中国科学院数学与系统科学研究院期刊网

15 May 2003, Volume 46 Issue 5
    

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  • Yi Ming YING(1),Jie Cheng CHEN
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 833-842. https://doi.org/10.12386/A2003sxxb0111
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    Suppose that Ω∈(1)∩L(log~+L)~2(S~(n-1)×S~(m-1)),h(r,s)∈L~∞(R_+~1×R_+~1)andP_(N_1),P_(N_2)∈(2),we shall prove the rouhg operator Tp(f)(x,y)=∫∫_(R~n×R~m)Ω(u',v')h(│u│,│v│)/│u│~n│v│~mf(x-P_(N1))(│u│)u',y-P_(N2)(│u│)ududv is L~p(R~n×R~m)-bounded.
  • Hong Cang YANG
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 843-850. https://doi.org/10.12386/A2003sxxb0112
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    Let M be a compact Riemannian manifold with boundary M. In this paper we consider folloing problem on the estimate of the first eigenvalue of M with Robin boundary value conditions where n is the outward unit normal vector of dM and a is a positive constant.
  • Yong Hong LONG(1),Pei De CHEN(
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 851-856. https://doi.org/10.12386/A2003sxxb0113
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    We use jumping-lines to characterize the two-parameter point processes, the jumping-lines are proved to have good measurability. We have also defined the stopping of two-parameter point processes, and obtained some simple structure of nitrations of the two-parameter processes.
  • Guo Zhong CUI(1),Cheng Shun JI
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 857-864. https://doi.org/10.12386/A2003sxxb0114
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    This paper deals with the initial boundary value problem of Boltzmann-Poisson system with absorbing-reflection boundary. The global existence of weak solutions is proved by using the stability of velocity averages and the compactness results of L1-theory under weaker conditions of the initial boundary value.
  • Xiao Ming WANG,Lin Cheng ZHAO
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 865-874. https://doi.org/10.12386/A2003sxxb0115
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    Let X be a random vector taking values on a k-dimensional unit sphere with probability density function (p.d.f.) /(x), and X1,...,Xn be a list of independent and identically distributed (i.i.d.) observations from X. The kernel estimator of f(x) considered here is of the form fn(x) = . where K is a kernel function defined on [0,+∞), ωk is the Lebesgue measure on Ωk. In this paper, we establish the uniformly strong consistency rates of fn(x) by deriving a law of the Logarithm for it.
  • Pei Xin CHEN(1),Shi Jie LU(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 875-882. https://doi.org/10.12386/A2003sxxb0116
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    Let (?) be a subspace lattice on a normed linear space. The necessary and sufficient conditions for a subspace to be a reflexive Alg?module are obtained. Suppose ?is a completely distributive subspace lattice, M is an arbitrary reflexive Alg(?)-module. The double commutant of M is the described. Furthermore, a class of lattices called V-generators dense lattices is introduced, which strictly includes the class of completely distributive lattices and the class of pentagon lattices. Let ?be a V-generators dense and commutative subspace lattice (GDCSL for short), M be any reflexive Alg(?)-module. The commutant C(Alg(?),.M) of Alg?modulo M and the algebra AlgLat.M are all decomposed as direct sums. A description for the first cohomology H1(Alg(?), M) with H1(Alg(?),B(H)=0 is given.
  • Guo Xing JI,Hong Ke DU
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 883-890. https://doi.org/10.12386/A2003sxxb0117
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    Suppose (?) is a subdiagonal algebra of a σ-finite von Neumann algebra M. with the factorization property in the sense that for every invertible operator T ∈ M, there are a unitary operator U ∈ M. and an invertible operator such that T = UA. We show that the algebraic commutant of (?) is self-adjoint. We also prove that the invertible group of (?) is σ-weakly connected.
  • Shun Sheng GUO,Qiu Lan QI
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 891-896. https://doi.org/10.12386/A2003sxxb0118
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    For Bernstein operators, we get the strong converse inequalities. Such inequalities have been proved by Ditzian Z., Ivanov K. G., Totik V. and Li Song with different methods. But these results are only normal estimates (with A = 1), the classical one (with A = 0) is not included. In this paper, we introduce the k-functional and extend the preuious results to a larger case 0< λ<1.
