中国科学院数学与系统科学研究院期刊网

15 March 2005, Volume 48 Issue 2
    

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  • Mu Fa CHEN
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 209-220. https://doi.org/10.12386/A2005sxxb0025
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    Motivated from the study on logarithmic Sobolev, Nash and other functional inequalities, the variational formulas for Poincare inequalities are extended to a large class of Banach (Orlicz) spaces of functions on the line. Explicit criteria for the inequalities to hold and explicit estimates for the optimal constants in the inequalities are presented. As a typical application, the logarithmic Sobolev constant is carefully examined.
  • Xiao Quan XU(1), Mao Kang LUO(
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 221-234. https://doi.org/10.12386/A2005sxxb0026
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    In this paper, the concepts of quasi Z-continuous domains and Z-meet continuous domains are introduced, and some relations between Z-continuous domains, quasi Z-continuous domains, Z-meet continuous domains and the Hausdorff separation of Z-Lawson topology are investigated. It is proved that if a subset system Z satisfies certain conditions and P is a quasi Z-qcontinuous domain, then the Z-way below relation <
  • Yong Zhen HU, Li Geng SI
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 235-244. https://doi.org/10.12386/A2005sxxb0027
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    The existence of periodic solutions of neutral periodic differential periodic system with infinite delay is considered. Using the exponential dichotomy and Krasnoselskii fixed point theorem, some sufficient conditions to guarantee the existence of T-periodic solution for the system are established.
  • Lei CHEN, Fu Xing SHEN
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 245-250. https://doi.org/10.12386/A2005sxxb0028
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    This article is based on the quantifier elimination of the theory of complete binary trees. The countable atomic model and saturated model are presented. We also calculate the CB rank of the types in one and two variables. Finally, the geometric meaning of CB rank in this theory is found.
  • Yu Wen WANG, Shuang Zhen LI
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 251-258. https://doi.org/10.12386/A2005sxxb0029
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    In this paper, the concept of quasi-linear projector is introduced in Banach space, and a unified definition for homogeneous generalized inverse of linear operators in Banach space is thus given. The homogeneous generalized inverses contain the bounded linear generalized invenses and the single valued metric generalized inverses. A unified criterion for the existence of the homogeneous generalized inverse of a linear operaor in Banach space is also given.
  • You Qing JI(1), Peng Hui WANG(
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 259-266. https://doi.org/10.12386/A2005sxxb0030
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    For two operators acting on an infinite dimensional Hilbert space, it is interesting to investigate whether the essential similarity is equivalent to the similarity in the Calkin algebra. In this paper we introduce an operator class ES((?)), and show that, for two operators in ES((?)), the similarities above are the same. Moreover, we show that ES((?)) is dense in B((?)) in norm topology.
  • Li Fang LIAN(1), Wei Gao GE(2)
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 267-274. https://doi.org/10.12386/A2005sxxb0031
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    In this paper, the existence of positive solutions is studied for higher order boundary value problems with a p-Laplacian operator, by useing the method of the compression and expansion of cone.
  • Zhi Lin YANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 275-280. https://doi.org/10.12386/A2005sxxb0032
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    In this paper, we compute, by using cone theory, the topological degree of a class of completely continuous fields where the condition on the lower boundedness of nonlinear operators is sharply weakened. Therefore our results substantially improve and generalize the existing ones in the literature. Finally we use our abstract results to establish the existence of nontrivial solutions for superlinear Hammerstein integral equations.
  • Chun Yan XUE, Wei Gao GE
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 281-290. https://doi.org/10.12386/A2005sxxb0033
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    The paper is concerned with the existence of solutions for the following multi-point boundary value prolem x"(t) = f(t,x(t), x'(t)) + e(t), t ∈(0,1); x'(0) = x'(ξ), x(1) =sum from i=1 to m-3 βix(ηi) where βi ∈ R, rum form i=1 to m-3βi= 1, 0 <η1<η2 <... <ηm-3 < 1, 0 <ξ< 1, and rum form i=1 to m-3βiηi=1. This is the case dim Ker L = 2. When the βi's have different signs, we prove existence results for the m-point boundary value problem at resonance by the use of Mawhin's coincidence degree theory. Since all the existence results obtained in previous papers are for the case dim Ker L=1, our work is new.
