中国科学院数学与系统科学研究院期刊网

Acta Mathematica Sinica, Chinese Series 2012 Vol.55

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Generalized Estimating Equation Estimators with Longitudinal Data
Mu ZHAO, Bai Cheng CHEN, Yong ZHOU
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 1-16.   DOI: 10.12386/A2012sxxb0001
Abstract3897)      PDF(pc) (714KB)(1723)       Save
Generalized estimating equations method as a powerful method for estimating parameters, is wildly used in many fields, such as biostatistics, econometrics and medical insurance, and so on. For longitudinal data, We should take account into within-subject correlation structure in order to improve efficiency of a estimator. It is often useful to suppose that there is a parametric assumption within-subject correlation in longitudinal data analysis. But unreasonable assumptions made on within-subject correlation structure can result in inefficient estimation for parameters or even result in misspecification. For the generalized estimating equations with longitudinal data, we propose the extended GMM methods and extended EL methods and construct the large sample properties for our estimators. One of the proposed EL methods which is called block empirical likelihood is robust because of avoiding any assumptions on withinsubject correlation structure. We also provide two simulation examples to illustrate the finite properties for our estimators.  
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Global Attractors for Schrödinger Equation Arising in Nonlinear Optics
Rui Feng ZHANG, Bian Min KOU
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 17-26.   DOI: 10.12386/A2012sxxb0002
Abstract2307)      PDF(pc) (549KB)(1328)       Save
We study a nonlinear Schrödinger equation modeling light waves propagating in a photorefractive crystal. We first construct the global weak attractor for this system. And then by exact analysis of the energy equation, we show that the global weak attractor is actually the global strong attractor. Further, we give the upper bound of the fractal and Hausdorff dimensions of the global attractor.  
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Bloch Constant on Classical Domain of the First Type
Jian Fei WANG, Tai Shun LIU
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 27-40.   DOI: 10.12386/A2012sxxb0003
Abstract1948)      PDF(pc) (542KB)(1052)       Save
In this paper, various subfamilies Hk(RI(m,n))of holomorphic mappings defined in the first classical domain RI(m,n)are introduced. When k tends to +∞, this family reduces to the class of locally biholomorphic mappings on RI(m,n). We establish the Bonk distortion theorems for Hk(RI(m,n)). In particular, when k = 1 and k → +∞, the theorems reduce to that of Fitzgerald and Gong, respectively. When m = n = 1, this distortion theorem coincides with Liu and Minda as the unit disk case. As applications of the Bonk distortion theorems, various estimates of Bloch constants for these subfamilies of holomorphic mappings on RI(m,n)are obtained. We not only give all Bloch estimates of holomorphic mappings between 1 < k < +∞ defined in RI(m,n), but also extend our early Bloch constant estimates of the unit ball to the classical domain of the first type RI(m,n).  
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Injectively Coresolving Classes and Projectively Resolving Classes
Yue Di ZENG, Jian Long CHEN
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 41-54.   DOI: 10.12386/A2012sxxb0004
Abstract2064)      PDF(pc) (432KB)(1083)       Save
In this paper, let C be a class of right R-modules closed under isomorphisms and direct summands. The relations between left(right)C-dimensions and left exact functors are considered for an(injectively)coresolving class C or a(projectively)resolving class C. In view of those, there are some applications.  
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Positive Solutions of Non-Positone Nonlinear Operator Equations and Its Applications
Jing Xian SUN, Xi An XU
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 55-64.   DOI: 10.12386/A2012sxxb0005
Abstract3101)      PDF(pc) (446KB)(1356)       Save
In this paper, firstly some existence results for unbounded connected component of solutions set of some nonlinear operator equations with parameter be obtained by using the global bifurcation theories, and then some existence results for positive solutions of a non-positone operator equation be obtained by using the positive connected property of the operator. The main results can be applied to various of differential boundary value problems to obtain the existence results for positive solutions without the assumption that the nonlinear terms are positone.  