  • Ping Zhi YUAN
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 897-902. https://doi.org/10.12386/A2003sxxb0119
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    Let Vn(R, Q) be the companion Lehmer sequence with parameters R and Q. Assume that R and Q are odd coprime integers such that D = R - 4Q > 0. In this paper, we find all odd indices n such that Qn(R,Q) or nQn(R,Q) is a square, where .
  • Chun Hong LI(1),Yong Xing GU(2
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 903-906. https://doi.org/10.12386/A2003sxxb0120
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    In this paper, we investigate the problem of shared values for several mero-morphic functions and obtain general results concerning the uniqueness theorems.
  • Dao Chun SUN(1),Zong Sheng GAO
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 907-912. https://doi.org/10.12386/A2003sxxb0121
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    Suppose that E(r) is an arbitrary non-empty closed set of real numbers(mod 2π), and that ρ(θ) is an upper semi-continuous bounded positive function (0 < ρ(θ) < M < θ) on E. Denote A:=sup{ρ(θ) |θ ∈ E}. Then there exists a meromorphic function f(z) of order A in the unit circle, such that every point eθ- (θ ∈ E) on the unit circle is a Borel point of order ρ(θ) of f(z) and f(z) has no other singular point.
  • Kun Hui LIU
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 913-924. https://doi.org/10.12386/A2003sxxb0122
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    First this paper discusses the analytic properties of diffusion equations and obtains some deep conclusions. Applying these conclusions, the of solutions existence a class of diffusion variational equations is proved. Also we point out that this kind of variational equations has a main theoretical meaning in the study of stochastic controls.
  • Qun LUO
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 925-930. https://doi.org/10.12386/A2003sxxb0123
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    In this paper, we obtain the existence theorem of Nash equilibrium for set-valued mappings, and study the generic stability of Nash equilibria for set-valued mappings. We prove that most of the game systems of set-valued mappings are essential.
  • Chun Hua FENG
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 931-936. https://doi.org/10.12386/A2003sxxb0124
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    In this paper, by means of the contraction mapping principle, we investigate the existence and uniqueness of almost periodic solutions for some delayed differential equations appearing in a power system. This result is of practical significance.
  • Zhen De WU(1),Min Ying GUO(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 937-942. https://doi.org/10.12386/A2003sxxb0125
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    Let Mn be a closed smooth n-manifold, which admits (Z2)k-actions with fixed point set data By Kosniowski-Stong formula we get a necessary condition. Special generators of the unoriented cobordism ring MO* are constructed to determine the group Jn,23 (P) n-dimensional cobordism classes in MOn containing a representative Mn admitting a (Z2)2-action with fixed point set of constant codimension 3, p - {(2, 1,0), (2,0, 1), (1,1,1)}.
  • Xiao Xia ZHANG(1),Mao Zheng GU
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 943-950. https://doi.org/10.12386/A2003sxxb0126
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    In this paper, we shall mainly discuss properties of actions of Kac-systems on C*-algebras corresponding to Hilbert C*-modules; and show that if one Kac-system coacts on two Morita equivalent C*-algebras, then the two co-crossed products are also Morita equivalent. Thus, Baaj and Skandalis' results are our special cases.
  • He WEI
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 951-960. https://doi.org/10.12386/A2003sxxb0127
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    In this paper, we introduce the concept of homotopy of continuous maps of locales, so as to establish the category of homotopy classes of locales. It is shown constructively that every continuous map of locales is homotopie to an inclusion map of locales. The concept of localic H-group is introduced, by applyig it we obtain a contravariant functor from the category of homotopy class of locales to the category of groups. In particular, we establish the fundamental group on a locale, and show that the fundamental group on a locale L at a point p is isomorphic to the fundamental group on the spectrum pt(L) of L at the point p, so the fundamental group is a homotopy invariant in the category of locales.
  • Yu Ming CHU(1),Ai Nong FANG(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 961-964. https://doi.org/10.12386/A2003sxxb0128
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    In this paper, we reduce the condition of functions from quasiconformality to ACL property by applining pure analytic method and technique, we obtain several oscillation inequalities of functions with ACL property and Ln-integrable gradient.
