中国科学院数学与系统科学研究院期刊网

10 September 2010, Volume 26 Issue 9
    

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  • Pierre BERNARD, Liang Zhen LEI
    Acta Mathematica Sinica. 2010, 26(9): 1613-1626. https://doi.org/10.1007/s10114-010-8105-8
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    The random decrement technique (RDT), introduced in the sixties by Cole [NASA CR-2005, 1973], is a very performing method of analysis for vibration signature of a structure under ambientloading. But the real nature of the random decrement signature has been misunderstood until now.Moreover, the various interpretations were made in continuous time setting, while real experimentaldata are obtained in discrete time. In this paper, the really implemental discrete time algorithms arestudied. The asymptotic analysis as the number of triggering points go to infinity is achieved, anda Law of Large Numbers as well as a Central Limit Theorem is proved. Moreover, the limit as thediscretization time step goes to zero is computed, giving more tractable formulas to approximate therandom decrement. This is a new approach of the famous “Kac–Slepian paradox” [Ann. Math. Stat.,30, 1215–1228 (1959)]. The main point might be that the RDT is a very efficient functional estimator ofthe correlation function of a stationary ergodic Gaussian process. Very fast, it is to classical estimatorswhat Fast Fourier Transform (FFT) is to ordinary Discrete Fourier Transforms.
  • Ferenc WEISZ
    Acta Mathematica Sinica. 2010, 26(9): 1627-1640. https://doi.org/10.1007/s10114-010-9529-x
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    A general summability method, the so-called θ-summability is considered for multi-dimensionalFourier transforms. Under some conditions on θ, it is proved that the maximal operator ofthe θ-means defined in a cone is bounded from the amalgam Hardy space W(hp, ?) to W(Lp, ?). This implies the almost everywhere convergence of the θ-means in a cone for all fW(L1, ?) ? L1.
  • Bruce D.CALVERT
    Acta Mathematica Sinica. 2010, 26(9): 1641-1652. https://doi.org/10.1007/s10114-010-7285-6
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    We consider a three-point boundary value problem for operators such as the one-dimensionalp-Laplacian, and show when they have solutions or not, and how many. The inverse operatorsare given by various formulas involving zeros of a real-valued function. They are shown to be orderpreserving,for some parameter values, and non-singleton valued for others. The operators are shownto be m-dissipative in the space of continuous functions.
  • Yan XU, Yan Pei LIU
    Acta Mathematica Sinica. 2010, 26(9): 1653-1666. https://doi.org/10.1007/s10114-010-9270-5
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    In this article, the authors discuss two kinds of new planar maps: pan-fan maps and circuitboundary maps, and provide explicit expressions about their enumerating functions with differentparameters. Meanwhile, two explicit counting formulas for circuit cubic boundary maps with twoparameters: the size and the valency of the root-face, are also extracted.
  • Li Xin CHENG, Zheng Hua LUO, Xue Fang LIU, Wen ZHANG
    Acta Mathematica Sinica. 2010, 26(9): 1667-1672. https://doi.org/10.1007/s10114-010-9036-0
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    This paper presents two counterexamples about ball-coverings of Banach spaces and showsa new characterization of uniformly non-square Banach spaces via ball-coverings.
  • Alexandre ALMEIDA, António M.CAETANO
    Acta Mathematica Sinica. 2010, 26(9): 1673-1692. https://doi.org/10.1007/s10114-010-8647-9
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    Hardy spaces with generalized parameter are introduced following the maximal characterizationapproach. As particular cases, they include the classical Hp spaces and the Hardy–Lorentzspaces Hp,q. Real interpolation results with function parameter are obtained. Based on them, thebehavior of some classical operators is studied in this generalized setting.
  • Fang ZHOU, He Guo LIU
    Acta Mathematica Sinica. 2010, 26(9): 1693-1700. https://doi.org/10.1007/s10114-010-8283-4
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    Let G and N be arbitrary groups. In this paper, we construct an associated group extensionεχ of N/Z(N) by G for any group homomorphism χ : G → OutN, and prove that χ can be lifted to a group action, that is, a group homomorphism from G to AutN, if and only if the extension εχ splits. Furthermore we obtain an explicit description for all such lifting homomorphisms and the number of its conjugacy classes, and give an application of the lifting technique of outer actions to the theory of group extensions.
  • Xin Yue CHENG
    Acta Mathematica Sinica. 2010, 26(9): 1701-1708. https://doi.org/10.1007/s10114-010-8472-1
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    In this paper, we study (α,β)-metrics of scalar flag curvature on a manifoldM of dimensionn (n ≥ 3). Suppose that an (α,β)-metric F is not a Finsler metric of Randers type, that is, Fk1α2 + k2β2 + k3β, where k1 > 0, k2 and k3 are scalar functions on M. We prove that F is of scalar flag curvature and of vanishing S-curvature if and only if the flag curvature K = 0 and F is a Berwaldmetric. In this case, F is a locally Minkowski metric.