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ω-Coherence in Milnor Squares
Fang Gui WANG
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 65-76.   DOI: 10.12386/A2012sxxb0006
Abstract2063)      PDF(pc) (452KB)(1105)       Save
A domain R is called ω-coherent if every finite type ideal is of finitely presented type. In this paper we show that ω-coherent domains are υ-coherent and if(RDTF,M)is a Milnor square, then for the case that F is the quotient field of D, R is ω-coherent if and only if D and T are ω-coherent and TM is a valuation domain; and for the case that F is not the quotient field of D, R is ω-coherent if and only if D is a field, [F:D] < ∞, M is a finite type ideal of R, T is ω-coherent and RM is coherent.  
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Existence of Some Elliptic Systems Involving the Pucci Operator
Zheng Zheng CHEN, Wei An LIU
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 77-90.   DOI: 10.12386/A2012sxxb0007
Abstract2611)      PDF(pc) (581KB)(1085)       Save
We study the existence of solutions for the fully nonlinear elliptic system 

where Ω⊂Rn, n ≥ 2 is a smooth bounded domain, -Mλ,∧+ is the Pucci operator with parameters 0 < λ ≤ Λ. Firstly, we show that the system has a bounded nonnegative solution if Fi, i=1,2 are uniformly bounded functions. Secondly, we prove that the system has a maximal nonnegative solution and a minimal nonnegative solution by using the method of super-subsolution combining with a fixed point theorem of increasing operator if {f1,f2}is quasi-increasing and the system has a supersolution and a subsolution. If {f1,f2} is either quasi-decreasing or blended quasi-monotony, the existence of a non-negative solution is presented by the Schauder fixed point theorem. For some particular type of Fi, the existence of positive solutions for the system is also obtained. We finally give some examples as application.  
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Consistent Invertibility and Perturbations of the Generalized Property(ω)
Xiao Hong CAO, Qiao Ling XIN
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 91-100.   DOI: 10.12386/A2012sxxb0008
Abstract2007)      PDF(pc) (484KB)(1322)       Save
A Hilbert space operator TB(H)may be said to be “consistent in invertibility” provided that for each SB(H), TS and ST are either both or neither invertible. The induced spectrum contributes the stability of generalized property(ω), for a bounded operator T acting on a Hilbert space, under perturbations by finite rank operators, by nilpotent operators and quisi-nilpotent operators commuting with T. The stability of generalized property(ω)of the operators which are the products of finitely normal operators are considered.  
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On the Positive Almost Periodic Solutions of some Neutral Integral Equation
Bin XU, Rong YUAN
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 101-110.   DOI: 10.12386/A2012sxxb0009
Abstract1767)      PDF(pc) (421KB)(1167)       Save
We discuss the existence of positive almost periodic solutions for some neutral integral equation, by constructing a new fixed point theorem in the cone. Some new results are obtained.  
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The Total Embedding Distributions of Necklaces
Yi Chao CHEN
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 111-116.   DOI: 10.12386/A2012sxxb0010
Abstract1989)      PDF(pc) (455KB)(1197)       Save
Gross, Klein and Rieper(1993)obtained the genus distri- butions of necklaces. Chen, Liu and Wang(2006), and Yang, Liu(2007), calculated total embedding distributions of necklaces, they obtained recurrence relations and ex- plicit formula, respectively. In this paper, we get a simpler explicit formula for the total embedding distributions of necklaces.  
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Fuzzy Soft Polygroups
Yun Qiang YIN, Jian Ming ZHAN
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 117-130.   DOI: 10.12386/A2012sxxb0011
Abstract6027)      PDF(pc) (400KB)(1206)       Save
This paper applies the concept of fuzzy soft sets to polygroup theory. The notions of(∈γ, ∈γ∨)-fuzzy soft polygroups and normal(∈γ, ∈γ∨)-fuzzy soft polygroups over a polygroup are introduced and their basic properties are investigated.  
