中国科学院数学与系统科学研究院期刊网

15 January 2008, Volume 24 Issue 1
    

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  • Li LIU, Chao Ping XING
    Acta Mathematica Sinica. 2008, 24(1): 1-6. https://doi.org/10.1007/s10114-007-1028-3
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    In the present paper, we make use of codes with good parameters and algebraic curves over finite fields with many rational points to construct dense packings of superballs. It turns out that our packing density is quite reasonable. In particular, we improve some values for the best-known lower bounds on packing density.
  • Hai Shan ZHANG
    Acta Mathematica Sinica. 2008, 24(1): 7-16. https://doi.org/10.1007/s10114-007-1011-z
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    The author constructs a class of indecomposable non-degenerate solvable Lie Algebras corresponding to a Cartan matrix A over the field of complex numbers and we determine all their derivations.
  • Chang Xing MIAO, You Bin ZHU
    Acta Mathematica Sinica. 2008, 24(1): 17-26. https://doi.org/10.1007/s10114-007-1031-8
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    The authors consider the well-posedness in energy space of the critical non-linear system of wave equations with Hamiltonian structure  where there exists a function F(λ, μ) such that ∂F(λ, μ)/∂λ=F1(λ, μ)/∂μ=F2(λ, μ). By showing that the energy and dilation identities hold for weak solution under some assumptions on the non-linearities, we prove the global well-posedness in energy space by a similar argument to that for global regularity as shown in "Shatah and Struwe's paper, Ann. of Math. 138, 503-518 (1993)".
  • Ru Yun MA, Bevan THOMPSON
    Acta Mathematica Sinica. 2008, 24(1): 27-34. https://doi.org/10.1007/s10114-007-1009-6
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    We are concerned with determining the values of λ, for which there exist nodal solutions of the fourth-order boundary value problem
    y''''= λa(x)f(y),0 < x < 1,
    y(0)=y(1)=y''(0)=y''(1)=0,
    where λ is a positive parameter, aC([0, 1], (0, ∞)), fC (R, R) satisfies f(u)u > 0 for all u ≠ 0. We give conditions on the ratio f(s)/s, at infinity and zero, that guarantee the existence of nodal solutions. The proof of our main results is based upon bifurcation techniques.
  • Gong Lin YUAN, Zeng Xin WEI
    Acta Mathematica Sinica. 2008, 24(1): 35-42. https://doi.org/10.1007/s10114-007-1012-y
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    We prove the superlinear convergence of a nonmonotone BFGS algorithm on convex objective functions under suitable conditions.
  • Ling Quan KONG
    Acta Mathematica Sinica. 2008, 24(1): 43-58. https://doi.org/10.1007/s10114-007-1006-9
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    This paper is concerned with a conjecture formulated by Coates et al in [4] which describes the relation between the integrality of the characteristic elements and their evaluations in the noncommutative Iwasawa theory. We give an almost equivalent description of the conjecture and prove a certain part of it.
  • Wei Dong LIU, Zheng Yan LIN
    Acta Mathematica Sinica. 2008, 24(1): 59-74. https://doi.org/10.1007/s10114-007-0995-8
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    Let {X,X1,X2,…} be a strictly stationary φ-mixing sequence which satisfies EX=0, EX2(log2 |X|)2 < ∞ and φ(n)=O(1/(log n)T) for some T > 2. Let Snk=1n Xk and an=O(√n/(log2n)γ) for some γ > 1/2. We prove that

