15 February 2013, Volume 29 Issue 2

    

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  Geometric Schrödinger-Airy Flows on Kähler Manifolds

  Xiao Wei SUN, You De WANG

  Acta Mathematica Sinica. 2013, 29(2): 209-240. https://doi.org/10.1007/s10114-013-2122-3

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  We define a class of geometric flows on a complete Kähler manifold to unify some physical and mechanical models such as the motion equations of vortex filament,complex-valued mKdV equations,derivative nonlinear Schrödinger equations etc.Furthermore,we consider the existence for these flows from S¹ into a complete Kähler manifold and prove some local and global existence results.
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  On Ad-Nilpotent b-Ideals for Orthogonal Lie Algebras

  Li Li LIU, Li LUO

  Acta Mathematica Sinica. 2013, 29(2): 241-262. https://doi.org/10.1007/s10114-012-1599-5

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  Krattenthaler,Orsina and Papi provided explicit formulas for the number of ad-nilpotent ideals with fixed class of nilpotence of a Borel subalgebra of a classical Lie algebra.Especially for types A and C they obtained refined results about these ideals with not only fixed class of nilpotence but also fixed dimension.In this paper,we shall follow their algorithm to determine the enumeration of ad-nilpotent b-ideals with fixed class of nilpotence and dimension for orthogonal Lie algebras,i.e., types B and D.
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  Various Expressions for Modulus of Random Convexity

  Xiao Lin ZENG

  Acta Mathematica Sinica. 2013, 29(2): 263-280. https://doi.org/10.1007/s10114-012-1398-z

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  We first prove various kinds of expressions for modulus of random convexity by using an L⁰(F,R)-valued function's intermediate value theorem and the well known Hahn–Banach theorem for almost surely bounded random linear functionals,then establish some basic properties including continuity for modulus of random convexity.In particular,we express the modulus of random convexity of a special random normed module L⁰(F,XX)derived from a normed space X by the classical modulus of convexity of X.
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  Unicyclic Graphs of Minimal Spectral Radius

  Ling Sheng SHI

  Acta Mathematica Sinica. 2013, 29(2): 281-286. https://doi.org/10.1007/s10114-013-1634-1

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  It was conjectured by Li and Feng in 1979 that the unicyclic graph formed by a cycle of order g linking to an endvertex of a path of length k minimizes the spectral radius of all unicyclic graphs of order g+k and girth g.In 1987,Cao proved that this conjecture is true for k≥g(g-2)/8 and false for k=2 and suffciently large g.In this note,we show that g>12 suffces for the counterexample and give more counterexamples with large girth for any integer k>1.
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  Stochastic Equations for Two-type Continuous-state Branching Processes with Immigration

  Ru Gang MA

  Acta Mathematica Sinica. 2013, 29(2): 287-294. https://doi.org/10.1007/s10114-012-1378-3

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  A two-dimensional stochastic integral equation system with jumps is studied.We first prove its unique weak solution is a two-type continuous-state branching process with immigration.Then the comparison property of the solution is established.These results imply the existence and uniqueness of the strong solution of the stochastic equation system.
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  The Rate of Approximation of Gaussian Radial Basis Neural Networks in Continuous Function Space

  Ting Fan XIE, Fei Long

  Acta Mathematica Sinica. 2013, 29(2): 295-302. https://doi.org/10.1007/s10114-012-1369-4

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  There have been many studies on the dense theorem of approximation by radial basis feedforword neural networks,and some approximation problems by Gaussian radial basis feedforward neural networks(GRBFNs)in some special function space have also been investigated.This paper considers the approximation by the GRBFNs in continuous function space.It is proved that the rate of approximation by GRNFNs with n^d neurons to any continuous function f defined on a compact subset K⊂R^d can be controlled by ω(f,n^-1/2),where ω(f,t)is the modulus of continuity of the function f.
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  Fokker-Planck Type Equations with Sobolev Di?usion Coeffcients and BV Drift Coeffcients

  De Jun LUO

  Acta Mathematica Sinica. 2013, 29(2): 303-314. https://doi.org/10.1007/s10114-012-1302-x

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  Combining Le Bris and Lions' arguments with Ambrosio's commutator estimate for BV vector fields,we prove in this paper the existence and uniqueness of solutions to the Fokker–Planck type equations with Sobolev diffusion coeffcients and BV drift coeffcients.
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  Lower and Upper Fuzzy Topological Subhypergroups

  Irina CRISTEA

  Acta Mathematica Sinica. 2013, 29(2): 315-330. https://doi.org/10.1007/s10114-012-1170-4

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  This paper provides a new connection between algebraic hyperstructures and fuzzy sets. More specifically,using both properties of fuzzy topological spaces and those of fuzzy subhypergroups, we define the notions of lower(upper)fuzzy topological subhypergroups of a hypergroup endowed with a fuzzy topology.Some results concerning the image and the inverse image of a lower(upper)topological subhypergroup under a very good homomorphism of hypergroups(endowed with fuzzy topologies)are pointed out.
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  On First Returning Time and Last Exit Time of a Class of Markov Chain

  Hui Zeng ZHANG, Min Zhi ZHAO, Lei WANG

  Acta Mathematica Sinica. 2013, 29(2): 331-334. https://doi.org/10.1007/s10114-012-1019-x

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  Let {X_n} be a Markov chain with transition probability p_ij=a_j-(i-1)+,∀#em/em#,j≥0,where a_j=0 provided j<0,a₀>0,a₀+a₁<1 and ∑_n=0^∞ a_n=1.Let μ=∑_n=1^∞ na_n.It is known that {X_n}is positive recurrent when μ<1;is null recurrent when μ=1;and is transient when μ>1.In this paper,the integrability of the first returning time and the last exit time are discussed.
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  Ruzsa’s Constant on Additive Functions

