,a new description of hyperbolic type GCMis given, which enable us to calculated the weights of some integrable modules over a hyperbolictype Kac-Moody algebra.

We give essential(or sufficient)conditions on A(z)that the equation y"+A(z)y=0possess one(or two linearly independent)solution with the exponent of convergence of its zerosless(or no less)than the growth orderof A(z).We obtain four theorems and generalize tworesults of I. Laine. We also prove tliat if A(z)is an entire of infinite order,then any two linearlyindependent solutions of y"+A(z)y=0 have no zeros unless the maximum value of the exponentsof convergence of their zeros is infinite.

This paper shows that for a one dimensional and noncritical contact process undercertain small perturbations,the stationary distributions are smooth in the perturbation param-eter. In particular,the stationary distributions of a one dimensional contact process are smoothin the infection parameter,except at the critical point.

In this paper,quasinjective modules and quasinjective hulls are generalized to thesituation of a hereditary torsion theory, the author defines and investigates T-quasinjective mod-ules,T-quasinjective hulls and TQI rings, then gives seven equivalent conditions that every rightideal in Gabriel topology G is T-quasinjective.

In this paper,the non-uniqueness of the solution of 2-dimensional Riemann problemfor a special class of 2 × 2 quasilinear hyperbolic systems is discussed, i.e。And some examples are given。

Let r be a positive real number,10 are holomorphic forms with weight r and multipliersystem υ of group r, and they expands linearly the whole space of cusp forms. Using this result, we also proved some properties of modular forms and deduced an identitywhich has an important position in the estimation of Fourier coefficients of half integal weightmodular forms.

In this paper,the point spectrum and residual spectrum of a u-scalar operator arestudied, and relations between a u-scalar operator and a selfadjoint operator are discussed.

Let S R￣n(n≥2)be a compact smooth hypersurface without boundary. Assumethat S is centrally symmetric with respect to the origin,and that the Gaussian curvature of S isnon-zero. Let dμ be a smooth positive measure on S,and dμ be the Fourier transform of dμ,Weshow that the null set of is a disjoint union of a compact set and countably many hyper-surfaceswhich are all diffemorphic to S￣(n-1)。

In this paper,we consider the problem of absolute stability for control systemswith several nonlinear elements. New necessary and sufficient condition for the existence of aLyapunov function of Lurie form is obtained,and thus a frequency criterion for absolute stabilityis drawn,which improves the results obtained by Rapoport and Kamenetskiy

For the bounded domain D in the space C￣n with orientable piecewise smooth bound-ary D of class C￣(1),and the well known Cauchy-Fantappie integral formula, the author definesakind of Cauchy-Fantappie kernel Ω which is homotopy equivalent to Bochner-Martinelli kernel.and uses homotopy method to prove that the singular integraI F(t) with kernel Ω and Holdercontinuity density f (t) possess Cauchy principal value and the C-F type integral F(z) possessinner and outer limit value F￣+(t)and F(t)satisfying the Holder condition; and the authorest ablishes a more general Plemelj formula which involves a solid angle coefficient α(t)at thepoint t ∈D。

This paper discusses some properties of right IF-rings,proves R is a right IF-ringif and only if it is a left coherent ring and is a flat module;thus proves right IF-rings andleft GQF-rings are equivatent secondly,studies some torsion theory properties of the coherentrings by right IF-rings,proves the relation between coherent rings andr r-coherent rings。

It is proved that a claJss of lattice-valued models is an elementary class if and onlyif it is closed under ultraproducts and elementary equiValence provided that the valued-lattice isfinite and has a strong characteristic form and the language bears a set of O-ary relation symbols。Some remarks are also given。

The stability of special a class of nonlinear integrodifferential equations is investigatedvia some transformations and the method of inequality analysis. Some simple criteria for stabilityare presented.Exalnples are given to illustrate the theory.

The general Weierstrass formula of the spacelike and timelike surface in 3-dimensionalMinkowski space is given.

Let R be a semiprime ring and C the center of R. In this paper following results areobtained:1.Suppose for any x_1,…,x_n∈R, there exists a polynomial f(t_1,…,t_n)(f dependingon x_1,…,x_n) such that f(x_1,…,x_n)∈C. If these polynomials satisfy the bounded condition,the sums of some coefficients of each f prime to each other, then R is commutative, which isageneralization of all related results in[ 2-27]. If f ls a polynomial, the sum of coefficients satisfiessome conditions, and for any x_1,…,x_n∈R, there exists an integer m(x_1,…,x_n)> 1 such thatf(x_1,…,x_n)￣m(x_1,…,x_n)=f(x_1,…,x_n), then R is commutative.

In this paper,we discussedthe ω￣*- closure of some special operator spaces and provedthe ω￣*-closure of all Toeplitz operators on the Bergman space is equal to (Theorem 1).In addition,an interesting characterization of Toeplitz operators on the Hardyspace H￣2(S)on the unit sphere S of C￣n (n>1) is obtained(Proposition 2).