  • Pu ZHANG
    Acta Mathematica Sinica. 2010, 26(9): 1709-1722. https://doi.org/10.1007/s10114-010-8562-0
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    Let μmΩ,b be the commutator generalized by μΩ, the n-dimensional Marcinkiewicz integral, and b ∈ BMO(Rn). The author establishes the weighted weak Llog L-type estimates for μmΩ,b when Ω satisfies a kind of Dini conditions, which improves the known result essentially.
  • Bai Shun LAI, Shu Qing ZHOU
    Acta Mathematica Sinica. 2010, 26(9): 1723-1738. https://doi.org/10.1007/s10114-010-8325-y
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    In this paper, we will analyze further to obtain a finer asymptotic behavior of positivesolutions of semilinear elliptic equations in Rn by employing the Li’s method of energy function.
  • Jun Gang LI, Shou Mei LI, Yukio OGURA
    Acta Mathematica Sinica. 2010, 26(9): 1739-1748. https://doi.org/10.1007/s10114-010-8298-x
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    In this paper, we shall firstly illustrate why we should introduce an It? type set-valuedstochastic differential equation and why we should notice the almost everywhere problem. Secondlywe shall give a clear definition of Aumann type Lebesgue integral and prove the measurability of theLebesgue integral of set-valued stochastic processes with respect to time t. Then we shall present somenew properties, especially prove an important inequality of set-valued Lebesgue integrals. Finally weshall prove the existence and the uniqueness of a strong solution to the It? type set-valued stochasticdifferential equation.
  • Tong Ling LV, Jun Yi, GUO Xin ZHANG
    Acta Mathematica Sinica. 2010, 26(9): 1749-1760. https://doi.org/10.1007/s10114-010-8091-x
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    In this paper we consider a risk model with two kinds of claims, whose claims numberprocesses are Poisson process and ordinary renewal process respectively. For this model, the surplusprocess is not Markovian, however, it can be Markovianized by introducing a supplementary process.We prove the Markov property of the related vector processes. Because such obtained processes belongto the class of the so-called piecewise-deterministic Markov process, the extended infinitesimal generatoris derived, exponential martingale for the risk process is studied. The exponential bound of ruinprobability in infinite time horizon is obtained.
  • M.Reza PEYGHAMI, Keyvan AMINI
    Acta Mathematica Sinica. 2010, 26(9): 1761-1778. https://doi.org/10.1007/s10114-010-7529-5
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    In this paper, motivated by the complexity results of Interior Point Methods (IPMs) forLinear Optimization (LO) based on kernel functions, we present a polynomial time IPM for solvingP*(κ)-linear complementarity problem, using a new class of kernel functions. The special case of ournew class was considered earlier for LO by Y. Q. Bai et al. in 2004. Using some appealing propertiesof the new class, we show that the iteration bound for IPMs matches the so far best known theoreticaliteration bound for both large and small updates by choosing special values for the parameters of thenew class.
  • Qin Long WANG, Yi Rong LIU
    Acta Mathematica Sinica. 2010, 26(9): 1779-1792. https://doi.org/10.1007/s10114-010-7535-7
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    In this paper, the definition of generalized isochronous center is given in order to studyunitedly real isochronous center and linearizability of polynomial differential systems. An algorithmto compute generalized period constants is obtained, which is a good method to find the necessaryconditions of generalized isochronous center for any rational resonance ratio. Its two linear recursiveformulas are symbolic and easy to realize with computer algebraic system. The function of time-angledifference is introduced to prove the sufficient conditions. As the application, a class of real cubicKolmogorov system is investigated and the generalized isochronous center conditions of the origin areobtained.
  • Zhong TAN, Ying Hui ZHANG
    Acta Mathematica Sinica. 2010, 26(9): 1793-1806. https://doi.org/10.1007/s10114-010-7584-y
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    We present a method for solving the optimal shape problems for profiles surrounded byviscous compressible fluids in two space dimensions. The class of admissible profiles is quite generalincluding the minimal volume condition and a constraint on the thickness of the boundary. The fluidflow is modelled by the Navier–Stokes system for a general viscous barotropic fluid with the pressuresatisfying p(e) = aelogd(e) for largee. Here d > 1 and a > 0.
  • Lun Chuan ZHANG, Mao Zheng GUO
    Acta Mathematica Sinica. 2010, 26(9): 1807-1814. https://doi.org/10.1007/s10114-010-7651-4
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    In this paper we will obtain a Stone type theorem under the frame of Hilbert C*-module,such that the classical Stone theorem is our special case. Then we use it as a main tool to obtain aspectrum decomposition theorem of certain stationary quantum stochastic process. In the end, we willgive it an interpretation in statistical mechanics of multi-linear response.
  • Xin Mei SHEN, Zheng Yan LIN
    Acta Mathematica Sinica. 2010, 26(9): 1815-1826. https://doi.org/10.1007/s10114-010-7574-0
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    In this paper, we obtain the uniform estimate for discounted aggregate claims in thecontinuous-time renewal model of upper-tailed independent and heavy-tailed random variables. Withconstant interest force and constant premium rate, we establish a uniform simple asymptotic formulafor ruin probability of the renewal model in the case where the initial surplus is large.