中国科学院数学与系统科学研究院期刊网

15 May 2007, Volume 50 Issue 3
    

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  • Xian Tao WANG(1); Man Zi HUANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 481-484. https://doi.org/10.12386/A2007sxxb0056
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    We prove that every bounded and convex domain in ■~n can be mapped onto B~n(0,1) by a quasiconformal mapping of ■~n,i.e.,it is a quasiball.This shows that the Riemann mapping theorem of n-dimensioanl quasiconformal mappings holds in the class of bounded and convex domains in ■~n.
  • Shi Sheng ZHANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 485-492. https://doi.org/10.12386/A2007sxxb0057
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    By using viscosity approximation methods for nonexpansive mappings in Banach spaces,some sufficient and necessary conditions for the iterative sequence to converge to a fixed point are obtained.The results presented in the is paper extend and improve some recent results.
  • Jian Lian CUI
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 493-496. https://doi.org/10.12386/A2007sxxb0058
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    Let H be a complex Hilbert space with dim Hβ3 andβ(H) the set of all bounded linear operators on H.Suppose thatΦ:β(H)→β(H) is a weakly continuous linear bijective map.We prove thatΦsatisfiesΦ(A)Φ(B)=Φ(B)Φ(A)~* whenever AB=BA~* for all A,B∈β(H) if and only ifΦhas the formΦ(A)= cUAU~(-1) for all A∈(?)(H),where c is a nonzero real number and U∈β(H) is a unitary operator.
  • Xin Xing CHEN; Jian Gang YING
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 497-506. https://doi.org/10.12386/A2007sxxb0059
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    We give an explicit formula of the connection probability of a given subset of nodes in the random mapping graphs and its asymptotic limit.The asymptotic distribution of the number of components is also given.
  • Jing Hai SHAO; Yong Hua MAO
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 507-516. https://doi.org/10.12386/A2007sxxb0060
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    In this paper,we give out variational formula for the first Dirichlet eigenval- ues of two kinds of transient birth-Death processes on trees.One is that the symmetric measure of the process is finite but the root of the tree is switched to an absorbing state;another is that the symmetric measure is infinite.
  • Ji Gao YAN(1); Chun SU(2)
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 517-526. https://doi.org/10.12386/A2007sxxb0061
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    Let {X,X_n,n≥1} be non-degenerate i.i.d.random variables,define a U-statistics U_n=2/(n(n-1))∑_≤j≤j≤nh(X_i,X_j),where h(x,y) is a 2-dimensional Borel measurable and symmetric kernel function.Under the condition of E|h(X_1,X_2)|~(4/3) or E|h(X_1,X_2)|~((4/3)+δ),0<δ≤1 separately,for a very extensive weighted functionφ(x) and a boundary function b(x),we discuss the precise asymptotics of U_n as follows: where a is an appropriate non-negative number.It not only makes the known results on this subject as the special case of our results,but also reduces their moment conditions.
  • Er Ling WEI(1); Yan Pei LIU(2)
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 527-534. https://doi.org/10.12386/A2007sxxb0062
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    Strong Embedding Conjecture states that:any 2-connected graph can be strongly embedded on some surface.In this paper,we discuss the structure of maximal planar graph and the characteristic of strong embedding,then give an O (n log n) com- plexity algorithm for computing the nonorientable strong maximum genus of maximal outplanar graph.From the strong embeddings of some graphs,a small circuit double cover can be obtained.
  • Ri Cheng LI; Kai MA; Zhen De W
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 535-538. https://doi.org/10.12386/A2007sxxb0063
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    The possible form of the total Stiefel-Whitney classes of vector bundles on RP(j)×CP(k) is determined in this paper.
  • Yue Xu ZHAO
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 539-546. https://doi.org/10.12386/A2007sxxb0064
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    In this paper,we investigate the precise asymptotics for partial sums of nonstationary NA sequences.Many authors added strictly stationary restrictions to NA sequences when they discussed such limit properties,which has inconvenienced the study of some problems.It is well known that nonstationary NA sequences exist in lots of practical situations,therefore it is of great theoretical and practical meaning to remove the strictly stationary restriction,which is just the main purpose of the present work;meanwhile,our results include some known theorems as special cases.
  • Yong Ping SUN
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 547-556. https://doi.org/10.12386/A2007sxxb0065
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    We consider the nonlocal boundary value problem for a nonlinear fourth- order ordinary differential equation of the form where a,b E L~1[0,1],g:(0,1)→[0,∞) is continuous,symmetric on (0,1) and maybe singular at t=0 and t=1.f:[0,1]×[0,∞)→[0,∞) is continuous and f(·,x) is symmetric on [0,1] for all x E [0,∞).Under some suitable growth conditions,we show the existence and multiplicity of symmetric positive solutions of that above problem by applying Krasnoselskii's fixed point theorem in a cone.
