中国科学院数学与系统科学研究院期刊网

Acta Mathematica Sinica, Chinese Series 2014 Vol.57

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The Boundedness of Hausdorff Operators on Campanato Spaces
Xiao Mei WU, Gui Lian GAO, Xiao YU
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 1-8.   DOI: 10.12386/A2014sxxb0001
Abstract1814)      PDF(pc) (417KB)(1170)       Save
We study several kinds of Hausdorff operators on Campanato spaces and obtain the sharp bounds for them. Furthermore, we also discuss the boundedness of multilinear Hausdorff operator on Morrey space.
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Local Ruin Probability in a Risk Model with Variable Premium Rates
Xiu Chun BI, Rong LI
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 9-16.   DOI: 10.12386/A2014sxxb0002
Abstract1809)      PDF(pc) (552KB)(791)       Save
We introduce a catastrophe risk model with variable premium rates and obtain a local result of the ruin probability under heavy-tailed claims. In addition, we extend the risk model and propose a regression-type size-dependence one under the framework of web Markov skeleton process, which has some theoretic and practical value in the field of actuarial, and allows applications in various areas.
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Relaxed Alternating Projection Method for Solving Linear Matrix Equation Problem under Closed Convex Constraint
Jiao Fen LI, Xi Yan HU, Lei ZHANG
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 17-34.   DOI: 10.12386/A2014sxxb0003
Abstract1742)      PDF(pc) (1421KB)(872)       Save
We discuss the existing relaxed alternating projection method for solving the linear matrix equation AXB=C under some closed convex constraints to X. The considered closed convex constrained set, denoted by R, is (1) the set of bounded matrices, (2) the set of Q-positive definite matrices, (3) the solution set of a linear matrix inequality. We prove the weak convergence of the matrix sequence generated by the proposed algorithm, and present some numerical examples for solving AXB=C under symmetric nonnegative and symmetric positive semidefinite matrices constraint to illustrate the feasibility and efficiency of the proposed algorithm, and to show its clear superiority comparing with alternating projection method and spectral projected gradient method.
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Perturbation of the Generalized Drazin Inverse in Banach Algebra
Xiao Ji LIU, Yong Hui QIN
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 35-46.   DOI: 10.12386/A2014sxxb0004
Abstract1694)      PDF(pc) (386KB)(821)       Save
We present the necessary and sufficient conditions for the element after perturbing and investigate the perturbation bounds for the generalized Drazin inverse by using block technology in Banach algebra.
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Totally Umbilical Property of Hyper-surfaces in a Positive Curvature Space Form and Higher Order Curvature
Qi WANG
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 47-50.   DOI: 10.12386/A2014sxxb0005
Abstract1993)      PDF(pc) (321KB)(832)       Save
We study the totally umbilical property of compact closed equal-distance immersed hyper-surfaces Mn in the positive curvature space form Sn+1(c) (c>0) and the higher order mean curvatures, and obtain a result which improves the relevant recent theorems in this research field.
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Hausdorff Dimension of Sets Arising from Dvoretzky Random Covering
Jun Min TANG
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 51-70.   DOI: 10.12386/A2014sxxb0006
Abstract1653)      PDF(pc) (551KB)(982)       Save
We consider the random intervals In(ω)=ωn+(-ln/2,ln/2) (mod 1), where {ln}n≥1 is a sequence of positive real numbers which is decreasing to zero and {ωn}n≥1 is an i.i.d. sequence with Gibbs distribution measure on the circle T= R/Z. Using the tools from multi-fractal analysis, we estimate the Hausdorff dimension of sets which are covered finitely or infinitely many times by {In(ω)}.
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Automorphisms of Generalized Orthogonal Graphs of Odd Characteristic
Li Jun HUO, Wen Bin GUO, Chang Li MA
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 71-88.   DOI: 10.12386/A2014sxxb0007
Abstract2560)      PDF(pc) (569KB)(896)       Save
In this paper, the automorphism group of the generalized orthogonal graph ΓGO2ν+δ(q,m,S) over Fq of odd characteristic is determined, where 1<m<ν.
