中国科学院数学与系统科学研究院期刊网

15 January 2002, Volume 45 Issue 1
    

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  • Sheng GONG,Tai Shun LIU
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 1-020. https://doi.org/10.12386/A2002sxxb0001
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    A commutative generalization of complex numbers is called bicomplex numbers. A holomorphic function of bicomplex number corresponds to a holomorphic mapping on C2 which satisfies the complex Cauchy-Riemann equations. It is known that the holomorphic solutions of complex Cauchy-Riemann equations are essentially the direct product of two holomorphic functions of one complex variable. In this short note, we prove that in the complex Banach space, the holomorphic solutions of the Cauchy-Riemann equations have the same property.
  • Feng Wen AN
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 7-14. https://doi.org/10.12386/A2002sxxb0002
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    We discuss a type of topological invariants on the infinite-dimensional manifolds, that is, Cr mapping degrees on Banach manifolds with orientable Fredholm structures. Our degree theory is an intrinsical extension and unification of the usual smooth mapping degrees on the finite-dimensional manifolds.
  • Li Min WANG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 15-20. https://doi.org/10.12386/A2002sxxb0003
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    For a regular semigroup with an inverse transversal, we discuss here how the structure of congruence lattice affect the semigroup. We characterize the congruence-free regular semigroups with Q -inverse transversals.
  • Shan Chao YANG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 21-28. https://doi.org/10.12386/A2002sxxb0004
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    It is disscused the strong consistency of M estimator of regression ametric in linear model. Some suitable sufficiency conditions are obtained. Comed to the corresponding result of Chen Xiru, Zhao Lincheng [1] , these greatly improve the moment conditions.
  • Ji Wen ZENG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 29-36. https://doi.org/10.12386/A2002sxxb0005
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    Let B be a p-block of a finite group G. We consider a free Abelian group with a basis of Brauer irreducible characters of the block B, and its factor group determined by Cartan matrix of the block B . Let C=(cij) and D=(dij) be the Cartan matrix and the decomposition matrix of B, respectively. We give some new results about the relations among C, defect group of B and the vertices of simple modules. We also get some new results about the decomposition numbers dij, the heights of ordinary irreducible characters of B and Cartan invariants.
  • Li Ning JIANG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 37-42. https://doi.org/10.12386/A2002sxxb0006
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    Let G be a finite group and H its subgroup. Suppose that D(G) is the group double of G and F the field algebra of G-spin model. This paper considers the sub-Hopf algebra D(H)of D(G) and proves that the D(H)-invariant space AH in F is a C*-algebra. There is a C*-representation of D(H) so that D(H) and AH are commutants of each other.
  • Hui Zhao LIU(1),Guang Lie WANG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 43-58. https://doi.org/10.12386/A2002sxxb0007
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    We consider an curvature flows with boundary condition. In contradiction to the former works [1-4] and others,here the speed of flow of surfaces is in inversely proportional to curvature of surface. We show that the corresponding first initial-boundary problem admits a classical convex solution for all time and then investigate asymptotic behaviour of the solution.
  • Peng Tong LI(1),Shi Jie LU(2)
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 59-64. https://doi.org/10.12386/A2002sxxb0008
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    If A is a completely distributive subspace lattice algebra on a Hilbert space, then the rank one subalgebra of A is weak dense in A if and only if, the weak closures of the first and the second preannihilators of A in the space of all trace class operators are reflexive. If A is a nest algebra, then Lat, A , the nest of all invariant subspaces of A, is maximal if and only if, all of the weak closed subspaces of A containing A-are reflexive.
  • Dao Wen QIU(1),Dong Gao DENG(2
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 65-74. https://doi.org/10.12386/A2002sxxb0009
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    In this paper, we discuss the T(1)Theorems by weakening the operator's kernels on spaces of homogeneous type and obtain the boundedness and endpoint estimates of the commutators of singular integral operators associated with the weaker kernels with BMO functions on Lp (1
  • Hong Xun YI
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 75-82. https://doi.org/10.12386/A2002sxxb0010
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    The problem of uniqueness of meromorphic functions is discussed, the following theorem is proved: there exists a set S with 8 elements such that any two nonconstant meromorphic functions f and g satisfying E(S,f)=E(S,g) and E({∞},f)=E({∞},g) must be identical.
  • Xian Zhang WEN
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 83-92. https://doi.org/10.12386/A2002sxxb0011
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    In this paper, by means of comparison theorem and Liapunov functionals, we consider the global attractivity of positive periodic solution of multispecies ecological competition-predator system with several delays. Some new results are obtained. Example shows that our conditions are feasible.
  • Jun Jie WEI(1),Shi Gui RUAN(2)
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 93-104. https://doi.org/10.12386/A2002sxxb0012
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    In this paper, we first establish a basic theorem on zeros of general transcendental functions. Based on the basic theorem, combining the global Hopf bifurcation theorem for general functional differential equations, which was established by Wu J. H. al using degree theory methods, we investigate the stability and global Hopf bifurcation for a lossless transmission line network which is described by a one delay differential-difference equation of neutral type.
  • Huan Yin CHEN(1),Fu An LI(2)
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 105-108. https://doi.org/10.12386/A2002sxxb0013
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    In this paper, we investigate the comparability structure over exchange rings. This provides a new class of exchange rings satisfying the comparability and generalizes the corresponding results of Goodearl and Chen.
