15 May 2012, Volume 55 Issue 3

    

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  Arrangement Problem on the Subspace of the Unitary Space and dz-Disjunct Matrix with Correction Capability

  Geng Sheng ZHANG, Xiao Yan CAO

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 385-404. https://doi.org/10.12386/A2012sxxb0038

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  The pooling design has many application in practice. A mathematical model of pooling design is a dz-disjunct matrix. In this paper, we construct a kind of new dz-disjunct matrices with the subspaces of the unitary space. In order to discuss the correction capability of the design, we study the following arrangement problem on the subspace of the unitary space. For a given subspace C of type (m, s) in unitary space Fq2(n) and an integer d, we find d subspaces of type (m?1, s?1), H1, H2,…Hd of C that maximize the number of the subspaces of type (r, s?4) contained in H1∪H2∪…∪Hd. Then we give the tighter bound of z which is a reflection of correction capability on dz-disjunct matrix by the preceding result.
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  The Simultaneous Approximation Average Errors of Lagrange Interpolation on the 1-fold Integrated Wiener Space

  Gui Qiao XU, Jie WANG

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 405-424. https://doi.org/10.12386/A2012sxxb0039

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  In this paper, for weighted approximation in L_p-norm, we determine strongly asymptotic orders for the average errors of both function approximation and derivative approximation by the Lagrange interpolation sequence which based on the extended Chebyshev nodes of the second kind on the 1-fold integrated Wiener space. These results show that the average errors of both function approximation and derivative approximation by above mentioned Lagrange interpolation sequence are weakly equivalent to the average errors of the corresponding best polynomial approximation sequence for approximation in L_p-norm. In the sense of Information-Based Complexity, if permissible information functionals consist of standard information, then the average errors of both function approximation and derivative approximation by above mentioned interpolation sequence are weakly equivalent to the corresponding sequences of minimal average radii of nonadaptive information.
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  Multiplicity of Solutions for a Non-periodic Schrödinger Equation and a Superlinear Schrödinger-Maxwell Equation

  An Min MAO, An Ran LI

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 425-436. https://doi.org/10.12386/A2012sxxb0040

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  Without the periodity and symmetricity, we present new results on the existence of infinitely solutions for some nonlinear superlinear Schrödinger equation in the entire space without Ambrosetti-Rabinowitz growth condition. Also, we get the existence of infinitely many large energy solutions for some superlinear Schrödinger- Maxwell equations.
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  Weighted Composition Operators from F(p,q,s) Space to β_μ in the Unit Ball

  Yan Hui ZHAO, Xue Jun ZHANG

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 437-448. https://doi.org/10.12386/A2012sxxb0041

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  Some questions of Weighted composition operators T_ψ,φ from F(p,q,s) space to β_μ space in the unit ball are studied. By the methods of functional analysis and several complex variables, the necessary and sufficient conditions are given for Weighted composition operators T_ψ,φF(p,q,s) space to β_μ space in the unit ball.
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  Measure Estimates and Translative Pairs in the Spectra-Tilings Relations

  Jian Lin LI, Li YAN, Hai Hong YAO

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 449-456. https://doi.org/10.12386/A2012sxxb0042

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  In the present paper we will study the relations between spectra and tilings in two special cases. We first estimate and compare the Lebesgue measure of sets in the spectra-tilings relations. This includes a generalization of several results when the density method fails to apply, and the comparison of Lebesgue measure of sets among the orthogonal pairs, packing pairs and covering pairs. We then clarify some spectratilings relations between the translative pairs (D,Λ+Γ) and (D+Λ,Γ). The research here is based on the fundamental properties of spectra and tilings, and is closely related to the dual Fuglede conjecture.
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  On the Properties of the Ergodic Matrix over Finite Field

  Yong Zhe ZHAO, Bo ZHAO, Shi Hui PEI

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 457-468. https://doi.org/10.12386/A2012sxxb0043

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  We analyzed the properties of the ergodic matrix over finite field, And deduced the theorem on the number of the ergodic matrices over finite fields. We also comprehensively analyzes the rank and cardinal number of the two-side exponentiation set about the given matrix M and the ergodic matrix pair (A,B). And given the related theorems about the structure and cardinal number of the set. The results have the important theoretical significance for constructing the public key cryptography based on the ergodic matrices.
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  The Solution of Fractional Difference Equations of Order (2, q)

  Jin Fa CHENG, Guo Chun WU

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 469-480. https://doi.org/10.12386/A2012sxxb0044

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  We first present a kind of new definition of fractional difference, fractional summation, and fractional equations, give methods for explicitly solving fractional difference equations of order (2, q) by use of the method of undetermined coefficients.
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  The Preimage Distribution of Some Perfect Nonlinear Functions

  Shi Chun YANG, Wen Quan WU, Qun Ying LIAO

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 481-488. https://doi.org/10.12386/A2012sxxb0045

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  Determining the preimage distribution of a perfect nonlinear function, is very useful for both the existence of perfect nonlinear functions and the construction of some linear codes based on perfect nonlinear functions. This is a well-known open problem. In this paper, for the equation of the preimage distribution of a perfect nonlinear function, we determine its all integer solutions when m = 5 and m = 6.
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  (NCI) Operators and (NFI) Operators