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On Approximation by Univariate Sigmoidal Neural Networks
Guo Chun MA, Dan Sheng YU, Ping ZHOU
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 89-100.   DOI: 10.12386/A2014sxxb0008
Abstract1766)      PDF(pc) (498KB)(1023)       Save
We first introduce a new type of neural network operators with sigmoidal functions, and give the pointwise and global estimates of the approximation by the networks. The new neural network operators can approximate the functions with a very good rate which can not be obtained by polynomial approximation. To further improve the approximation rate for functions of smoothness, we also introduce a new type of combinations of neural network operators, and give pointwise and global estimates of the approximation by the combinations. A numerical example is given to demonstrate our new method.
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Trace-Kernel Operator Semigroup of Free Monogenic Inverse Semigroup
Wei LONG, Li Min WANG
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 101-108.   DOI: 10.12386/A2014sxxb0009
Abstract2139)      PDF(pc) (424KB)(839)       Save
For congruence ρ on an inverse semigroup, there are maximal element ρT and minimal element ρt in a trace class; by the same token, there are maximal element ρK and minimal element ρk in a kernel class. So we can find four operators Γ= {K, k, T, t} on congruence lattice C(S) of an inverse semigroup S. Inthis paper,we gained extremum congruence which is not identity relation on free monogenic inverse semigroup Ix. Then establishing relations in Γ on congruence lattice C(S), we obtain trace-kernel operator semigroup Γ+/Σ* of Ix finally.
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Quantization on Generalized Heisenberg-Virasoro Algebra
Hai Bo CHEN, Ran SHEN, Jian Gang ZHANG
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 109-116.   DOI: 10.12386/A2014sxxb0010
Abstract1496)      PDF(pc) (392KB)(791)       Save
In a recent paper, Lie bialgebra structures on generalized Heisenberg- Virasoro algebra L are considered by the authors. In this paper, the explicit formula of the quantization on generalized Heisenberg-Virasoro algebra is presented.
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The Existence for Self-Orthogonal Cyclic Codes over Finite Fields
Qun Ying LIAO, Yan Bin LI, Huan LIAO
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 117-124.   DOI: 10.12386/A2014sxxb0011
Abstract1727)      PDF(pc) (466KB)(958)       Save
We obtain a necessary and sufficient condition for that there exists a nontrivial self-orthogonal or self-dual cyclic codes over finite fields and the explicit enumerating formula. As a corollary, a simple and easy criterion for several classes of non-trivial self-orthogonal cyclic codes is given.
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Nonexistence of Solutions for a Singular Semilinear Elliptic Equation
Wen Shu ZHOU, Xiao Dan WEI, Xu Long QIN
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 125-130.   DOI: 10.12386/A2014sxxb0012
Abstract1872)      PDF(pc) (394KB)(778)       Save
We study the nonexistence of solutions for a singular semilinear elliptic equations. The results improve and implement a work by Arcoya et al. [Existence and nonexistence of solutions for singular quadratic quasilinear equations, J. Differential Equations, 2009, 246: 4006-4042], whose proofs are very simple and based on Poincaré inequality, Lusin theorem and Egoroff theorem.
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Existence of Positive Solution for a Quasilinear System with Nonlinear Boundary Condition
Guo Ying YANG, Jun Xiang CHENG
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 131-138.   DOI: 10.12386/A2014sxxb0013
Abstract2699)      PDF(pc) (406KB)(917)       Save
In this paper, we consider the quasilinear elliptic systems with the nonlinear boundary condition and weight function. With the help of the Nehari manifold, we obtain the system has at least two nontrival positive solutions under the proper region of parameters.
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Mean Curvature Flow with a Forcing Field in Direction of the Position Vector of Submanifolds
Shun Zi GUO, Guang Han LI, Chuan Xi WU
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 139-150.   DOI: 10.12386/A2014sxxb0014
Abstract2275)      PDF(pc) (675KB)(945)       Save
This paper considers the evolution by mean curvature vector plus a forcing field in the direction of its position vector of a closed submanifold of dimension n (≥ 2) in Rn+p. Suppose that mean curvature vector is nonzero everywhere and that the full norm of the second fundamental form is bounded by a fixed multiple (depending only on n) of the length of the mean curvature vector at every point. It is shown that such submanifolds may contract to a point in finite time if the forcing field is small, or exist for all time and expand to infinity if it is large enough. Moreover, if the evolving submanifolds undergo suitable homotheties and the time parameter is transformed appropriately into a parameter t, 0 ≤ t < ∞, it is also shown the normalized submanifolds in any case converge smoothly to a round sphere in some (n + 1)-dimensional subspace of Rn+p as t→∞.
