A BINARY INFINITESIMAL FORM OF TEICHMLLER METRIC AND ANGLES IN AN ASYMPTOTIC TEICHMLLER SPACE

The geometry of Teichmller metric in an asymptotic Teichmller space is studied in this article. First, a binary infinitesimal form of Teichmller metric on AT(X) is proved.Then, the notion of angles between two geodesic curves in the asymptotic Teichmller space AT(X) is introduced. The existence of such angles is proved and the explicit formula is obtained. As an application, a sufficient condition for non-uniqueness geodesics in AT(X) is obtained.     

THE CODIMENSION FORMULA ON QUASI-INVARIANT SUBSPACES OF THE FOCK SPACE

Let M be an approximately finite codimensional quasi-invariant subspace of the Fock space. This paper gives a formula to calculate the codimension of such spaces and uses this formula to study the structure of quasi-invariant subspaces of the Fock space. Especially, as one of applications, it is showed that the analogue of Beurling's theorem is not true for the Fock space L_a~2 in the case of n > 2.     

ON CRITERION OF THE EXTREMALITY ANDCONSTRUCTION OF HAMILTON SEQUENCESFOR A CLASS OF TEICHMLLER MAPPINGS

gi. Introductionj is a TeichmUller self-mapping of the unit disk D = {lzl < 1}, if f is a quasiconformalself-mapping of D with a complex dilatation of the formwhere W(z) is holomorphic in D, and k is a constant. Let Q(f) denote the cias$of allquasicochrmal self-mappings of D that aams with j on the boundary OD, f will be calledextremal if IIUlll@ S lip,ll., for mp g E Q(f). Let B(D) depote the class of functionsw(x) holomorphic in D, with the additional restriction 0 < Ilwll ~ 11 Ic(~)…     

ON THE APPROXIMATION OF TCHEBYCHEFF-FOURIER SERIES IN THE C SPACE AND L_p~ω SPACE

The degree of approximation to a function f(x)∈C[-1,1] by (U, λ) means and f(x) ∈ Lpw by (Jr) means are discussed, some results in the literatures [1],[2],[3] have been improved.     

THE TRANSFINITE BASIS OF THE BIDUAL SPACE OF THE LONG JAMES SPACE

A transfinite basis of the bidual space of the long James space is presented in this paper. Moreover, we prove that the space J(w+r) has the approximation property, where J (ω) is the James space, r is any finite integer.     

A NEW CHARACTERIZATION OF THE CLOSEDNESS OF THE SUM OF TWO SUBSPACES

In this article, a new characterization of the closedness of the sum of two closed subspaces of a Hilbert space is established.     

ON THE SHEAF OF GENERALIZED FUNDAMENTAL GROUP AND COVERING SPACE

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INVARIANT SUBSPACES AND EIGEVALUES OF ELEMENTS IN C-ALGEBRAS

Let A be a C~*-algebra and x an element in A. the following invariant subspace problem is considered: Does there exist an irreducible representation π of A such that π(x) has a non-trivial invarint subspace? And a positive solution of the problem for finite separable matroid C~*-algebras is given. Also the eigenvalues Of elements in C~*-algebras is considered. Some versions of Fredholm Alternatives are given.     

SOME RESULTS ON THE REFLEXIVITY OF OPERATOR SUBSPACES

In this paper, the properties B^n p,q, and B^n 1,q are introduced.A lot of results on the reflexivity of operator operator subspaces which generalize the results in [1] are obtained.     

THE TRACE SPACE INVARIANT AND UNITARY GROUP OF C^＊—ALGEBRA

Let A be a unital C-algebra, n ∈ N ∪ {∞}. It is proved that the isomorphism △n : is isometric for some suitable distances. Asan application, the author has the split exact sequence with iA contractive (and isometric if n = ∞) under certain condition of A.     

A SPECIAL COMPLETE HYPER-ELLIPTIC INTEGRAL OF THE FIRST KIND

In this paper, we study a class of complete Abelian integral. We give an exact number and the upper bound of the number of zero points of the integral under some conditions.     

THE STRUCTURAL PROPERTIES OF THE DISCRETE POSITIVE REAL MATRIX

In this paper, the structural properties of the discrete positive real matrix (DPRM) are discussed by means of coprime fraction of a rational function matrix. Some structural properties of the DPRM are the same with the continuous positive real matrix (CPRM), but the other properties are unique with the DPRM.     

SOME PROPERTIES OF THE POSITIVE REAL MATRIX

In this paper,some properties of the rational positive real matrix are discussed by means ofcoprime fraction of a rational matrix.Some equivalent conditions which are natural extension of therational positive real function,are given for testing a rational positive real matrix.     

ON THE STABILITY OF FUSION FRAMES （FRAMES OF SUBSPACES）

A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame (frame of subspaces) is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3(iii)] with extra information about the bounds.     

THE CHARACTERISTICS OF HYPERSPHERES IN MINKOWSKI SPACE

Y-Riemannian metric gY is an important tool in Finsler geometry, where Y is a smooth non-zero vector field on Finsler manifold. If Y is a geodesic field, it is very effective to study flag curvature using Y-Riemann metric. In this paper, using a special Y-Riemann metric ( that is, so called v-Riemann metric ), we study hyperspheres in a Minkowski space and give some characteristics of hyperspheres in a Minkowski space.     

A FORMULA OF THE KINEMATIC MEASURE IN NONEUCLIDEAN SPACE AND SOME PROBLEMS ON THE GEOMETRIC PROBABILITIES

Let P_n, be the n-dimensional projective space. Let x_0,x_1,…,x_n be the homogeneous coordinates of point x. Consider the quadric φ(x) =x_0~2+x_1~2+…x_(n-1)~2+εx_n~2, where ε can take the value of +1 or -1. We assume the homogeneous coordinates of the points x that do not belong to φ = 0 are normalized, such that     

BOUNDEDNESS AND COMPACTNESS FOR THE COMMUTATOR OF THE ω-TYPE CALDERóN-ZYGMUND OPERATOR ON LORENTZ SPACE

In this paper,the authors consider the ω-type Calderón-Zygmund operator T_ω and the commutator [b,T_ω] generated by a symbol function b on the Lorentz space L^p,r(X)over the homogeneous space(X,d,μ).The boundedness and the compactness of the commutator [b,T_ω] on Lorentz space L^p,r(X) are founded for any p ∈(1,∞) and r ∈ [1,∞).     

STOCHASTIC ANALYSIS OF THE STOCHASTIC FUNCTIONAL ON THE BASIC SPACE

The concept of tho basic space is introduced in this paper, which contains tho white noise space and tho abstract Wiener space. Many results of stochastic analysis of the stochastic functional on white noiso space ([4]) and abstract Wiener space ([12]) are generalisod into this space, for example, Fourier transformation, Fourier-Wiener transformation and Malliavin's calculus, etc.     

THE DISTANCE BETWEEN DIFFERENT COMPONENTS OF THE UNIVERSAL TEICHMULLER SPACE

The model of the universal Teichmuller space by the derivatives of logarithm is the union of infinite disconnected components. In this paper, it is proved that the distance between different components is 0, and the distance from the center of a component to every other component is 2.     

NUMERICAL SOLUTION OF THE SPACE FRACTIONAL DIFFERENTIAL EQUATION

In this paper, a space fractional differential equation is considered. The equation is obtained from the parabolic equation containing advection, diffusion and reaction terms by replacing the second order derivative in space by a fractional derivative in space of order. An implicit finite difference approximation for this equation is presented. The stability and convergence of the finite difference approximation are proved. A fractional-order method of lines is also presented. Finally, some numerical results are given.