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On the Dual Risk Model with Interest and Constant Dividend Barrier
Hai Li YUAN, Yi Jun HU
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 131-140.   DOI: 10.12386/A2012sxxb0012
Abstract2037)      PDF(pc) (516KB)(1015)       Save
We consider the dual risk model with interest and a constant dividend barrier. First, the integral-differential equation satisfied by the expected discounted dividend payments is given, and the closed form for the expected discounted dividend payments is provided in the case where profits follow an exponential distribution. Second, the integral-differential equation satisfied by the moments of the discounted dividend payments is given, and the closed form for the moments of the discounted dividend payments is also obtained in the case where profits follow an exponential distribution. Finally, we provide the numerical results for the expected discounted dividend payments in the case of exponential distribution.  
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Laplace-Stieltjes Transforms of Infinite Order in the Right Half-Plane
Yin Ying KONG
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 141-148.   DOI: 10.12386/A2012sxxb0013
Abstract1922)      PDF(pc) (414KB)(1075)       Save
By using a Type-function of the infinite order, the growth and the distribution of values of the Laplace-Stieltjes transforms convergent in the right half-plane are investigated. Some results similar to the Dirichlet series are obtained.  
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Existence of Monotone Positive Solutions for Semipositone Right Focal Boundary Value Problems with Dependence on the Derivatives
Xin An HAO, Li Shan LIU
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 149-160.   DOI: 10.12386/A2012sxxb0014
Abstract2433)      PDF(pc) (442KB)(1079)       Save
We study the existence of monotone positive solutions for the semipositone right focal boundary value problems 
 
where λ > 0 is a parameter, n ≥ 3, 1 < k ≤ n-1 is fixed, f may change sign for 0 < t < 1 and we allow f is both semipositone and lower unbounded. Without making any monotone type assumption, the existence results of at least one and two monotone positive solutions are obtained by means of the fixed point theorems in cones.  
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Fixed Smoothing Parameter of Pickands-Type Estimator's Large Quantile Estimation
Ke LIU, Xiang REN
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 161-168.   DOI: 10.12386/A2012sxxb0015
Abstract1634)      PDF(pc) (346KB)(973)       Save
Let {Xi}i=1 be i.i.d random sequence with common distribution F(x)which belongs to one of the domains of attraction of D(Gγ),(γ∈R). The large quantile of F(x)is estimated under some conditions as the smoothing parameter is fixed, and the asymptotic distribution is obtained. And lead to asymptotic confidence interval.  
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Estimation of the Optimal Constants in the Lp-Poincaré Inequalities on the Half Line
He Yan JIN, Yong Hua MAO
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 169-178.   DOI: 10.12386/A2012sxxb0016
Abstract3065)      PDF(pc) (414KB)(895)       Save
We will apply analytic methods to give the variational formula of the optimal constants in the Lp-Poincaré inequalities on the half line with finite measure and Dirichlet boundary condition. Moreover, by using iterating methods and the variational formula, we can get the explicit estimation of the optimal constants.  
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Bounded Fatou Components of Transcendental Entire Functions with Gaps
Cun Ji YANG, Yu Hua LI
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 179-186.   DOI: 10.12386/A2012sxxb0017
Abstract1807)      PDF(pc) (426KB)(1045)       Save
We discuss the boundedness of Fatou components of transcendental entire function with certain gaps. We prove that every component of its Fatou set is bounded.  
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The Normalizer Property for Integral Group Rings of Finite Groups with Abelian Sylow 2-Subgroups
Jin Ke HAI, Zheng Xing LI
Acta Mathematica Sinica, Chinese Series    2012, 55 (1): 187-192.   DOI: 10.12386/A2012sxxb0018
Abstract2155)      PDF(pc) (392KB)(1159)       Save
Mazur conjectured that the normalizer property holds for finite groups with abelian Sylow 2-subgroups. Let G be a finite group and let N be a normal subgroup of G such that Z(G/N)has only trivial units. In this paper, a connection is established between the automorphisms of G induced by units in Z(G/N)and Coleman automorphisms of N. Based on this connection, we confirm that if G is a finite group with abelian Sylow 2-subgroups and Z(G/F*(G))has only trivial units then Mazur's conjecture holds for G.  
