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A distribution space for Hilbert transform and its applications

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science china mathematics 2008年第12期51卷 2217-2230页

作者： YANG LiHua school of mathematics and Computing science, sun yat-sen university, guangzhou 510275, china school of mathematics and Computing science Sun Yat-Sen University Guangzhou 510275 China

In this paper, a new distribution space is constructed and the definition of the classical Hilbert transform is extended to it. It is shown that is the biggest subspace of on which the extended Hilbert transform is a homeomorphism and both the classical Hilbert transform for L p functions and the circular Hilbert transform for periodic functions are special cases of the extension. Some characterizations of the space are given and a class of useful nonlinear phase signals is shown to be in . Finally, the applications of the extended Hilbert transform are discussed.

关键词： Hilbert transform distribution time-frequency analysis 44A15 46F12

On the diophantine equation X^2-(1+a^2)Y^4 =-2a

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science china mathematics 2010年第8期53卷 2143-2158页

作者： YUAN PingZhi 1 & ZHANG ZhongFeng 2 1 school of mathematics,South china Normal university,guangzhou 510631,china 2 school of mathematics & computational science,sun yat-sen university,guangzhou 510275,china 1. school of mathematics South China Normal University Guangzhou 510631 China2. School of Mathematics & Computational Science Sun Yat-Sen University Guangzhou 510275 China

Let a≥1 be an *** this paper,we will prove the equation in the title has at most three positive integer solutions.

关键词： algebraic approximations continued fractions elliptic curves quartic equations

TOTAL REWARD CRITERIA FOR UNCONSTRAINED/CONSTRAINED CONTINUOUS-TIME MARKOV DECISION PROCESSES

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Journal of Systems science & Complexity 2011年第3期24卷 491-505页

作者： Xianping GUO Lanlan ZHANG school of mathematics and computational science Sun Yat-sen University Guangzhou 510275 China school of Public Health and Tropical Medicine Southern Medical University Guangzhou 510515 China

This paper studies denumerable continuous-time Markov decision processes with expected total reward criteria. The authors first study the unconstrained model with possible unbounded transition rates, and give suitable conditions on the controlled system＇s primitive data under which the authors show the existence of a solution to the total reward optimality equation and also the existence of an optimal stationary policy. Then, the authors impose a constraint on an expected total cost, and consider the associated constrained model. Basing on the results about the unconstrained model and using the Lagrange multipliers approach, the authors prove the existence of constrained-optimal policies under some additional conditions. Finally, the authors apply the results to controlled queueing systems.

关键词： Constrained-optimal policy continuous-time Markov decision process optimal policy total reward criterion unbounded reward/cost and transition rates.

Chemical weathering and chemical runoffs in the seashore granite hills in South china

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science china Earth sciences 2010年第8期53卷 1195-1204页

作者： GAO QuanZhou & TAO Zhen school of Geography and Planning, sun yat-sen university, guangzhou 510275, china 1. school of Geography and Planning Sun Yat-sen University Guangzhou 510275 China

Surface runoffs and the contents of major ions and dissolved silicon were surveyed and analyzed based on weekly sampling for one year in a granite watershed of Zhuhai City, Guangdong Province. The results demonstrated that the slope runoff played an essential role in feeding the rivulet during precipitation, whereas the groundwater was more important for the rivulet in the non-raining stages. Dissolved silicon, Na+, HCO3-, and Clions constituted the major chemical components of the rivulet water. Atmospheric CO2 and H2SO4 sourced from the oxidation of pyrite were the main erosive mediums in the natural chemical weathering. Natural chemical weathering, the wet and dry deposition of sea-salt, and acids precipitation contributed approximately equal shares of anions to the rivulet water. The ratio of NO3- to SO42- was more than 1.0 in the runoff of the studied seashore watershed, whereas it is less than 1.0 in the Xijiang River that is adjacent to the study area. This implied that the chemical composition of runoff is controlled mainly by the differences in atmospheric acid precipitation caused by human activities and lithology within the catchments under the same bio-climate zone. The CO2 flux consumed by the rock chemical weathering processes within the seashore granite watershed in South china was (0.35-1.37)×105 mol km-2 a-1.