  • Zhen Feng ZHANG(1),Tian Ze WAN
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 965-980. https://doi.org/10.12386/A2003sxxb0129
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    In this paper, we give an explicit numerical upper bound for the moduli of arithmetic progressions, in which the ternary Goldbach problem is solvable. Our result implies a quantitative upper bound for the Linnik constant.
  • Yu Feng LU(1),Shun Hua SUN(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 981-984. https://doi.org/10.12386/A2003sxxb0130
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    In this paper, we study Toeplitz operators on Dirichlet spaces and partially answer the problem in [1]. Meanwhile, we give density theorems for Toeplitz operators on Dirichlet spaces.
  • Qiu Yi DAI(1),Yong Geng GU(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 985-992. https://doi.org/10.12386/A2003sxxb0131
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    Initial-boundary value problem for a class of semilinear parabolic equation with singular term is studied in this paper. Criterions for the existence of global classical solution or for the appearance of quenching phenomenon of the above problem are given. Also, life span of the quenching solution is estimated. As the same time, the above results are used to study Dirichlet problem for a class of semiliear elliptic equation with supercritical Sobolev exponent and an existence result of positive solutions is obtained.
  • Pei Wen YANG
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 993-998. https://doi.org/10.12386/A2003sxxb0132
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    In this paper, it is shown that if f∈ LP(G), P > 4, the distribution solution Tcf of the inhomogeneous Dirac equation u= f on a bounded domain G in quaternionic analysis is Holder continuous on G. The Riemann-Hilbert boundary value problems for the equation u = f on the ball and bicylinder are investigated. The solvable conditions and the integral expressions of the general solution are given, and the Holder continuity of the general solutions is proved.
  • Ping Yan CHEN(1),Xiang Dong LI
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 999-100. https://doi.org/10.12386/A2003sxxb0133
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    We establish the integral test for the weighted partial sums of independent identically distributed random variables with a certain tail behavior assumption, and obtain the Chover's law of iterated logarithm (LIL) as a corollary. As applications, the corresponding limit results for some classical summability methods are also established.
  • Yan Ping GUO(1),Wei Gao GE(2),
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 1007-101. https://doi.org/10.12386/A2003sxxb0134
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    Using an upper and lower approach, this paper establishes the existence of positive solutions for singular second order boundary value problems of the form (py'Y + p(t)q(t)f(t,y,py') = 0,0 < t < 1, where f(t,y,z) is singular at y = 0 and z = 0.
  • Xiao Mei ZHANG(1),Ding Bian QI
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 1017-102. https://doi.org/10.12386/A2003sxxb0135
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    By means of a variational approach, we provide sufficient conditions for the existence of periodic solutions for scalar second order differential equations with asymmetric nonlinearities. Main result of this paper is illustrated with examples and can be seen as a supplement to the Landesman-Lazer condition.
  • Yong Ming LI(1),De Xue ZHANG(2
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 1025-103. https://doi.org/10.12386/A2003sxxb0136
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    It is proved in this paper that for a TO topological molecular lattice (L,η), the following conditions are equivalent: (1) (L, η) is a regular injective TO topological molecular lattice; (2) L is a complete set ring and of which the set of complete coprimes forms a continuous lattice, and η is the Scott co-topology on the continuous lattice of complete coprimes; (3) There exists an injective TO space such that (L, η) is homeomorphic to the Soberification (in the sense of topological molecular lattice) of (P(X),TC). Besides, the structures of (not necessarily TO) regular injective topological molecular lattices, the structures of general injective topological molecular lattices and that of regular injective molecular lattices are also given. As applications, a new (and simple) proof of the structures of exponentiable topological molecular lattices is given.
  • Jin Wang LIU(1),Zhuo Jun LIU(2
    Acta Mathematica Sinica, Chinese Series. 2003, 46(5): 1031-103. https://doi.org/10.12386/A2003sxxb0137
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    Let be an endomorphism of k[x1,x2,... ,xn], and >, >' be rational or-derings. If for any monomials p and q, p > q p o lm>'( ) >' q o lm>'( ), then we say that the homomorphism is compatible with term orderings > and >'. In this paper, we give a simple method to decide if a homomorphism is compatible with term orderings > and >'.