    The results of Gut and Sp?taru (2000) are special cases of ours.
  • Kwang Ik KIM, Zu Han LIU
    Acta Mathematica Sinica. 2008, 24(1): 75-86. https://doi.org/10.1007/s10114-007-1014-9
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    We study the minimizers of the Ginzburg-Landau model for variable thickness, superconducting, thin films with high κ, placed in an applied magnetic field hex, when hex is of the order of the "first critical field", i.e. of the order of |ln ε|. We obtain the asymptotic estimates of minimal energy and describe the possible locations of the vortices.
  • M. IMDAD, Javid ALI
    Acta Mathematica Sinica. 2008, 24(1): 87-94. https://doi.org/10.1007/s10114-007-0990-0
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    We prove that (E.A) property buys the required containment of range of one mapping into the range of other in common fixed point considerations up to a pair of mappings. While proving our results, we utilize the idea of implicit functions due to Popa, keeping in view their unifying power.
  • Abdelghani OUAHAB
    Acta Mathematica Sinica. 2008, 24(1): 95-106. https://doi.org/10.1007/s10114-007-0999-4
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    A recent nonlinear alternative for contraction maps in Fréchet spaces due to Frigon and Granas (Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22, (2), 161-168 (1998)), combined with semigroup theory, is used to investigate the existence and uniqueness of mild solutions for first-and second-order functional semi linear and neutral damped differential equations in Fréchet space.
  • Leszek GASIŃSKI
    Acta Mathematica Sinica. 2008, 24(1): 107-120. https://doi.org/10.1007/s10114-007-0997-6
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    The authors study evolution hemivariational inequalities of semilinear type containing a hysteresis operator. For such problems we establish an existence result by reducing the order of the equation and then by the use of the time-discretization procedure.
  • Dong HAN, Xin Sheng ZHANG, Wei An ZHENG
    Acta Mathematica Sinica. 2008, 24(1): 121-138. https://doi.org/10.1007/s10114-007-0978-9
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    We consider the asymptotic probability distribution of the size of a reversible random coagulation-fragmentation process in the thermodynamic limit. We prove that the distributions of small, medium and the largest clusters converge to Gaussian, Poisson and 0-1 distributions in the supercritical stage (post-gelation), respectively. We show also that the mutually dependent distributions of clusters will become independent after the occurrence of a gelation transition. Furthermore, it is proved that all the number distributions of clusters are mutually independent at the critical stage (gelation), but the distributions of medium and the largest clusters are mutually dependent with positive correlation coefficient in the supercritical stage. When the fragmentation strength goes to zero, there will exist only two types of clusters in the process, one type consists of the smallest clusters, the other is the largest one which has a size nearly equal to the volume (total number of units).
  • Ying Ying TAN, Yi Zheng FAN
    Acta Mathematica Sinica. 2008, 24(1): 139-146. https://doi.org/10.1007/s10114-007-1000-2
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    Let G be a mixed graph which is obtained from an undirected graph by orienting some of its edges. The eigenvalues and eigenvectors of G are, respectively, defined to be those of the Laplacian matrix L(G) of G. As L(G) is positive semidefinite, the singularity of L(G) is determined by its least eigenvalue λ1(G).This paper introduces a new parameter edge singularity εs(G) that reflects the singularity of L(G), which is the minimum number of edges of G whose deletion yields that all the components of the resulting graph are singular. We give some inequalities between εs(G) and λ1(G) (and other parameters) of G. In the case of εs(G)=1, we obtain a property on the structure of the eigenvectors of G corresponding to λ1(G), which is similar to the property of Fiedler vectors of a simple graph given by Fiedler.
  • Hua QIU, Wei Yi SU
    Acta Mathematica Sinica. 2008, 24(1): 147-158. https://doi.org/10.1007/s10114-007-1015-8
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    The distributional dimension of fractal sets in Rn has been systematically studied by Triebel by virtue of the theory of function spaces. In this paper, we first discuss some important properties about the B-type spaces and the F-type spaces on local fields, then we give the definition of the distributional dimension dimD in local fields and study the relations between distributional dimension and Hausdorff dimension. Moreover, the analysis expression of the Hausdorff dimension is given. Lastly, we define the Fourier dimension in local fields, and obtain the relations among all the three dimensions.
  • Donald W. BARNES
    Acta Mathematica Sinica. 2008, 24(1): 159-166. https://doi.org/10.1007/s10114-007-1008-7
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    Engel subalgebras of finite-dimensional n-Lie algebras are shown to have similar properties to those of Lie algebras. Using these, it is shown that an n-Lie algebra, all of whose maximal subalgebras are ideals, is nilpotent. A primitive 2-soluble n-Lie algebra is shown to split over its minimal ideal, and all the complements to its minimal ideal are conjugate. A subalgebra is shown to be a Cartan subalgebra if and only if it is minimal Engel, provided that the field has sufficiently many elements. Cartan subalgebras are shown to have a property analogous to intravariance.
  • Ye Zhou LI, Jun WANG
    Acta Mathematica Sinica. 2008, 24(1): 167-176. https://doi.org/10.1007/s10114-007-0981-1
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    This paper is devoted to studying the growth problem, the zeros and fixed points distribution of the solutions of linear differential equations f''+e-zf'+Q(z)f=F(z), where Q(z) ≡ h(z)ecz and c ∈ R.