关键词： chemical weathering granite ion sea-salt acid deposition CO2

Spontaneous chiral-symmetry breaking of lattice QCD with massless dynamical quarks

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science china(Physics,Mechanics & Astronomy) 2007年第1期50卷 6-14页

作者： LUO XiangQian Department of Physics,school of Physics and Engineering,sun yat-sen university,guangzhou 510275,china 1. Department of Physics School of Physics and Engineering Sun Yat-Sen University Guangzhou 510275 China

One of the most challenging issues in QCD is the investigation of spontaneous chiral-symmetry breaking, which is characterized by the non-vanishing chiral condensate when the bare fermion mass is zero. In standard methods of the lattice gauge theory, one has to perform expensive simulations at multiple bare quark masses, and employ some modeled functions to extrapolate the data to the chiral limit. This paper applies the probability distribution function method to computing the chiral condensate in lattice QCD with massless dynamical quarks, without any ambiguous mass extrapolation. The results for staggered quarks indicate that this might be a promising and efficient method for investigating the spontaneous chiral-symmetry breaking in lattice QCD, which deserves further investigation.

关键词： lattice QCD spontaneous chiral-symmetry breaking dynamical quarks

A provable secure fuzzy identity based signature scheme

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science china(Information sciences) 2012年第9期55卷 2139-2148页

作者： WANG ChangJi 1,2 1 school of Information science and Technology,sun yat-sen university,guangzhou 510275,china 2 Guangdong Province Information Security Key Laboratory,sun yat-sen university,guangzhou 510275,china 1. school of Information science and Technology Sun Yat-sen University Guangzhou 510275 China2. Guangdong Province Information Security Key Laboratory Sun Yat-sen University Guangzhou 510275 China

To use biometrics identities in an identity based encryption system,Sahai and Waters first introduced the notion of fuzzy identity based encryption(FIBE) in *** et *** it to digital signature and introduced the concept of fuzzy identity based signature(FIBS) in 2008,and constructed an FIBS scheme based on Sahai and Waters's FIBE *** this paper,we further formalize the notion and security model of FIBS scheme and propose a new construction of FIBS scheme based on bilinear *** proposed scheme not only provides shorter public parameters,private key and signature,but also have useful structures which result in more efficient verification than that of Yang et al.'s FIBS *** proposed FIBS scheme is proved to be existentially unforgeable under a chosen message attack and selective fuzzy identity attack in the random oracle model under the discrete logarithm assumption.

关键词： identity based cryptosystem fuzzy identity based encryption fuzzy identity based signature

Twisted Ate pairing on hyperelliptic curves and applications

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science china(Information sciences) 2010年第8期53卷 1528-1538页

作者： ZHANG FangGuo 1,2 1 school of Information science and Technology, sun yat-sen university, guangzhou 510275, china 2 Guangdong Key Laboratory of Information Security Technology, guangzhou 510275, china 1. school of Information science and Technology Sun Yat-Sen University Guangzhou 510275 China2. Guangdong Key Laboratory of Information Security Technology Guangzhou 510275 China

In this paper we show that the twisted Ate pairing on elliptic curves can be generalized to hyperelliptic curves, and give a series of variations of the hyperelliptic Ate and twisted Ate pairings. Using the hyperelliptic Ate pairing and twisted Ate pairing, we propose a new approach to speeding up the Weil pairing computation. For some hyperelliptic curves with high degree twist, computing Weil pairing by our approach may be faster than Tate pairing, Ate pairing, and all other known pairings.

关键词： Ate pairing Weil pairing hyperelliptic curves pairing-based cryptosystems twisted curves

COMPLETE HYPERSURFACES WITH CONSTANT MEAN CURVATURE AND FINITE INDEX IN HYPERBOLIC SPACES

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Acta Mathematica Scientia 2011年第1期31卷 353-360页

作者：邓勤涛 Department of mathematics Sun Yat-Sen University Laboratory of Nonlinear Analysis and School of Mathematics and StatisticsHuazhong Normal University

In this article, we prove that any complete finite index hypersurface in the hyperbolic space H4（-1）（H5（-1）） with constant mean curvature H satisfying H2 6634 （H2 114785 respectively） must be compact. Specially, we verify that any complete and stable hypersurface in the hyperbolic space H4（-1）（resp. H5（-1）） with constant mean curvature H satisfying H2 6643 （resp. H2 114785 ） must be compact. It shows that there is no manifold satisfying the conditions of some theorems in [7, 9].

关键词： k-weighted bi-Ricci curvature finite index constant mean curvature

MANIFOLDS WITH POINTWISE PINCHED RICCI CURVATURE

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Acta Mathematica Scientia 2010年第3期30卷 819-829页

作者：顾会玲 Department of mathematics Sun Yat-sen University

In this article, the author proves a compactness result about Riemannian manifolds with an arbitrary pointwisely pinched Ricci curvature tensor.

关键词： Ricci pinching condition Yamabe flow asymptotic behavior