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Complete Convergence for Weighted Sums of Arrays ρ-Mixing Random Variables
De Hua QIU
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 151-162.   DOI: 10.12386/A2014sxxb0015
Abstract1379)      PDF(pc) (425KB)(723)       Save
The complete convergence for weighted sums of arrays ρ-mixing random variables is discussed under general conditions by utilizing the Rosenthal type inequality of ρ-mixing random variables. General complete convergence theorems and convergence for moving average processes generated by sequences of ρ-mixing random variables are obtained, which improve and extend the related known works in the literature.
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Mean-square Convergence Rate of Stochastic-Theta Methods for a Class of Stochastic Differential Delay Equations
Jun LIU
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 163-170.   DOI: 10.12386/A2014sxxb0016
Abstract1813)      PDF(pc) (404KB)(617)       Save
We provide a mean-square convergence rate of stochastic theta methods for a class of stochastic differential delay equations whose coefficients are not Lipschitz but only Hölder continuous.
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Real Vector Cone Metric Space and Fixed Point Theorems
Fei HE, Jing Hui QIU
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 171-180.   DOI: 10.12386/A2014sxxb0017
Abstract1929)      PDF(pc) (451KB)(776)       Save
We introduce real vector cone metric spaces, where cone metric is the mapping on a real vector space without topological structures. We also prove some new fixed point theorems in real vector cone metric spaces. By using nonlinear scalarization functions, we establish the equivalence between these and some other fixed point results in metric and in real vector cone metric spaces. Our results improve and generalize some results from the literature.
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Meromorphic Solutions of Painlevé Ⅲ Difference Equations
Ji Long ZHANG, Lian Zhong YANG
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 181-188.   DOI: 10.12386/A2014sxxb0018
Abstract1581)      PDF(pc) (390KB)(706)       Save
We investigate the properties of meromorphic solutions of Painlevé Ⅲ difference equations. In particular, we study the existence of Borel exceptional value, the exponent of convergence of zeros, poles and fixed points of a transcendental meromorphic solution. Several sharp examples of meromorphic solutions of some Painlevé Ⅲ difference equations are given.
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Nodal Solutions for p-Laplacian Problems with Jumping Nonlinearities
Guo Wei DAI, Ru Yun MA
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 189-194.   DOI: 10.12386/A2014sxxb0019
Abstract1538)      PDF(pc) (416KB)(647)       Save
We study the existence of nodal solutions for the p-Laplacian problems with jumping nonlinearities at zero and infinity. More precisely, we show that there exists at least one nodal solution to the problems if nonlinearities crossing the Fučik spectrum.
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On the Diophantine Equation x2+By2p=z3
Zhong Feng ZHANG, Jia Gui LUO
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 195-198.   DOI: 10.12386/A2014sxxb0020
Abstract1565)      PDF(pc) (285KB)(832)       Save
In this paper, for some choices of integers B, we give all the integer solutions of equation x2+By2p=z3 with xyz≠0 and x, y, z pairwise coprime for prime p ≥ 11.
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Numerical Upper Bounds for the Mean Values of Smooth Weyl Sums of Fractional Moments
Tian Qin WANG, Hua Ke LIU
Acta Mathematica Sinica, Chinese Series    2014, 57 (1): 200-208.   DOI: 10.12386/A2014sxxb0021
Abstract1416)      PDF(pc) (480KB)(609)       Save
We discuss some relationship of the numerical upper bounds for the mean values of smooth Weyl sums of fractional moments. Some new results on the numerical upper bounds of the mean values are given when the moments are in the interval [4, 5].
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On the Diophantine Equation X2-(a2+4p2n)Y4 = -4p2n
Ping Zhi YUAN, Zhong Feng ZHANG
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 209-222.   DOI: 10.12386/A2014sxxb0022
Abstract1738)      PDF(pc) (458KB)(1045)       Save
Let a, n ≥ 1 be integers, p a prime. We prove that, under some conditions the Diophantine equations X2- a2 + 4p2n)Y4 = -4p2n and X2-(a2+p2n)Y4 = -p2n have at most two coprime positive integer solutions (X, Y).