  Jin Hui FANG, Yong Gao CHEN

  Acta Mathematica Sinica. 2013, 29(2): 345-354. https://doi.org/10.1007/s10114-012-0702-2

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  A function f:N→R is called additive if f(mn)=f(m)+f(n) for all m,n with (m,n)=1. Let μ(x)=max_n≤x(f(n)-f(n+1)) and ν(x)=max_n≤x(f(n+1)-f(n)).In 1979,Ruzsa proved that there exists a constant c such that for any additive function f,μ(x)≤cν(x²)+c_f,where c_f is a constant depending only on f.Denote by R_af the least such constant c.We call R_af Ruzsa's constant on additive functions.In this paper,we prove that R_af≤20.
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  Asymptotic Behavior of Product of Two Heavy-tailed Dependent Random Variables

  Vahid RANJBAR, Mohammad AMINI, Jaap GELUK, Abolghasem BOZORGNIA

  Acta Mathematica Sinica. 2013, 29(2): 355-364. https://doi.org/10.1007/s10114-012-0680-4

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  Let X and Y be positive weakly negatively dependent(WND)random variables with finite expectations and continuous distribution functions F and G with heavy tails,respectively.The asymptotic behavior of the tail of distribution of XY is studied and some closure properties under some suitable conditions on F(x)=1-F(x) and G(x)=1-G(x) are provided.Moreover,subexponentiality of XY when X and Y are WND random variables is derived.
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  On the Growth of Solutions of Second Order Linear Di?erential Equations with Extremal Coeffcients

  Jian Ren LONG, Peng Cheng WU, Zheng ZHANG

  Acta Mathematica Sinica. 2013, 29(2): 365-372. https://doi.org/10.1007/s10114-012-0648-4

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  In this paper,we consider the differential equation f''+A(z)f'+B(z)f=0,where A and B≠0 are entire functions.Assume that A is extremal for Yang's inequality,then we will give some conditions on B which can guarantee that every non-trivial solution f of the equation is of infinite order.
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  Generalized Einstein Tensor for a Weyl Manifold and Its Applications

  Abdülkadir ÖZDEĞER

  Acta Mathematica Sinica. 2013, 29(2): 373-382. https://doi.org/10.1007/s10114-012-0582-5

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  It is well known that the Einstein tensor G for a Riemannian manifold defined by G_α^β=R_α^β-1/2(Rδ_α^β,R_α^β=g^βγ R_γα where R_γα and R are respectively the Ricci tensor and the scalar curvature of the manifold,plays an important part in Einstein's theory of gravitation as well as in proving some theorems in Riemannian geometry.In this work,we first obtain the generalized Einstein tensor for a Weyl manifold.Then,after studying some properties of generalized Einstein tensor,we prove that the conformal invariance of the generalized Einstein tensor implies the conformal invariance of the curvature tensor of the Weyl manifold and conversely.Moreover,we show that such Weyl manifolds admit a one-parameter family of hypersurfaces the orthogonal trajectories of which are geodesics.Finally,a necessary and su?cient condition in order that the generalized circles of a Weyl manifold be preserved by a conformal mapping is stated in terms of generalized Einstein tensors at corresponding points.
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  Additive Lie (ξ-Lie) Derivations and Generalized Lie (ξ-Lie) Derivations on Prime Algebras

  Xiao Fei QI, Jin Chuan HOU

  Acta Mathematica Sinica. 2013, 29(2): 383-392. https://doi.org/10.1007/s10114-012-0502-8

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  The additive (generalized) ξ-Lie derivations on prime algebras are characterized.It is shown,under some suitable assumptions,that an additive map L is an additive generalized Lie derivation if and only if it is the sum of an additive generalized derivation and an additive map from the algebra into its center vanishing all commutators;is an additive (generalized) ξ-Lie derivation with ξ≠1 if and only if it is an additive (generalized) derivation satisfying L(ξA)=ξL(A<)for all A.These results are then used to characterize additive (generalized) ξ-Lie derivations on several operator algebras such as Banach space standard operator algebras and von Neumman algebras.
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  Compressible Subsonic Potential Flow Past a 2D Given Sharp Angular Unbounded Domain

  Hui YANG

  Acta Mathematica Sinica. 2013, 29(2): 393-404. https://doi.org/10.1007/s10114-012-0414-7

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  In this paper,we focus on the two-dimensional subsonic flow problem around an infinite long ramp.The flow is assumed to be steady,isentropic and irrotational,namely,the movement of the flow is described by a second elliptic equation.By the use of a separation variable method,Strum–Liouville theorem and scaling technique,we show that a nontrivial subsonic flow around the infinite long ramp does not exist under some certain assumptions on the potential flow with a low Mach number.
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  Dividend-Reinsurance Strategy in the Sparre Andersen Model

  Ji Yang TAN, Lin XIAO, Shao Yue LIU, Xiang Qun YANG

  Acta Mathematica Sinica. 2013, 29(2): 405-416. https://doi.org/10.1007/s10114-012-0353-3

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  In this paper,we introduce a reinsurance strategy into the Sparre Andersen risk model with a horizon dividend barrier,which is named dividend-reinsurance strategy.It is shown that the value function of the new strategy far exceeds that of the optimal barrier strategy(even that of the optimal dividend strategy).Some results on the advantages of the new strategy are obtained,and the methods for computing the value functions are provided.Numerical illustrations for Erlang(2)and compound Poisson risk models are also given.