中国科学院数学与系统科学研究院期刊网

15 February 2008, Volume 24 Issue 2
    

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  • Huo Xiong WU, Shan Zhi YANG
    Acta Mathematica Sinica. 2008, 24(2): 177-184. https://doi.org/10.1007/s10114-007-1005-x
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    This paper is devoted to the study of a class of singular integral operators defined by polynomial mappings on product domains. Some rather weak size conditions, which imply the Lp boundedness of these singular integral operators as well as the corresponding maximal truncated singular integral operators for some fixed 1 < p < ∞, are given.
  • María BURGOS, El Amin KAIDI, Antonio Morales CAMPOY, Antonio M. PERALTA, Maribel RAMÍREZ
    Acta Mathematica Sinica. 2008, 24(2): 185-200. https://doi.org/10.1007/s10114-007-0985-x
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    We revise the notion of von Neumann regularity in JB*-triples by finding a new characterisation in terms of the range of the quadratic operator Q(a). We introduce the quadratic conorm of an element a in a JB*-triple as the minimum reduced modulus of the mapping Q(a). It is shown that the quadratic conorm of a coincides with the infimum of the squares of the points in the triple spectrum of a. It is established that a contractive bijection between JBW*-triples is a triple isomorphism if, and only if, it preserves quadratic conorms. The continuity of the quadratic conorm and the generalized inverse are discussed. Some applications to C*-algebras and von Neumann algebras are also studied.
  • Zhi Yuan HUAN, Pei Yan LI, Ying WU
    Acta Mathematica Sinica. 2008, 24(2): 201-214. https://doi.org/10.1007/s10114-007-1019-4
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    The classical Lévy-Meixner polynomials are distinguished through the special forms of their generating functions. In fact, they are completely determined by 4 parameters: c1, c2, γ and β. In this paper, for -1 < q < 1, we obtain a unified explicit form of q-deformed Lévy-Meixner polynomials and their generating functions in term of c1, c2, γ and β, which is shown to be a reasonable interpolation between classical case (q = 1) and fermionic case (q = -1). In particular, when q = 0 it's also compatible with the free case.
  • Tian Ping ZHANG, Wen Peng ZHANG
    Acta Mathematica Sinica. 2008, 24(2): 215-222. https://doi.org/10.1007/s10114-007-0942-8
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    The main purpose of this paper is to use the properties of the Gauss sums, primitive characters and the mean value of Dirichlet L-functions to study the hybrid mean value of the error term E(n, 1, c, q) and the hyper-Kloosterman sums K(h, n+1, q), the asymptotic property of the mean square value Σc=1pE2(n, 1, c, p), and give two interesting mean value formulae.
  • De Liang HSU, Jia Yu LI
    Acta Mathematica Sinica. 2008, 24(2): 223-226. https://doi.org/10.1007/s10114-007-1007-8
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    We prove a compactness theorem for k-indexed stationary harmonic maps, and show a regularity theorem for this kind of maps which says that the singular set of a k-indexed stationary harmonic map is of Hausdorff dimension at most m-3.
  • Dong LIU, Lei LIN
    Acta Mathematica Sinica. 2008, 24(2): 227-240. https://doi.org/10.1007/s10114-007-1003-z
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    Toroidal Leibniz algebras are the universal central extensions of the iterated loop algebras ġ⊕C[t1±1 ,...,tv±1 ] in the category of Leibniz algebras. In this paper, some properties and representations of toroidal Leibniz algebras are studied. Some general theories of central extensions of Leibniz algebras are also obtained.
  • Siu Ah NG
    Acta Mathematica Sinica. 2008, 24(2): 241-252. https://doi.org/10.1007/s10114-007-1024-7
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    We use methods from nonstandard analysis to obtain a short and simple derivation of the Lévy-Khintchine formula via an explicit construction of certain laws of the infinitesimal increments. Consequently, any arbitrary Lévy process is representable as the standard part of a hyperfinite sum of infinitesimal increments.
  • Bao Quan YUAN
    Acta Mathematica Sinica. 2008, 24(2): 253-266. https://doi.org/10.1007/s10114-007-0973-1
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    The author studies the Cauchy problem of the dissipative quasi-geostrophic equation in weak Morrey spaces. The global well-posedness is established for any small initial data in the weak space Mp,λ*(Rn), with 1 < p < ∞ and λ = n-(2α-1)p, and for a small external force in a time-weighted weak Morrey space.
  • Jaume LLIBRE, Alexandrina–Alina TARŢA
    Acta Mathematica Sinica. 2008, 24(2): 267-274. https://doi.org/10.1007/s10114-007-0983-z
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    We provide sufficient conditions for the existence of periodic orbits of some systems of delay differential equations with a unique delay. We extend Kaplan-Yorke's method for finding periodic orbits from a delay differential equation with several delays to a system of delay differential equations with a unique delay.