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Construction and Properties of Fractal Interpolation Surfaces with Variable Free Parameters
Hong Yong WANG, Shou Zhi YANG
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 223-234.   DOI: 10.12386/A2014sxxb0023
Abstract1844)      PDF(pc) (1173KB)(734)       Save
A new construction of fractal interpolation surfaces (FISs) on rectangular grids using iterated function systems (IFSs) is proposed and some of their properties are studied in this paper. The IFSs employed are endowed with variable free parameters and are proved that they can generate continuous bivariate FISs, which can be used as self-affine and non-self-affine fractal interpolation models on arbitrary data points. Some inequalities concerning the sensitivity of the resulting bivariate fractal interpolation functions (FIFs) are deduced in two metric senses. The estimation of the error between the bivariate FIF and a bivariate data generating function is given. Finally, under certain conditions, the uniform convergence of the bivariate FIFs to the data generating function is proved.
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The Characteristics of Logic Functions Determined by R0-Implication Operator
Jian Ren ZHOU, Hong Bo WU
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 235-248.   DOI: 10.12386/A2014sxxb0024
Abstract1501)      PDF(pc) (1089KB)(761)       Save
The R0-implication operator is a new implication operator that was proposed by Wang Guojun in 2000. In the present, the R0-implication operator has been applied to studying of fuzzy controlling, approximate reasoning, fuzzy recognition, fuzzy systems, quantitative logic. The common point of applications is that the function determined by a formula through R0-implication operator plays a key role. In this paper, the characteristics of the function determined by a formula through R0-implication operator are investigated intensively in R0-style propositional logic system. The necessary and sufficient conditions are obtained for a function f: [0, 1]n → [0, 1] to be induced by a formula through the R0-implication operator in R0-style propositional logic system.
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Subnormality of the Reproducing Kernel Hilbert Spaces on the Unit Ball
Xian Min XU
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 249-260.   DOI: 10.12386/A2014sxxb0025
Abstract1754)      PDF(pc) (483KB)(712)       Save
Let Bd be the unit ball ofd-dimensional complex Euclid space Cd, Hdg (BdR) the reproducing kernel Hilbert space with U-invariant reproducing kernel K(z,w) = g(<z,w>), where g(z) = ∑n=0 anzn (an ≥ 0) is the generating function of the space Hdg (BdR). In this paper, we show that the multiplier algebra of the space Hdg (BdR) is a proper subset of H(BdR), and there exists a holomorphic self-mapping ø from BdRinto BdRsuch that the multiplication operator Møis not bounded when the sequence {an}n=0 is bounded andd ≥ 2. Furthermore, we prove that if the coefficients sequence {an}n=0 of the generating function g is a bounded, non-decreasing sequence, i.e. there exists a positive number M such that 0 ≤ a0a1 ≤ … ≤ M, n = 0, 1, 2, …, then the space Hdg (BdR) is not subnormal, in other words, there is not any positive measure μ on Cd such that ||f|| Hdg2 =∫ Cd |f(z)|2(z), for each fHdg (BdR), and then von Neumann's inequality does not hold on the space Hdg (BdR).
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On a Class of N-Laplacian Equations via Morse Theory
Guo Qing ZHANG, Jing SUN
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 261-271.   DOI: 10.12386/A2014sxxb0026
Abstract1483)      PDF(pc) (450KB)(719)       Save
We investigate a class of N-Laplacian equations with subcritical growth. Based on Trudinger-Moser inequality and Morse theory, we prove the existence of nontrivial solutions when there is no Mountain Pass geometry, without imposing the Ambrosetti-Rabinowitz condition or a global sign condition.
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The Integer Parts of a Nonlinear Form with Integer Variables and Powers 2, 3 and 4
Wei Ping LI, Bai Yun SU, Tian Ze WANG
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 273-280.   DOI: 10.12386/A2014sxxb0027
Abstract1634)      PDF(pc) (411KB)(692)       Save
We prove that if λ1, λ2, λ3, λ4 are positive real numbers, and at least one of λi/λj (1 ≤ i < j ≤ 4) is irrational, then, the integer parts of λ1x12 +λ2x23 +λ3x34 +λ4x44 are prime infinitely often for natural numbers x1, x2, x3, x4. This greatly improves of the former result.