  • Hui Hui PANG Wei Gao GE
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 557-566. https://doi.org/10.12386/A2007sxxb0066
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    In this paper,we deal with the second-order four-point boundary value problem.By applying the coincidence degree theory,the method of lower and upper solutions is established.Then some existence theorems for BVPs at resonance are proved.
  • Qi Sheng LI(1); Wen Ting TONG(
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 567-576. https://doi.org/10.12386/A2007sxxb0067
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    This paper concerns the related comparability and related power compa- rability of rings and modules,and some new characterizations for the related compa- rability are given.The relations between the related power comparability of rings and the related power comparable structures of modules are obtained.It is shown that if a module M has the related power comparability then so does each direct summand of M.For a separative exchange ring R,we further give the connections between the related comparability and the related power comparability.
  • Li Juan WANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 577-582. https://doi.org/10.12386/A2007sxxb0068
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    A continuous map from a closed interval into itself is a 3-order Feigenbaum's map if it is a solution of the functional equation f~3(λx)=λf(x).We consider the likely limit sets of 3-order nonsingle-valley Feigenbaum's maps and their Hausdorff dimensions.3-order nonsingle-valley Feigenbaum's maps must bring about chaos,and chaos also brings about the complication of the problem on the existence of likely limit sets.We testify the existence of the maps' likely limit sets by using the method of fractal geometry,estimate their Hausdorff dimensions.As an application,we give a idiographic example in order to prove the existence of 3-order nonsingle-valley Feigenbaum's maps.
  • Ya Ping FANG; Nan Jing HUANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 583-590. https://doi.org/10.12386/A2007sxxb0069
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    In this paper,we investigate the relationship of strict feasibility and solv- ability for the multivalued vector variational inequality.We derive some theorems which state that the multivalued vector variational inequality is solvable whenever it is strictly feasible under suitable conditions.
  • Zhao Juan ZHENG; Shao Bin TAN
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 591-600. https://doi.org/10.12386/A2007sxxb0070
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    Let =C_q[x_1~(±1),x_2~(±1)] be the non-commutative torus over the complex field, and A=\C,Der  be the Lie algebra of Derivations over .In this paper we study the automorphism group Aut L_q for the Lie algebra L_q=Der+A.
  • Zhi Bo HUANG; Zong Xuan CHEN
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 601-614. https://doi.org/10.12386/A2007sxxb0071
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    Let f_1 and f_2 be two linearly independent solutions of the differential equation f″+A(z)f=0,where A(z) is an entire function with order a(A)=+∞and hyper-orderσ_2(A)=0.Set E=f_1f_2.In this paper,we investigate the zeros distribution of solutions of equation f″+ A(z)f=0 in an angular domain.A relation between a cluster ray of the zeros and Borel direction of E with hyper order+∞is established.
  • Hua Shui ZHAN(1); Jun Ning ZHA
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 615-628. https://doi.org/10.12386/A2007sxxb0072
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    The paper gives a new definition of the weak solution for Cauchy Problem of the following quasilinear degenerate parabolic equation: and to tains the stability of the solutions under some constructive conditions.
  • Shu Li WANG; Li Xin GAO; Jin S
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 629-640. https://doi.org/10.12386/A2007sxxb0073
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    In this paper,the conjugate problem-u″(t)=b(t)f(u(t)) subject to u′(0)= u(1)=0 and u′_+(η)-u′_(η)=αu′(1) of the three-point boundary value problem -v″(t)=b(t)f(v(t)) subject to v′(0)=0,v(1)=αv(η) is put forward and investigated. The problem is translated to Hammertein's integral equation with the use of Green's function.Then,by using the first eigenvalue of the relevant linear problem and applying the fixed point index theory,the eigenvalue criteria of the existence for single and multiple positive solutions of the conjugate problem are given under some conditions concerning the first eigenvalue of the linear problem corresponding to it.
  • Chun Hui QIU; Tong De ZHONG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 641-652. https://doi.org/10.12386/A2007sxxb0074
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    By means of the invariant integral kernel (the Berndtsson kernel),com- plex Finsler metric and non-linear connection associated with Chern-Finsler connec- tion to research the integral representations for the differential forms of type (p,q) on a bounded domain with piecewise smooth C~((1)) boundaries on a complex Finsler manifold, the Koppelman-Leray-Norguet formulas are obtained,and the ■-equations are solved. As an application,with the help of the complex Finsler metric and non-linear connec- tion associated with Chern-Finsler connection,we give the Koppelman-Leray-Norguet formulas of (p,q) differential forms and the solutions of ■-equation on a bounded do- main with piecewise smooth C~((1)) boundaries on a Stein manifold.Moreover,we obtain the integral formulas of (p,q) differential forms and the solutions of ■-equation on a real non-degenerate strictly pseudoconvex polyhedra on a Stein manifold.
