中国科学院数学与系统科学研究院期刊网

15 September 2005, Volume 48 Issue 5
    

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  • Guo Hua ZHANG, Rui KUANG, Xian
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 833-840. https://doi.org/10.12386/A2005sxxb0101
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    A dynamical system is null if its sequence entropy is zero for any sequence. Substitutions of constant length on two symbols and their corresponding minimal dynamical systems arc divided into three types: finite, discrete and continuous. It is easy to see that such a substitution of finite type is null, and Goodman showed that the one of continuous type is not null. In this paper we completely determine which substitution of discrete type is null.
  • Shi Ping LU(1), Wei Gao GE(2)
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 841-850. https://doi.org/10.12386/A2005sxxb0102
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    By employing the continuation theorem of coincidence degree principle developed by Mawhin, a kind of second order p-Laplacian differential equation with a deviating argument((?)p(y'(t)))'+f(y'(t))+ g(y(t-τ(t)))=e(t) is studied. Some new results on the existence of periodic solutions are obtained.
  • Xin Han DONG, Mi YANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 851-858. https://doi.org/10.12386/A2005sxxb0103
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    We consider the function space Fα consisting of Cauchy-Stieltjes integrals. First, we give an equivalent definition of this space, then study the relation between this space and the logarithmic function of areally mean p-valent function, and finally we discuss further this relation for the case of univalent functions. From this investigation, we obtain a growth estimation about the coefficients of bounded univalent functions, which is the best result up to now.
  • Yao Chen ZHU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 859-866. https://doi.org/10.12386/A2005sxxb0104
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    In this note the algebraic independence of values of certain functions defined by infinite products and power series with algebraic coefficients at certain algebraic and transcendental numbers is given.
  • Shu Qin WANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 867-878. https://doi.org/10.12386/A2005sxxb0105
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    Let g be a general affine Lie algebra associated with a Lie algebra g equipped with a symmetric invariant bilinear form <,>. It is known that for every complex number l, we have a canonical vertex algebra Vg(l,o), and if (g, <, >) satisfies certain conditions, Vg(l,o) is a vertex operator algebra. In this paper, we consider g to be a finite-dimensional solvable Lie algebra equipped with a nondegenerate symmetric invariant bilinear form, and we show that Vg(l,o) contains a Virsoro-vector ω so that (Vg(l,0), Yv, 1,ω) is a vertex operator algebra.
  • Lu Chuan ZENG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 879-888. https://doi.org/10.12386/A2005sxxb0106
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    The auxiliary principle technique is extended to study a class of generalized strongly nonlinear mixed variational-like inequalities for set-valued mappings without compact values. Firstly, the existence of solutions to the auxiliary problems for this class of generalized strongly nonlinear mixed variational-like inequalities is shown. Secondly, the iterative algorithm for solving this class of generalized strongly nonlinear mixed variational-like inequalities is given by using this existence result. Finally, not only the existence of solutions of this class of generalized strongly nonlinear mixed variational-like inequalities is shown, but also the convergence of iterative sequences generated by the algorithm is proven.
  • Qing Nian PAN(1), Zhi Feng HAO
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 889-894. https://doi.org/10.12386/A2005sxxb0107
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    Solving the quantum Yang-Baxter equation is the original motivation for the definition of weakly-quasitriangular Hopf algebra. The paper gives a kind of method to construct weakly-quasitriangular Hopf algebra, which is called Yang-product. The Yang-product yields solutions to the quantum Yang-Baxter equation.
  • Hai Bo YU, Wen Huan SHEN
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 895-900. https://doi.org/10.12386/A2005sxxb0108
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    The group of self-homotopy equivalences Aut (X ∨ Y) is represented as a product of two subgroups Autx(X ∨ Y) and Aut Y(X ∨ Y) under the assumption that the self-equivalences of X ∨ Y can be diagonalized.