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Existence and Nonexistence of Sign-Changing Solutions for a Singular Elliptic Problem
Yan Fang PENG, Bi Wen LI
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 281-294.   DOI: 10.12386/A2014sxxb0028
Abstract1724)      PDF(pc) (478KB)(795)       Save
We consider the following singular elliptic equation
,
which involves the Caffarelli-Kohn-Nirenberg inequalities. By virtue of the Ljusternik-Schnirelaman theory and a Pohozaev-type identity, we obtain the existence and nonexistence results of sing-changing solutions for the above problem.
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Some Inequalities in Orlicz Spaces
Ting Ting LI, Yalatu SU
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 295-300.   DOI: 10.12386/A2014sxxb0029
Abstract4258)      PDF(pc) (313KB)(670)       Save
In this paper, the characteristic inequalities ofLpBanach space is extended to Orlicz spaces partially. Using the method of Orlicz spaces theory, we establish some inequalities in Orlicz spaces.
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Global Stability and Bifurcation of a Ratio-Dependent Predator-Prey Model with Prey Refuge
Liu Juan CHEN, Feng De CHEN
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 301-310.   DOI: 10.12386/A2014sxxb0030
Abstract1893)      PDF(pc) (595KB)(724)       Save
A ratio-dependent predator-prey model incorporating a prey refuge is investigated and a series of sufficient conditions on global stability, limit cycle and Hopf bifurcation are obtained. The results show that when the transformation rate, mortality and the half-saturation constant of predator population satisfy certain conditions,prey refuge has no influence on the coexistence of predator and prey species. Once the condition is not satisfied, then prey refuge has stabilization effect. Numerical simulations are performed to illustrate the feasibility of our results.
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The Set of m-th Equal Partition Points of n-Simplex and Decision of the Zero Polynomial
Jia XU, Yong YAO, Jing Zhong ZHANG
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 311-320.   DOI: 10.12386/A2014sxxb0031
Abstract1532)      PDF(pc) (526KB)(626)       Save
In this paper, the set of m-th equal partition points of n-simplex is defined by recursion. A necessary and sufficient condition for deciding the zero polynomial is presented, i.e., for a polynomial f of m degree in n variables, it is the zero polynomial iff it vanishes at m-th equal partition points of an arbitrary n-simplex. As applications, this result is presented on the properly posed set of nodes for interpolation and the parallel numerical method of mechanical theorem proving.
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The Generalized 3-Connectivity of Random Graphs
Ran GU, Xue Liang LI, Yong Tang SHI
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 321-330.   DOI: 10.12386/A2014sxxb0032
Abstract1766)      PDF(pc) (518KB)(706)       Save
The generalized connectivity of a graph G was introduced by Chartrand et al. Let S be a nonempty set of vertices of G, and k(S) denote the largest number of internally disjoint trees connecting S in G. Then for an integer r with 2 ≤ rn, the generalized r-connectivity kr(G) of G is the minimum k(S) where S runs over all the r-subsets of the vertex set of G. Obviously, k2(G) = k(G), is the vertex connectivity of G, and hence the generalized connectivity is a natural generalization of the vertex connectivity. In this paper, we study the generalized 3-connectivity of random graphs and prove that for every fixed integer k ≥ 1, p = (logn + (k + 1) loglogn - logloglogn)/n is a sharp threshold function for the property k3(G(n, p)) ≥ k, which could be seen as a counterpart of Bollobás and Thomason's result for vertex connectivity.
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Automorphism Groups of Vertex Operator Algebras Associated with the Affine Nappi-Witten Algebra Ĥ4
Song WANG
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 331-338.   DOI: 10.12386/A2014sxxb0033
Abstract1876)      PDF(pc) (430KB)(628)       Save
We study the automorphism groups of vertex operator algebras associated with Ĥ4 and give a complete description.
