中国科学院数学与系统科学研究院期刊网

15 February 2014, Volume 57 Issue 2
    

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  • Ping Zhi YUAN, Zhong Feng ZHANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 209-222. https://doi.org/10.12386/A2014sxxb0022
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    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).
  • Hong Yong WANG, Shou Zhi YANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 223-234. https://doi.org/10.12386/A2014sxxb0023
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    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.
  • Articles
  • Jian Ren ZHOU, Hong Bo WU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 235-248. https://doi.org/10.12386/A2014sxxb0024
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    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.
  • Xian Min XU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 249-260. https://doi.org/10.12386/A2014sxxb0025
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    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).
  • Guo Qing ZHANG, Jing SUN
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 261-271. https://doi.org/10.12386/A2014sxxb0026
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    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.
  • Wei Ping LI, Bai Yun SU, Tian Ze WANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 273-280. https://doi.org/10.12386/A2014sxxb0027
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    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.
  • Articles
  • Yan Fang PENG, Bi Wen LI
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 281-294. https://doi.org/10.12386/A2014sxxb0028
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    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.
  • Ting Ting LI, Yalatu SU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 295-300. https://doi.org/10.12386/A2014sxxb0029
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    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.
  • Liu Juan CHEN, Feng De CHEN
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 301-310. https://doi.org/10.12386/A2014sxxb0030
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    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.
  • Jia XU, Yong YAO, Jing Zhong ZHANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 311-320. https://doi.org/10.12386/A2014sxxb0031
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    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.
  • Articles
  • Ran GU, Xue Liang LI, Yong Tang SHI
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 321-330. https://doi.org/10.12386/A2014sxxb0032
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    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.
  • Song WANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 331-338. https://doi.org/10.12386/A2014sxxb0033
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    We study the automorphism groups of vertex operator algebras associated with Ĥ4 and give a complete description.
  • Wen Jie XING, Li Hong WANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 339-350. https://doi.org/10.12386/A2014sxxb0034
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    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.
  • Articles
  • Shuang Ping TAO, Zhuan Xi REN
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 351-364. https://doi.org/10.12386/A2014sxxb0035
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    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.
  • Xian Zhen JIANG, Jin Bao JIAN, Guo Dong MA
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 365-372. https://doi.org/10.12386/A2014sxxb0036
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    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.
  • Ding Tao PENG, Jian YU, Nai Hua XIU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 373-386. https://doi.org/10.12386/A2014sxxb0037
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    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.
  • Zhan Fei ZUO
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 387-394. https://doi.org/10.12386/A2014sxxb0038
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    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.
  • Long Xiang FANG, Xin Sheng ZHANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 395-408. https://doi.org/10.12386/A2014sxxb0039
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    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.
  • Mei Yan JIAO
    Acta Mathematica Sinica, Chinese Series. 2014, 57(2): 409-416. https://doi.org/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.