  • Ming Xue LIU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 291-292. https://doi.org/10.12386/A2005sxxb0034
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    we prove that the converse proposition of the famous Lomonosov lemma is true and obtain a new necessary and sufficient condition for the existence of a nontrivial closed invariant subspace for a subalgebra (?) of (?)(X) in a Banach space X.
  • Cong Jun ZHANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 293-298. https://doi.org/10.12386/A2005sxxb0035
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    In this paper, we obtain some existence results for a class of abstract equilibrium problem; our results give answers to the open problem raised by Isac, Sehgal and Singh. Furthermore, we study the equilibrium problems with lower and upper bounds under restricted conditions, and obtain more results. Finally, we generalize these open problems to the case of two spaces.
  • Lun ZHU(1), Chang Ping XIONG(2
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 299-310. https://doi.org/10.12386/A2005sxxb0036
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    Let (?) be a subalgebra with the unit operator I in B(H), where H is a real Hilbert space. We say that a linear mapping (?) from (?) into B(H) is a generalized Jordan*-left derivation if (?)(T2) = T*(?)(T) + (?)(T)T - T*(?)(I)T for any T ∈(?); (?) is called a generalized*-left kernel-into-range preserving mapping if (?)(T)(ker(T)) (?) ran(T*). In this paper, we show the following main result. If a generalized*-left preserving kernel-into-range mapping on real nest algebras is continuous in the weak operator topology, then (?) is a generalized*-left inner derivation, i.e. (?)(T) = T*A + BT for some A, B∈B(H); In particular, (?) is also a generalized Jordan*-left derivation.
  • Zai Hui GAN, Jian ZHANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 311-318. https://doi.org/10.12386/A2005sxxb0037
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    This paper is concerned with the Cauchy problem for a class of nonlinear Klein-Gordon equations with several competing potential functions. In terms of the characteristics of the ground state, the sharp conditions for blowing up and global existence are derived out by applying the potential well argument and the concavity method. And the question that how small the initial data are, the global solutions exist is answered.
  • Wen De LIU, Yong Zheng ZHANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 319-330. https://doi.org/10.12386/A2005sxxb0038
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    A family of finite-dimensional modular Lie superalgebras of Cartan types HO is constructed in this paper. They are proved to be simple. By establishing dimension formulas of Lie superalgebras of Cartan-type W, H, K, S and HO, we study the isomorphism relations between HO and W, S, H and K.
  • Yong HE
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 331-338. https://doi.org/10.12386/A2005sxxb0039
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    In this paper, we characterize the structure of (?)*-covered regular semigroups and classify weakly covered regular semigroups and covered regular semigroups. By using the main results, we also obtain the structural characterizations for (?)-covered completely regular semigroups, weakly covered completely regular semigroups and covered completely regular semigroups.
  • Long Guang HUANG(1), San Yang
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 339-342. https://doi.org/10.12386/A2005sxxb0040
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    The relationship between weak vector variational inequality with a mapping from a topological vector space to continuous linear mapping space and its scalarization is discussed. A sufficient condition is presented on the connectedness of solution set for the weak vector variational inequality in a topological vector space. The conceptions of weakly and strongly uniformly continuous are introduced. The result on connectedness is derived by discussing the properties of set-valued mapping induced by solution set of a scalar variational inequality related to the weak vector variational inequality.
  • Tai Zhong ZHANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 343-346. https://doi.org/10.12386/A2005sxxb0041
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    We prove a sufficient and necessary condition for a weighted composition operator of the Bloch space on the unit ball of high dimension to be bounded.
  • Chang Jiang ZHAO(1), Gang Song
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 347-354. https://doi.org/10.12386/A2005sxxb0042
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    The purpose of the present paper is to point out the equivalence properties of some classical inequalities which are some dramatic inequalities of particular importance in Convex Geometric Analysis.