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Nearest Neighbor Estimation for Functional Data
Wen Jie XING, Li Hong WANG
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 339-350.   DOI: 10.12386/A2014sxxb0034
Abstract1551)      PDF(pc) (575KB)(624)       Save
We consider the asymptotic properties of the nearest neighbor estimation for functional data. Under α-mixing and some regularity assumptions, we investigate the consistency and asymptotic normality of the nearest neighbor estimation for the nonparametric regression models with functional data. For the empirical data analysis, we consider three different distributions of the errors. The results show that the advantages of the nearest neighbor estimation lie in its easy computation, robustness and good performance under finite sample.
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Weighted Estimates for Commutators of n-Dimensional Hausdorff Operators
Shuang Ping TAO, Zhuan Xi REN
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 351-364.   DOI: 10.12386/A2014sxxb0035
Abstract1741)      PDF(pc) (466KB)(708)       Save
In this apper, we establish the boundedness of commutators generated by the n-dimensional Hausdorff operator and weighted Lipschitz or CO functions on some function spaces, such as weighted Lebesgue spaces and weighted Herz type spaces.
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Two Conjugate Gradient Methods with Sufficient Descent Property
Xian Zhen JIANG, Jin Bao JIAN, Guo Dong MA
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 365-372.   DOI: 10.12386/A2014sxxb0036
Abstract1708)      PDF(pc) (617KB)(745)       Save
In this paper, two improved conjugate gradient methods are proposed for unconstrained optimization. The two presented methods can generate sufficient decent directions at every iteration depending on no line search, moreover, the global convergence of the two proposed methods are proved under the standard Wolfe line search. Some elementary numerical experiments are reported, which show that the two proposed methods are promising.
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Generic Uniqueness of Solutions of Several Types of Nonlinear Problems
Ding Tao PENG, Jian YU, Nai Hua XIU
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 373-386.   DOI: 10.12386/A2014sxxb0037
Abstract1780)      PDF(pc) (418KB)(632)       Save
We first present several generic uniqueness theorems for set-valued mappings, then apply them to investigate the uniqueness of the solutions of max-min problems, vector optimization problems and fixed point problems etc. As results, we prove that, in the sense of Baire's category, most of the problems in the space consisting of max-min problems (respectively, vector optimization problems and fixed point problems) have unique solution.
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Fixed-Point Iterations and Δ-Convergence Theorem for Mappings of Asymptotically Nonexpansive Type
Zhan Fei ZUO
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 387-394.   DOI: 10.12386/A2014sxxb0038
Abstract1547)      PDF(pc) (427KB)(582)       Save
We analyze a three-step iterative scheme for mappings of asymptotically nonexpansive type in uniformly convex hyperbolic spaces. The new iterative scheme includes Ishikawa-type and Krasnoselski-Mann iteration as special cases. As an application, we obtain a Δ-convergence theorem of the three-step iterative scheme for mappings of asymptotically nonexpansive type in CAT(0) spaces. The results obtained in this paper represent an extension as well as refinement of previous known results.
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Quasi-Likelihood Estimation for OU Processes Driven by α-Stable Motions
Long Xiang FANG, Xin Sheng ZHANG
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 395-408.   DOI: 10.12386/A2014sxxb0039
Abstract1713)      PDF(pc) (640KB)(991)       Save
For OU processes driven by α-stable motions, its transition density function has no explicit form, while the conditional characteristic function is known. In this paper, we present an quasi-likelihood estimation procedure for parameters of the discretely sampled process of OU processes driven by α-stable motions. The proposed procedure is based on the conditional characteristic function, and the quasi-likelihood estimator is proved to be consistent and asymptotically efficient under some mild conditions. Finally, Monte Carlo simulations are conducted to demonstrate the accuracy and stability of proposed estimator.
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Linear Maps Preserving Commutativity up to a Factor on Nest Subalgebras of Von Neumann Algebras
Mei Yan JIAO
Acta Mathematica Sinica, Chinese Series    2014, 57 (2): 409-416.   DOI: 10.12386/A2014sxxb0040
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We characterize the linear map Φ: AlgMα → AlgMβ which statisfies the property that Φ(I) = I and AB = ζBA ⇔ Φ(A)Φ(B) = ζΦ(B)Φ(A) for A,B ∈ AlgMα and for some scalar ζ. It is proved that every surjective weakly continuous linear map preserving identity and commutativity up to a factor in both directions between two nest subalgebras with non-trivial nests of any factor von Neumann algebra is either an isomorphism or an anti-isomorphism.
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