The purpose of the present paper is to estimate the covering index of minimalisometric immersions from spheres into the unit sphere and get some conditions of embedings.In the proof of this paper, we have a method to product some new minimal immersons fromspheres to the unit sphere with some covering index besides.

In this paper,we give a lower bound for the Hausdorff dimensions of recurrent sets.Hence,we determine the Hausdorff and Bouligand dimensions of a class of recurrent sets.Thisresult contains and extends some results which have been proved by Bedford,Dekking,Wenzhi-ying and Zhong hong-liu.

Let G be a finite no-Abelian group and Irr(G)be the set of all irreducible charactersof G. In this paper,we consider the set of quotients and investigate howcertain assumptions on these numbers affect the structure of G. For example, suppose is the prime number decomposition of the natural number n. Set and W(G)=max.We show that if G is non-solvable with W(G)=4,then G is exactly one of the following groups: Z_p× A_5, SL(2,5),S_5, PSL(2,7),PSL(2, 11)andPSL(2, 13)。

In this paper,we consider the dimension of the space of bounded harmonic functionson a class of Riemannian manifolds. An upper bound of the dimension is obtained. In themeanwhile, a volume comparison theorem of Bishop-Gromov type on the geodesic balls is alsogiven on such kinds of manifolds

Let R be a ring and F a left Gabriel topology on R. We say that R is a F-V-ring if the quotient category(R,F)-Mod has the property that every simple object is injective.In this paper, using the vN-injectivity and quasi-injectivity of left R-modules, we give somecharacterizations of F-V-rings,

A two-paranieter generalized Poisson process,i.e. Poisson sheet, is defined. Some el-ementary properties,locally matingale-property,and different two-parameter Markov properties,of Poisson sheet,are followed.It’s jump lines and sample functions are studied.An imaginal,clear cut,and deep going depiction for jump lines and sample functions is given. It can be saidthat it is clear at a glance.

The criterions for the automorphism group of the lexicographic products of two and G. Sabidussi￣[2].In this paper, the corresponding criterion for endomorphism monlid is given. In the meantime, the following result is obtained:If X and Y are K￣3 free connectedgraphs, and either of two graphs has odd girth,then the endomorphism monoid End X[Y] of the lexicographic product X[Y]of X and Y coincides with the wreath product End X[ End Y]Of their monoid End Xand End Y.

In this paper,we extend some properties of holomorphic maps to Banach spaces,and use these properties to study convex maps and starlike maps in bounded domains in C￣n.

Let H be an arbitrary Hopf algebra over a field k.At first,we deal with the right H-extension A/A￣(coH) and the Hopf module category In this paper we give several sufficientand necessary conditions for A/A￣(coH) being right H-Galois extension, and several equivalentconditions for the Hopf module category satisfying the structure theorem. Then we discussthe irreducible actions and the Galois extensions of division rings.

Let{X_n}be a stable random walk on whose distribution is in the domain ofattraction of a stable low of index a, andis its p-multiple points. In this paper,the discrete Hausdorff dimension problelli for isinvestigated.As aresult,it is proved that, if a

Let be the space of square integrable functions on the prod-uctspace D×D of two unit disks with the weighted measure In this paper, we will give a complete orthogunal decomposition define a series of the Toeplitz and Hankel type operators and we develop boundedness,compact-ness and S_p-criteria for them.

This paper gets inequalities on double determinant over the quaternion field. Forexample,the Minkowski’s inequality and convexity inequality of double determinant and so on.It gives the relation between the determinant and the double determinant, as well as the relationbetween the two kinds of definition of the determinant respectively in the paper [1] and paper[4],if matrlx is the positive selfconjugate。 It puts forth the concept of generalization positiveselfconjugate matrix over the quaternion field and gets some of its basic properties.

In this paper,we study the oscillatory behavior for second order nonlinear functionaldifferential equation. On some conditions,we obtain the nonoscillatory solutions only have twokind, and necessary conditions for existence of each kind nonoscillatory solutions.At the sametime, we establish some sufficient conditions for oscillatory solutions.

In this paper we first give a concept on mixed monotone semiflows and a condition forfunctional differential equations to generate a mixed monotone semiflows.Using mixed propertyof the semiflows, We obtain some new resuIts on the asymptotically stability and the globallyasymptotically stability for functional differential equations.

The stability problem of solutions of nonlinear analvtic difference svstems is studied byintroducing the concept of k-stability.Some new simple criteria for stability are given.Examples are employed to illustrate the theory.

In this paper,the authors discuss the L￣p-boundedness of singular integral alonglower-dimensional sets and its“local”version. For certain“collvex”surface,the authors provethat they are bounded on L￣P(R￣n),p>1. The results extend the corresponding ones of E.M.Stein￣[1].

Let R be a ring. We consider the following two conditions:(*)Every maximal essential right ideal of R is either a GP-injective right R-module or aright anuihilator. (*) Every maximal essential right ideal of R is a YJ-injective right R-module.The aim of this paper is to investigate rings satisfying(*)or(*).Several new characteristicpropertles of strongly regular rings and division rings are also given.