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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.   DOI: 10.12386/A2012sxxb0038
Abstract1709)      PDF(pc) (660KB)(1147)       Save
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 H1H2∪…∪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.   DOI: 10.12386/A2012sxxb0039
Abstract1738)      PDF(pc) (522KB)(1075)       Save
In this paper, for weighted approximation in Lp-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 Lp-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.   DOI: 10.12386/A2012sxxb0040
Abstract2203)      PDF(pc) (432KB)(1324)       Save
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 βμ in the Unit Ball
Yan Hui ZHAO, Xue Jun ZHANG
Acta Mathematica Sinica, Chinese Series    2012, 55 (3): 437-448.   DOI: 10.12386/A2012sxxb0041
Abstract3197)      PDF(pc) (417KB)(1107)       Save
Some questions of Weighted composition operators Tψ,φ from F(p,q,s) space to βμ 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 Tψ,φF(p,q,s) space to βμ 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.   DOI: 10.12386/A2012sxxb0042
Abstract1930)      PDF(pc) (493KB)(1119)       Save
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.   DOI: 10.12386/A2012sxxb0043
Abstract1964)      PDF(pc) (522KB)(1098)       Save
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.   DOI: 10.12386/A2012sxxb0044
Abstract2048)      PDF(pc) (503KB)(1065)       Save
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.   DOI: 10.12386/A2012sxxb0045
Abstract1902)      PDF(pc) (448KB)(1125)       Save
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.   DOI: 10.12386/A2012sxxb0046
Abstract1778)      PDF(pc) (481KB)(1029)       Save
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.   DOI: 10.12386/A2012sxxb0047
Abstract2128)      PDF(pc) (537KB)(1050)       Save
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.   DOI: 10.12386/A2012sxxb0048
Abstract3160)      PDF(pc) (371KB)(1574)       Save
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.   DOI: 10.12386/A2012sxxb0049
Abstract3028)      PDF(pc) (457KB)(1174)       Save
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)+Ak-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.   DOI: 10.12386/A2012sxxb0050
Abstract1848)      PDF(pc) (333KB)(1223)       Save
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.   DOI: 10.12386/A2012sxxb0051
Abstract3108)      PDF(pc) (418KB)(1183)       Save
Let N be a nest on a Banach space X, and D be a weakly closed Jordan module of AlgN. Suppose that for every NN, 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.   DOI: 10.12386/A2012sxxb0052
Abstract2465)      PDF(pc) (443KB)(1203)       Save
We will obtain some weighted strong type and weak type estimates of Bochner-Riesz operators TR(n-1)/2 on the weighted Morrey spaces Lp,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 TRδ (δ ≥ (n ? 1)/2) is a bounded operator on the weighted Morrey spaces Lp,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.   DOI: 10.12386/A2012sxxb0053
Abstract1783)      PDF(pc) (429KB)(1032)       Save
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 Im={A1,A2,…,An+1}be a point set in En, then Im is an n-pseudo-symmetric point set if and only if the simplex with vertex set Im 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.   DOI: 10.12386/A2012sxxb0054
Abstract2012)      PDF(pc) (402KB)(968)       Save
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.