  Li Qiong LIN, Huai Jie ZHONG, Yun Nan ZHANG

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 489-498. https://doi.org/10.12386/A2012sxxb0046

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  We give the concepts of two classes of operators which are closely related to the invariant subspaces, namely (NCI) operators and (NFI) operators. We consider the properties of these two classes of operators, such as the existence, the similar invariance and the relations between the strongly irreducible operators and them. We also consider the problem whether every operator with spectrum {0} is a small and compact perturbation of an (NFI) operator on a separable Banach space.
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  Large Deviations for 2-D Stochastic Navier-Stokes Equations with Jumps

  Hui Yan ZHAO

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 499-516. https://doi.org/10.12386/A2012sxxb0047

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  In this paper, under the existence and uniqueness of the solution of stochastic 2-D Navier-Stokes equation, we prove Freidlin-Wentzell’s large deviation principle for 2-D Stochastic Navier-Stokes Equation driven by multiplicative noise with Poisson jumps by using weak convergence approach.
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  On the Infinite Sum of Reciprocal Fibonacci Numbers

  Ting Ting WANG

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 517-524. https://doi.org/10.12386/A2012sxxb0048

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  We use the elementary method and the properties of the floor function to study the infinite sums derived from the reciprocals of the cubic of the Fibonacci numbers, and give a new and interesting identity involving the reciprocals of this sums.
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  Zeros of Solutions of Higher Order Homogeneous Linear Differential Equations

  Shuang Ting LAN, Zong Xuan CHEN

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 525-534. https://doi.org/10.12386/A2012sxxb0049

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  We investigate the exponent of convergence of zeros of solutions for some higher order homogeneous linear differential equation. When A₀ is an entire function that its taylor expansion is a gap power series and A₀ is the dominant coefficient, we proved that any two linearly independent solutions f1 and f2 of equation
  f^(k)+A_k-2f^(k-2)+…+A₁f′+A₀f=0
  satisfy max{λ(f₁),λ(f₂)}=∞, where λ(f) denotes the exponent of convergence of zeros of meromorphic function f.
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  The Value Distribution of Laplace-Stieltjes Transforms in the Right Half Plane

  Hong Shen ZHANG, Dao Chun SUN

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 535-542. https://doi.org/10.12386/A2012sxxb0050

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  For the Laplace-Stieltjes transforms of τ (2 < τ < +∞) order in the right half plane, given some conditions, then there exists a Borel point dealing with small functions about type function in the imaginary axis. For the Laplace-Stieltjes transforms of infinite order in the right half plane, given some conditions, then there exists a infinite order Borel point dealing with small functions in the imaginary axis.
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  Weakly Closed Jordan Modules of Nest Algebras on Banach Spaces

  Feng Jie LI, Peng Tong LI

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 543-550. https://doi.org/10.12386/A2012sxxb0051

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  Let N be a nest on a Banach space X, and D be a weakly closed Jordan module of AlgN. Suppose that for every N ∈ N, either dim(N/N_-)≠1 or N is topologically complementary. Then D must be an associative module of AlgN.
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  Some Estimates for Bochner-Riesz Operators on the Weighted Morrey Spaces

  Hua WANG, He Ping LIU

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 551-560. https://doi.org/10.12386/A2012sxxb0052

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  We will obtain some weighted strong type and weak type estimates of Bochner-Riesz operators T_R^(n-1)/2 on the weighted Morrey spaces L^p,k(w) for 1 ≤ p < ∞ and 0 < κ < 1. We will also prove that the commutator formed by a BMO(Rⁿ) function b(x) and T_R^δ (δ ≥ (n ? 1)/2) is a bounded operator on the weighted Morrey spaces L^p,k(w) for 1 < p < ∞ and 0 < κ < 1.
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  Pseudo-Symmetric Point Sets and Regular Simplices

  Ya Jun SHEN, Yao ZHANG, Gang Song LENG

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 561-566. https://doi.org/10.12386/A2012sxxb0053

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  A sufficient and necessary condition that an ordered vectors-set is a pseudosymmetric point set in Eⁿ is explored. Based on this condition, several equivalent ways of characterizing regular simplices are obtained. A relationship between a pseudosymmetric point set and a regular simplex is given, i.e., let I_m={A₁,A₂,…,A_n+1}be a point set in Eⁿ, then I_m is an n-pseudo-symmetric point set if and only if the simplex with vertex set I_m is regular.
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  k-Jordan Derivable Maps on Nest Algebras

  Lei LIU, Guo Xing JI

  Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 567-576. https://doi.org/10.12386/A2012sxxb0054

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  Let β be a nest on a Hilbert space of dimension greater than 1, algβ be the associated nest algebra, and k be a non-zero rational number. In this paper, We prove that a k-Jordan derivable map δ on algβ, δ(k(ab+ba)) = k[δ(a)b+aδ(b)+δ(b)a+bδ(a)] for all a, b ∈ algβ, is an additive derivation on algβ. In particular, it is an inner derivation when H is infinite dimensional. Related results concerning k-Jordan triple derivable maps are given.