  • Xin Tao YE(2), Chong LI(1)
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 901-908. https://doi.org/10.12386/A2005sxxb0109
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    The convergence problem of family of the deformed Euler-Halley iterations with parmeters for solving nonlinear operator equations in Banach spaces is studied. Under the assumption that the derivative of the operator satisfies the Lipschitz condition, the semi-local quadratic convergences of the family of deformed Euler-Halley iterations are established.
  • Rui Pu BAI(1), Dao Ji MENG(2)
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 909-918. https://doi.org/10.12386/A2005sxxb0110
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    In this paper, we propose two special classes of nilpotent n-Lie algebras which are characteristically nilpotent n-Lie algebras and nilpotent n-Lie algebras of maximal rank. We also give the characteristic structure on nilpotent n-Lie algebras of maximal rank and present the necessity and sufficiency on characteristically nilpotent n-Lie algebras.
  • Hui Min SONG(2), Guio Zheng LI
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 919-928. https://doi.org/10.12386/A2005sxxb0111
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    Let G(V, E) be a loop-less graph with at least one edge, and let f be an integer function on V such that 1 ≤ f(v) ≤ d(v) for any v ∈ V. An f-edge cover-coloring is an edge coloring C such that each color appears at each vertex v at least f(v) times. The f-edge cover chromatic index of G, denoted by X'fc(G), is the maximum k such that an f-edge cover k-edge coloring exists. In this paper we provide a Vizing type theorem for X'fc(G) which generalizes a known result. We also investigate graph G or function f such that X'fc(G) attains the upper bound in the Vizing type theorem. A variation
  • Qing Zhai FAN, Xiao Chun Fang
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 929-934. https://doi.org/10.12386/A2005sxxb0112
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    In this paper, we will introduce a class of C*-algebras which have tracially stable rank one; we show that if A is a unital C*-algebra with tracially stable rank one and B is an AF-algebra, then A (?)B has tracially stable rank one; if A is a separable simple unital C* -algebra which has tracially stable rank one and SP property then it has stable rank one. We also get some properties about K-group of a separable unital C*-algebra with tracially stable rank one.
  • Chun Hua WANG(1), Cai Jun ZHOU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 935-938. https://doi.org/10.12386/A2005sxxb0113
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    In this paper, we study a well-known inequality on Noether rings with one dimension by another method. We will replace the length function with the multiplicity; thus we can rewrite the inequality and extend the inequality to rings with dimension more than one.
  • Wei Hong HE(1), Jun LUO(1), Zu
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 939-946. https://doi.org/10.12386/A2005sxxb0114
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    For self-similar sets E (?) n with the Open Set Condition and of Hausdorff dimension s > 0, we introduce the isodiametric inequality Hs|E(X) ≤|X|s and the corresponding extremal sets U (?) Rn with positive diameter such that Hs|E(U) = |U|s. Here Hs|E(·) is the s dimensional Hausdorff measure restricted to E, and |X| is the diameter of the set X in the standard Euclidean metric. If s = n, disks/balls are the unique extremal sets; if s ∈ (1,n), we have few ideas on properties of the extremal domains, but a few negative candidates. We can see that these isodiametric inequalities are related to the searching for exact value of Hs(E). Particularly, we take the Sierpinski gasket as an example, showing what the difficulty is or where it lies to find the the exact value of its In3/In2 dimensional Hausdorff measure. In some sense, this explains why, except for trivial examples, there are up to now no concrete self-similar sets with the Open Set Condition and of Hausdorff dimension larger than 1 such that the exact value of its Hausdorff measure has been calculated.
  • Qun Ying LIAO(1), Qi SUN(2)
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 947-954. https://doi.org/10.12386/A2005sxxb0115
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    The authors propose an algorithm for computing multiplication tables of optimal normal bases over finite fields, which is better than those corresponding results of Sun. In particular, this algorithm is very helpful to elliptic curves public-key cryptic systems.
