中国科学院数学与系统科学研究院期刊网

15 January 1995, Volume 38 Issue 1
    

  • Select all
    |
    论文
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0011
    Abstract ( )   Knowledge map   Save
    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.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0010
    Abstract ( )   Knowledge map   Save
    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.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0012
    Abstract ( )   Knowledge map   Save
    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)。
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0013
    Abstract ( )   Knowledge map   Save
    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.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0008
    Abstract ( )   Knowledge map   Save
    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
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0007
    Abstract ( )   Knowledge map   Save
    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.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0006
    Abstract ( )   Knowledge map   Save
    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.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0009
    Abstract ( )   Knowledge map   Save
    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.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0005
    Abstract ( )   Knowledge map   Save
    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.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0004
    Abstract ( )   Knowledge map   Save
    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.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0003
    Abstract ( )   Knowledge map   Save
    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。
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0001
    Abstract ( )   Knowledge map   Save
    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.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0002
    Abstract ( )   Knowledge map   Save
    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.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0018
    Abstract ( )   Knowledge map   Save
    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)。
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0017
    Abstract ( )   Knowledge map   Save
    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
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0016
    Abstract ( )   Knowledge map   Save
    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。
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0015
    Abstract ( )   Knowledge map   Save
    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。
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(1): . https://doi.org/10.12386/A1995sxxb0014
    Abstract ( )   Knowledge map   Save
    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。