  • Wen Zheng ZHAO
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 355-364. https://doi.org/10.12386/A2005sxxb0043
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    In this paper we define a (f,T)-compatible pair (B,H). Using such a pair (B, H), we can construct a new braided monoidal category, which is submonoidal category of left H-modules category HM, and obtain a kind of new quantum Yang-Baxter operators. We also construct a Hopf algebra in the Yetter-Drinfel category HHYD by twisting the com ultiplication of B.
  • Qing Liu YAO
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 365-376. https://doi.org/10.12386/A2005sxxb0044
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    The positive solutions and symmetric positive solutions of the general Lidstone boundary value problem with all even-order derivatives are considered. By choosing suitable Banach space and cone, the existence of n positive solutions or symmetric positive solutions is established for the problem, where n is an arbitrary natural number. The basic tools used are equivalent norm and Krasnosel'skii fixed point theorem of cone expansion-compression type. The main conditions of the results are local. In other words, the problem may possess n positive solutions provided the "height" of the nonlinear term f on some bounded sets are appropriate.
  • Xi Shun YUE
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 377-384. https://doi.org/10.12386/A2005sxxb0045
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    This paper deals with the uniqueness of limit cycles from Poincare bifurcation of Lienard equation by usmg the implicit function theorem and the first order Mel'nikov function. Meanwhile, the case of non-existence of closed orbit is also investigated, some criteria are obtained. After modifying the first order Mel'nikov function, a new decision function is introduced, so the decision conditions become more simple.
  • Huan Yin CHEN(1), Fu An LI(2)
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 385-390. https://doi.org/10.12386/A2005sxxb0046
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    In this paper, we extend the notion of comparability for regular rings to that for ideals over regular rings and obtain several characterizations of the comparability for ideals. Furthermore, we show that Roth's problem has an affirmative solution for ideals with stable range one.
  • Qi Qing YU(1), George Y. C. WO
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 391-396. https://doi.org/10.12386/A2005sxxb0047
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    Consider a linear regression model, Y =β'X + ∈, where Y may be right censored and the cdf F0 of ∈ is unknown. We show that a modified semi-parametric MLE, denoted by β, is strongly consistent under certain regularity conditions. Moreover, if F0 is discontinuous, then P(β≠βi.o.)=0, which means that P(β=β if the sample size is large)=1. The latter property has not been reported for the existing estimators. On the contrast, most estimators, such as the Buckley-James estimator and M-estimators β, satisfy that P(β≠βi.o.)=1.
  • Zhong Kui LIU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 397-402. https://doi.org/10.12386/A2005sxxb0048
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    Let A, B be associative rings with identity, and (S,≤) a strictly totally ordered monoid which is also Artinian and finitely generated. For any bimodule AMB, we show that the bimodule [[AS,≤]][MS,≤][[BS,≤]] defines a Morita duality if and only if AMB defines a Morita duality and A is left noetherian, B is right noetherian. As a corollary, it is shown that the ring [[AS,≤]] of generalized power series over A has a Morita duality if and only if A is a left noetherian ring with a Morita duality induced by a bimodule AMB such that B is right noetherian.
  • Xue Jun GUO, Guabg Tian SONG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 403-406. https://doi.org/10.12386/A2005sxxb0049
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    In this paper, we discuss a method to compute the tame kernel of number field. Confining to imaginary quadratic field, we prove that (?)v : K2S'F/K2SF→k* is bijective when Nv > δD6.
  • De Rong QIU(1), Xian Ke ZHANG(
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 407-412. https://doi.org/10.12386/A2005sxxb0050
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    We study the classification of elliptic curves E over the rationals Q according to the torsion subgroups Etors(Q). More precisely, we classify those elliptic curves with Etors(Q) being cyclic with even orders. We also give explicit formulas for generators of Etors(Q). These results, together with the recent results of K. Ono for the non-cyclic Eaors (Q), completely solve the problem of the explicit classification and parameterization when E has a rational point of order 2.