  • Li Jun HEI, Jian Hua WU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 955-962. https://doi.org/10.12386/A2005sxxb0116
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    In this paper, we discuss a simple food web model consisting of one predator and two competing prey populations in an un-stirred chemostat with a single nutrient input. The necessary and sufficient conditions for the existence of coexistence states are established, and the main tools used here are Dancer fixed point index and the degree theory.
  • Hai Bo CHEN(1), Yi Rong LIU(2)
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 963-972. https://doi.org/10.12386/A2005sxxb0117
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    In this paper, we study the computation of quantities of equator (singular point quantities of infinity at Gauss sphere) in a class of planar polynomial differential system with a general form. Two linear recursion formulas for computation of quantities of equator are obtained. To compute quantities of equator with these recursion formulas, we only need to force addition, substraction, multiplication and division to the coefficients of the system, then avoid complex integrating operations and solving equations. It is symbolic and easy to realize without errors with computer algebra system.
  • Xian ZHANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 973-978. https://doi.org/10.12386/A2005sxxb0118
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    In this paper, we introduce some types of ordered contractive mappings and obtain some fixed point theorems of nonlinear mappings in ordered Banach spaces.
  • Shi Sheng ZHANG(1), You Xian T
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 979-984. https://doi.org/10.12386/A2005sxxb0119
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    Under more general conditions, a partial answer to Halpern's open question is given. The results presented in this paper also extend and improve some recent results.
  • Pei He WANG, Chun Li SHEN
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 985-992. https://doi.org/10.12386/A2005sxxb0120
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    In this paper, we come into talking about the essential spectrum of the Laplacian on a Riemannian manifold which possesses a pole.
  • Wei Gang SU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 993-998. https://doi.org/10.12386/A2005sxxb0121
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    Let S and T be quasisimilar operators. By introducing the concepts of the RT-class operator, the -R-class operator and the RR-class operator, this paper gives some sufficient and necessary conditions under which each component of σre(5) intersects σre(T), and gives some sufficient conditions under which each component of σre(S) intersets some subsets of σ3(T), and also gives some sufficient and necessary conditions under which an operator is an RT-class operator and an RR-class operator respectively.
  • Zi Fei SHEN, Min Bo YANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 999-101. https://doi.org/10.12386/A2005sxxb0122
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    With the aids of variational methods and delicate estimates, the existence of nontrivial solutions is obtained for elliptic equations with singular potential-△u-μ u/|x|2=|u|2*(s)-2u/|x|s+ λu,u∈H0 (1,2)(Ω)where Ωis an open bounded domain with smooth boundary,μ,λA are two positive parameters.
  • Qi Gui YANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 1011-102. https://doi.org/10.12386/A2005sxxb0123
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    By means of monotone functionals and the generalized interval means method, some new oscillation criteria for self-adjoint differential matrix system of the form [P(t)X'(t)]' + Q(t)X(t) = 0 are obtained.
  • Xiao Yong XI
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 1021-102. https://doi.org/10.12386/A2005sxxb0124
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    It is proved in this paper that if L is a bicomplete continuous DCPO, then the Isbell and Scott topologies agree on function spaces [X →L] for all RW-spaces X iff L is an L-Domain with a least element. Moreover, it is obtained that, if X is a core compact and locally connected space, then the Isbell and Scott topologies agree on functions space [X →L] for all continuous L-Domain L with a least element if and only if X is an RW-space. Particularly, if X is a continuous DCPO, then the Isbell and Scott topologies agree on function spaces [X →L] for all continuous L-Domain L with a least element iff X is an RW-space. This also gives a partial solution to the open problem presented by Lawson and Mislove.
  • Li Rong YU(2), Li Bo LUO(1)
    Acta Mathematica Sinica, Chinese Series. 2005, 48(5): 1029-103. https://doi.org/10.12386/A2005sxxb0125
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    We generalize the Chinese Remainder Theorem, use it to study the number theory models, and compare and analyse several number theory theorems in non standard number theory models.