  • Ji Ming YANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 653-660. https://doi.org/10.12386/A2007sxxb0075
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    Let F=F_q(q=p~f,f≥1,p is an odd prime number).In this paper,we get an explicit formula for the number of F-rational solutions of the following systems of equations defined over ∑_(i=s_(r-1)+1~(s_r)∑_(j=1)~(m_i-m_(i-1))a_(m_(i-1)+j)x_1~(d_m(i-1)+j,1)…x_(n_i)~d_(m_(i-1)+j,n_i)=b_r,r=1,…,k where dij>0 satisfying certain conditions,a_i∈F~*,b_i∈F,0= s_0<s_1<…<s_k,0=m_0<m_1<…<m_s_k,0=n_0o<n_1<…<n_s_k, m_1≤n_1,…,m_s_k≤n_s_k.
  • Ji Tuan ZHOU; Lin Zhang LU
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 661-668. https://doi.org/10.12386/A2007sxxb0076
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    The classification of primes in the doubly stochastic circulant matrices is now explored.Since any n×n doubly stochastic circulant matrix has a unique representation as a polynomial of degree n-1 in the shift operatorω_n,the classification problem of primes in the doubly stochastic circulant matrices can be reduced to the solution of an equation over a doubly stochastic circulant matrix.By this means,the problem of deciding whether an n×n doubly stochastic circulant matrix A of order 3 is a prime is completely solved.A class of primes in the n×n doubly stochastic circulant matrices of order 4 is also presented.
  • Jin Su HE
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 669-678. https://doi.org/10.12386/A2007sxxb0077
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    Let (X,‖·‖) be a Banach space and Z be a nonempty subset of X.Let J:Z→R be a lower semicontinuous function bounded from below.The present paper concerns the problems of the characterization and the existence of the optimal solution of the perturbed optimization problem min_(zeZ)(J(z)+‖x-z‖),denoted by (J,x)-inf.The new notion of the J-sun set is introduced and the characterizations of the optimal solution of the problem (J,x)-inf for J-suns are provided in terms of Kolmogorov Criterion.Moreover,some existence results of the solution of the problem (J,x)-inf are given with the aid of some compactness of sets or the directional derivative of the optimal-value functional.
  • Lei JIAO; Pei Biao ZHAO
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 679-692. https://doi.org/10.12386/A2007sxxb0078
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    The celebrated Erlangen program given by Klein,describing the invariant of transform group in Euclidean space,has introduced some different geometries such as Affine Geometry,Conformal Geometry,etc.The authors will focus their attention on similar problems in Sub-Riemannian manifolds (i.e.Carnot-Caratheodory {M,Q,g}) with the view of Felix Klein,and obtain some interesting invariants,for instance,con- formal invariants and projective invariants.These results can be regarded as natural generalizations of those conclusions in Euclidean setting.Because of the essential dif- ference between Sub-Riemannian manifolds and Riemannian manifolds,so that,we wish to use the unique non-holonomic connection to solve the posed problems.
  • Song Ran WANG; Xin Han DONG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 693-700. https://doi.org/10.12386/A2007sxxb0079
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    The Cauchy transform F(z) ofα-Hausdorff measure restricted on 3-level Sierpinski gasket with a=1+1og2/log3,similarly to the case on Sierpinski gasket,presents some unusual geometric behavior.In this paper,we consider some auxiliary functions related to F(z) and get some their of important properties by making use of Laplace transform and the results in Dong X.H.and Lau K.S.(2003).These properties play a key role in the study of the geometric and asymptotic behavior of F(z).
  • Pei Guang WANG; Ying WANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 701-706. https://doi.org/10.12386/A2007sxxb0080
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    By means of a twin fixed point theorem in a cone,the existence of at least two positive solutions of a three-point boundary value problem for second order dynamic equations on time scales is obtained.
  • Yu Hong GUO
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 707-710. https://doi.org/10.12386/A2007sxxb0081
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    An identity between partitions and compositions was obtained by Agarwal in the year 2003.The object of this paper is to show other identities between partitions and compositions.In addition,we shall give several new combinatorial properties of the composition of n in wit.h no part 1 appear by the Fibonacci number.
  • Jing Cheng LIU; Ju Xiang LI; X
    Acta Mathematica Sinica, Chinese Series. 2007, 50(3): 711-720. https://doi.org/10.12386/A2007sxxb0082
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    In this paper,the necessary and sufficient conditions are given for the composition operator C_φ to be bounded or compact from Bloch type spaces β~p to β~q for all 0<p<∞and 0<q<∞on the unit ball of C~n.At the same time,several corollaries are obtained.