  • Yan Xia REN
    Acta Mathematica Sinica. 2008, 24(2): 275-284. https://doi.org/10.1007/s10114-007-1001-1
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    The global supports of super-Poisson processes and super-random walks with a branching mechanism Ψ(z) = z2 and constant branching rate are known to be noncompact. It turns out that, for any spatially dependent branching rate, this property remains true. However, the asymptotic extinction property for these two kinds of superprocesses depends on the decay rate of the branching-rate function at infinity.
  • Yu LI
    Acta Mathematica Sinica. 2008, 24(2): 285-304. https://doi.org/10.1007/s10114-007-1022-9
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    Let G be a Lie group whose Lie algebra g is quadratic. In the paper "the non-commutative Weil algebra", Alekseev and Meinrenken constructed an explicit G-differential space homomorphism L , called the quantization map, between the Weil algebra Wg = S(g*)⊕∧(g*) and Wg=U(g)⊕Cl(g) (which they call the noncommutative Weil algebra) for g . They showed that L induces an algebra isomorphism between the basic cohomology rings Hbas * (Wg) and Hbas * (Wg). In this paper, we will interpret the quantization map L as the super Duflo map between the symmetric algebra and the universal enveloping algebra U of a super Lie algebra  which is canonically associated with the quadratic Lie algebra g . The basic cohomology rings Hbas* (Wg) and Hbas* (Wg) correspond exactly to S and U inv, respectively. So what they proved is equivalent to the fact that the super Duflo map commutes with the adjoint action of the super Lie algebra, and that the super Duflo map is an algebra homomorphism when restricted to the space of invariants.
  • Bin Yong SUN
    Acta Mathematica Sinica. 2008, 24(2): 305-310. https://doi.org/10.1007/s10114-007-1016-7
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    The torsion conjecture says: for any abelian variety A defined over a number field k, the order of the torsion subgroup of A(k) is bounded by a constant C(k, d) which depends only on the number field k and the dimension d of the abelian variety. The torsion conjecture remains open in general. However, in this paper, a short argument shows that the conjecture is true for more general fields if we consider linear groups instead of abelian varieties. If G is a connected linear algebraic group defined over a field k which is finitely generated over Q, Γ is a torsion subgroup of G(k). Then the order of Γ is bounded by a constant C'(k, d) which depends only on k and the dimension d of G.
  • Ming FANG
    Acta Mathematica Sinica. 2008, 24(2): 311-318. https://doi.org/10.1007/s10114-007-0984-y
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    Let A be a QF-3 standardly stratified algebra and f be a Schur functor corresponding to some projective-injective faithful A-module, denoted by Ae. The main result of this paper is to prove that, if the dominant dimension of A is sufficiently large, then f induces a full embedding from F(Δ) to eAe-mod which preserves Ext-groups up to certain degrees, where F(Δ) denotes the full subcategory of A-mod whose objects are filtered by standard A-modules. We check this criterion on some typical examples, quantized Schur algebras Sq(n, r) with nr and finite-dimensional algebras associated with the Bernstein-Gelfand-Gelfand category O of semisimple complex Lie algebras.
  • Ding Jun YAO, Rong Ming WANG
    Acta Mathematica Sinica. 2008, 24(2): 319-328. https://doi.org/10.1007/s10114-007-1004-y
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    The authors consider two discrete-time insurance risk models. Two moving average risk models are introduced to model the surplus process, and the probabilities of ruin are examined in models with a constant interest force. Exponential bounds for ruin probabilities of an infinite time horizon are derived by the martingale method.
  • Wen Chi KUO, Coenraad C. A. LABUSCHAGNE, Bruce A. WATSON
    Acta Mathematica Sinica. 2008, 24(2): 329-342. https://doi.org/10.1007/s10114-007-1025-6
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    The concepts of conditional expectations, martingales and stopping times were extended to the Riesz space context by Kuo, Labuschagne and Watson (Discrete time stochastic processes on Riesz spaces, Indag. Math., 15 (2004), 435–451). Here we extend the definition of an asymptotic martingale (amart) to the Riesz spaces context, and prove that Riesz space amarts can be decomposed into the sum of a martingale and an adapted sequence convergent to zero. Consequently an amart convergence theorem is deduced.
  • Guo Dong LIU, Wen Peng ZHANG
    Acta Mathematica Sinica. 2008, 24(2): 343-352. https://doi.org/10.1007/s10114-007-1013-x
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    The authors establish an explicit formula for the generalized Euler Numbers E2n(x) , and obtain some identities and congruences involving the higher-order Euler numbers, Stirling numbers, the central factorial numbers and the values of the Riemann zeta-function.