中国科学院数学与系统科学研究院期刊网

15 June 1992, Volume 8 Issue 2
    

  • Select all
    |
    Articles
  • Li Gui-song
    Acta Mathematica Sinica. 1992, 8(2): 113-121. https://doi.org/10.1007/BF02629932
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let f:Mn→Nv(n,p)+m be a map.Suppose that m=n-1 or n<4.We obtain the necessary and sufflcient conditions forf to be homotopic to apth order immersion.Some concrete pth order immersion results of RPn are also proved.
  • Lin Longwei, Xie Feipeng
    Acta Mathematica Sinica. 1992, 8(2): 122-134. https://doi.org/10.1007/BF02629933
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Consider a pair of genuinely nonlinear strictly hyperbolic conservation laws Ut+F(U)x=0 with initial data U(O,X)=Uo(X).Suppose that the initial data Uo(X)=U1(X)+U2(X),where U1(X) will issue rarefaction waves only,U2(X) has any finite total variation and sufficiently small deviation.We prove that the Cauchy problem has a global solution.
  • Shen Yaotian, Yan Shusen
    Acta Mathematica Sinica. 1992, 8(2): 135-147. https://doi.org/10.1007/BF02629934
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper,we consider a class of quasilinear elliptic eigenvalue problems with limiting nonlinearity.First,we use the concentration-compactness principle to get the existence of a minimum u∈H01(ω,RN) of the minimization problem

    then we apply the reverse Hölder inequality to prove that u∈L(ω,RN).
  • Zhang Mei-rong
    Acta Mathematica Sinica. 1992, 8(2): 148-157. https://doi.org/10.1007/BF02629935
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper we give a method for solving the functional equations arising from the differential embedding problem.We also obtain the conditions for embedding one-dimensional diffeomorphisms into differential flows.
  • Weigu Li
    Acta Mathematica Sinica. 1992, 8(2): 158-176. https://doi.org/10.1007/BF02629936
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper,we study a two-parameter family of systems Ec in which E0 as a contour consisting of a saddle point and two periodic motions of saddle type,i.e.,the situation is similar to that described by Lorenz equations for parameters b=8/3,σ=10,r=rl=24.06,and get some results concerning bifurcation phenomenon and dynamical behavior of the orbits of Ec in a small neighborhood of the contour for |ε| near zero.Thus,under a few natural assumptions which are verified numerically,we can explain some numerical results of Lorenz equations for parameters near the above values in a mathematically precise way,which is different from the methods of J.Guckenheimer et al.([3],[4]),by considering Lorenz equation as a one-or two-dimensional map.
  • Li Zunxian
    Acta Mathematica Sinica. 1992, 8(2): 177-183. https://doi.org/10.1007/BF02629937
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper the "residual complex" is defined when a group and its subgroups act on a complex.With its aid a homological spectral sequence of group products is given.And the author makes a concentrated study of the structure of the residual complex and proves that it becomes a clear "step complex" if the group can be expressed as an amalgamated free product of its subgroups.
  • Jiang Jifa
    Acta Mathematica Sinica. 1992, 8(2): 184-188. https://doi.org/10.1007/BF02629938
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    This paper considers the problem of the existence and uniqueness of the connecting orbit for a cooperative vector field F in the retangular box B.Suppose that the origin O and the point P with positive components are vertices of B,only containing the equilibria O and P,and that the Jacobian matrices of F at O and P are irreducible.Then there is a unique orbit of F contained inB which joins O and P.
  • Lü Fang
    Acta Mathematica Sinica. 1992, 8(2): 189-203. https://doi.org/10.1007/BF02629939
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper it will be shown that the spectrum of every unicellular unilateral weighted shift operator on a symmetric Banach space is the singleton set {0}.From this,we give an affirmative answer to Rosenthal-Shields' problem.
  • Zhan Tao
    Acta Mathematica Sinica. 1992, 8(2): 204-224. https://doi.org/10.1007/BF02629940
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In the present paper we establish a sharp asymptotic formula for

    with an error term (σ is a suitable positive constant) uniformly inq and T,which improves the best result hitherto given.