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Extension of Multiwavelet Sampling Theorem
You Fa LI, Shou Zhi YANG, Tao QIN
Acta Mathematica Sinica, Chinese Series    2012, 55 (4): 577-588.   DOI: 10.12386/A2012sxxb0055
Abstract1763)      PDF(pc) (563KB)(891)       Save
Sampling theorem plays a key role in digital signal communication and image processing since a continuous signal is usually recovered and processed by using its discrete samples. In this paper, we shall study the extension of sampling theorem related to generalized interpolating refinable function vectors introduced in Han Bin [J. Comput. Appl. Math., 2009, 227: 254-270]. Precisely, for an existing generalized interpolating d-refinable function vector ø=(ø1,…,ør)T, i.e.øl(m/r + k)= δkδl-1-m,Ⅴk∈Z,m=0,1,…,r-1,l=1,…,r.we construct a set of functions{ør+1,...,ødr} such that ø#=(øTr+1,…,ødr)T is also a continuous d-refinable function vector and satisfies øl(m/dr+k)=δkδθd,r(l)-m, Ⅴk|∈Z,m=0,1,…,dr-1,l=r+1,…,dr,with θd,r(l)=l-r+Rl-1-r,d-1,Rl-1-r,d-1=[l-1-r/d-1].The multiwavelet sampling theorem associated with ø# is established. Obviously, the sampling theorem in the multiwavelet subspaces of ø is extended. Moreover, we estimate the truncated error of the sampling theorem, which is desirable for application.
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The Boundedness of some Operators with Rough Kernel on the Weighted Morrey Spaces
Hua WANG
Acta Mathematica Sinica, Chinese Series    2012, 55 (4): 589-600.   DOI: 10.12386/A2012sxxb0056
Abstract2122)      PDF(pc) (464KB)(872)       Save
Let Ω ∈ Lq(Sn?1) with 1 < q ≤ ∞ be homogeneous of degree zero and has mean value zero on Sn?1. In this paper, we will study the boundedness of homogeneous singular integrals and Marcinkiewicz integrals with rough kernel on the weighted Morrey spaces Lp,κ(w) for q’ ≤ p < ∞ (or q’ < p < ∞) and 0 < κ < 1. We will also prove that the commutator operators formed by a BMO(Rn) function b(x) and these rough operators are bounded on the weighted Morrey spaces Lp,κ(w) for q’ < p < ∞ and 0 < κ < 1.
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Representations of Not-finitely Graded Centerless Super-Virasoro Algebras
Ya Feng YU
Acta Mathematica Sinica, Chinese Series    2012, 55 (4): 601-612.   DOI: 10.12386/A2012sxxb0057
Abstract1763)      PDF(pc) (468KB)(855)       Save
In this paper, the notion of not-finitely graded centerless super-Virasoro algebras is introduced, and a class of modules of the intermediate series over the notfinitely graded centerless super-Virasoro algebras is determined.
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The Hamming Weight and Nonlinearity of a Type of Rotation Symmetric Boolean Function
Bin WANG, Xi Yong, ZHANG Wei, Hong CHEN
Acta Mathematica Sinica, Chinese Series    2012, 55 (4): 613-626.   DOI: 10.12386/A2012sxxb0058
Abstract1914)      PDF(pc) (571KB)(833)       Save
Rotation symmetric Boolean functions have important applications in Cryptology. In this paper, we study the fast evaluation of a special type of rotation symmetric Boolean function and the recurrence relation about its Hamming weight. Then, we factor the function into several sub-functions. Finally, we prove that the nonlinearity of the function is the same as its Hamming weight with the recurrence relations about Fourier-transform values of these sub-functions. The conclusions and the methods used to deal with exponential sums in this paper may be applied for the further research on a conjecture of Cusick.
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Hochschild Homology Groups of a Class of Self-Injective Koszul Special Biserial Algebras
Jun Chao, ZHOU Yun, Ge XU, Yuan CHEN
Acta Mathematica Sinica, Chinese Series    2012, 55 (4): 627-640.   DOI: 10.12386/A2012sxxb0059
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Based on the minimal projective bimodule resolution given by Snashall and Taillefer, we explicitly calculate the dimension of each Hochschild homology group of a class of self-injective Koszul special biserial algebras ΛN in terms of combinatorics, and thus show intuitively that the Han’s conjecture holds true for ΛN by means of calculation.
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