  • Yu Ping TANG(1),Xu ZHANG(2)
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 109-116. https://doi.org/10.12386/A2002sxxb0014
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    In this note we analyze the exact controllability of singularly perturbed damped wave equation with homogeneous Dirichlet boundary conditions under more general geometric control condition than that of [1]. We show that the null controllability of the heat equation can be obtained as a singular limit of the exact controllability of such sort of wave equations.
  • Qi Cai WEI
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 117-126. https://doi.org/10.12386/A2002sxxb0015
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    In this paper, based on large deviation formulas established in stronger topology generated by H lder norm, we obtain the functional limit theorems for C-R increments of k-dimensional Brownian motion in H lder norm.
  • Zhao Yong HUANG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 127-138. https://doi.org/10.12386/A2002sxxb0016
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    In this paper, the notion of (minimal)approximation extensions is introduced, the existence and uniqueness of minimal approximation extensions over Gorenstein algebras are established, an application to minimal approximation extensions is given.
  • Pei Ci CHEN,Yuan Lan ZHOU
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 139-150. https://doi.org/10.12386/A2002sxxb0017
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    In this paper, we defined universally the tensor product of semimodules, and constructed the direct lim rlim Ci for any directed set of indices and an arbitrary directed direct system in the category C of semimodules over a semiring R , also the cokernel of any morphism f. We discussed some properties of the tensor product of semimodules. The main results are as the following: the tensor functor preserves right exactness of semimodules and coproduct, and also coproduct preserves flatness of semimodules, the tensor functor preserves direct limits and cokernel.
  • Bao Xue ZHANG(1),Xian Hai ZHU(
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 151-156. https://doi.org/10.12386/A2002sxxb0018
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    A note by Wang and Shao (1992), in which the constrained Kantorovich inequalities are considered in matrix versions expressed in terms of the loewner tial ordering, is extended to cover nonnegative Hermitian matrices by the singular value decomposition of matrix. Furthermore, the constrained Wielandt inequalities are also investigated.
  • Zhen GUO(1),Wei Huan CHEN(2),J
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 157-164. https://doi.org/10.12386/A2002sxxb0019
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    Let f: Mn→RN be an affine immersion of a Riemannian manifold into Euclidean space, we establish the condition under which there exists another affine immersion overline f:Mn→RN with the same Gauss map as that of f. Furthermore, using this condition, we give the answer for the question: what extent does the Gauss map of an affine immersion determine the affine immersion up to.
  • Ke LIANG,Shao Qiang DENG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 165-170. https://doi.org/10.12386/A2002sxxb0020
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    This paper uses the theory of Lie groups and their representations to discuss the equivariant isometric minimal immersions of compact Riemannian symmetric spaces to the Grassmann manifold.
  • Xian Ping GUO,Yong Long DAI
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 171-182. https://doi.org/10.12386/A2002sxxb0021
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    This paper deals with the discounted cost model for coutinuous time Markov decision processes with arbitrary transition rates and possible unbounded costs. Getting rid of the traditional condition that the Q -process deduced from a given policy is needed to be unique, we first consider the case of the Q-processes being not unique, of the costs possibly being unbounded, and of the action space being arbitrary. By first using the "α-discounted cost optimality inequality"instead of the traditional optimality equation, we not only prove the existence of optimal stationary policies, but also derive the existence of (∈>0) -optimal stationary policies, of the monotone optimal stationary policies, and of the (∈≥0) -optimal decision processes. Moreover, some new results are obtained. Finally, a substantial applied example of birth and death processes witn controlled migration rates is used to show that our assumptions here are satisfied, whereas the conditions in [1-14] fail to hold.
  • Ji Feng GUO
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 183-186. https://doi.org/10.12386/A2002sxxb0022
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    In this paper, some Ou-Iang type discrete inequalities defined on Nn are established, which are natural generalization and improvement of some known results obtained by Yang E. H.
  • De Wu REN,Qi SUN
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 187-190. https://doi.org/10.12386/A2002sxxb0023
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    For odd square-free n>1, the cyclotomic polynomial φn(x) satisfies the identity of Schinzel, φn(x)=P2n,m(x)-(-1/m)mxQ2n, m(x), where Pn,m(x)and Qn,m(x) are polynomials with integer coefficients and m|n . We give two simple identities to compute Pn,m(x) and Qn,m(x).
  • Hong Ya GAO
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 191-196. https://doi.org/10.12386/A2002sxxb0024
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    The reverse H lder inequality, Lp integrability and weak monotonicity of the component function of weakly quasiregular mappings are obtained by using Hodge decomposition.
  • Jian Hua ZHANG(1),Hong Ke DU(2
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 197-202. https://doi.org/10.12386/A2002sxxb0025
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    This paper is devoted to the study of perturbations of nest subalgebras in factor von Neumann algebras. A sufficient condition is given for the similarity of nests in factor von Neumann algebras. is proved that close nest subalgebras in arbitrary factor von Neumann algebras are similar via an invertible operator close to the identity.
  • Rui Qing WANG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(1): 203-208. https://doi.org/10.12386/A2002sxxb0026
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    the adjacent lattice methods of Kneser are generalized, some adjacent lattice properties of the positive definite unimodular genera of rank 4n and determinant 1 over Z[/d] are given, and the classification of all the positive unimodular lattices of rank 4 over Z[/3]are obtained.