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On the weak convergence of super-Brownian motion with immigration

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Science china mathematics 2009年第9期52卷 1875-1886页

作者： ZHANG Mei school of Mathematical sciences, Beijing normal university, Beijing 100875, china school of Mathematical sciences Beijing Normal University Beijing 100875 China

We prove fluctuation limit theorems for the occupation times of super-Brownian motion with immigration. The weak convergence of the processes is established, which improves the results in references. The limiting proc... 详细信息

关键词： super-Brownian motion with immigration occupation time process central limit theorem tightness 60J80 60F05

Leakproof secret sharing protocols with applications to group identification scheme

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Science china(information sciences) 2012年第5期55卷 1172-1185页

作者： TANG ChunMing 1,2 & GAO ShuHong 3 1 school of mathematics and information Science,Guangzhou university,Guangzhou 510006,china 2 State Key Laboratory of information Security,Institute of Software Science,Chinese Academy of sciences,Beijing 100049,china 3 Department of Mathematical sciences,Clemson university,SC 29634,USA 1. school of mathematics and information Science Guangzhou University Guangzhou 510006 China2. State Key Laboratory of Information Security Institute of Software Science Chinese Academy of Sciences Beijing 100049 China3. Department of Mathematical Sciences Clemson University Clemson SC 29634 USA

In a traditional (t,n)-threshold secret sharing scheme,t or more honest participants can reconstruct the secret *** the reconstruction process,the individual shares and the secret key K are revealed,hence K is shared once *** this paper,we firstly give the definition of leakproof secret sharing scheme which is composed of a distribution protocol and a proof protocol,then propose two leakproof secret sharing protocols,a computationally secure protocol and an information-theoretically secure *** our protocols,t or more participants can jointly prove that they hold the secret K by using a multi-prover zero-knowledge argument of *** a result,the secret K will be shared for as many times as ***,each participant can detect the dealer in the distribution protocol from cheating,and any verifier can prevent non-qualified set of participants in proof protocol from *** an example of the practical impact of our work we use our techniques to construct group identification schemes with zero-knowledge.

关键词： secret sharing leakproof secret sharing multi-prover zero-knowledge argument proof of knowl-edge group identification scheme

Infinitely many radial solutions to elliptic prob-lems with critical Sobolev and Hardy terms

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Science china mathematics 2008年第9期51卷 1609-1618页

作者： TANG ZhongWei school of Mathematical sciences, Beijing normal university, Beijing 100875, china 1. school of Mathematical sciences Beijing Normal University Beijing 100875 China

Let Ω ? ? N be a ball centered at the origin with radius R > 0 and N ? 7, 2* = $ \frac{{2N}} {{N - 2}} $ . We obtain the existence of infinitely many radial solutions for the Dirichlet problem ?Δu = $ \frac{\mu } {{|x|^2 }}u + |u|^{2^* - 2} u + \lambda u $ in Ω, u = 0 on ?Ω for suitable positive numbers μ and λ. Such solutions are characterized by the number of their nodes.

关键词： nodal solutions compactness critical Sobolev and Hardy terms 35J60 35B33

Some scaled limit theorems for an immigration super-Brownian motion

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Science china mathematics 2008年第2期51卷 203-214页

作者： ZHANG Mei school of Mathematical sciences,Beijing normal university,Beijing 100875,china 1. school of Mathematical sciences Beijing Normal University Beijing 100875 China

In this paper,the small time limit behaviors for an immigration super-Brownian motion are studied,where the immigration is determined by Lebesgue *** first prove a functional central limit theorem,and then study the l... 详细信息

关键词： super-Brownian motion with immigration functional central limit theorem large deviation moderate deviation 60J80 60F05

A specific family of cyclotomic polynomials of order three

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Science china mathematics 2010年第9期53卷 2269-2274页

作者： JI ChunGang school of Mathematical sciences,Nanjing normal university,Nanjing 210097,china 1. school of Mathematical sciences Nanjing Normal University Nanjing 210097 China

Let A(n) be the largest absolute value of any coefficient of n-th cyclotomic polynomial Φn(x).We say Φn(x) is flat if A(n) = *** this paper,for odd primes p < q < r and 2r ≡±1(mod pq),we prove that Φpqr(x) is fla... 详细信息

Let A(n) be the largest absolute value of any coefficient of n-th cyclotomic polynomial Φn(x).We say Φn(x) is flat if A(n) = *** this paper,for odd primes p 3 and q ≡ 1(mod 3).

关键词： cyclotomic polynomial flat cyclotomic polynomial ternary cyclotomic polynomial

On the error term in Weyl’s law for the Heisenberg manifolds (Ⅱ)

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Science china mathematics 2009年第5期52卷 857-874页

作者： ZHAI WenGuang school of Mathematical sciences, Shandong normal university, Jinan 250014, china 1. school of Mathematical sciences Shandong Normal University Jinan 250014 China

In this paper we study the mean square of the error term in the Weyl's law of an irrational (2l + 1)-dimensional Heisenberg manifold. An asymptotic formula is established.

关键词： Heisenberg manifold Weyl’s law error term mean square

Commutators of pseudo-differential operators

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Science china mathematics 2008年第3期51卷 453-460页

作者： LIN Yan school of Mathematical sciences, Beijing normal university, Beijing 100875, china 1. school of Mathematical sciences Beijing Normal University Beijing 100875 China

In this paper, the boundedness of commutators generated by pseudo-differential operators and BMO functions is discussed on Lebesgue spaces.

关键词： pseudo-differential operator BMO function commutator Lebesgue space 42B20 35S05 47G30

Hausdorff measures of the image, graph and level set of bifractional Brownian motion

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Science china mathematics 2010年第11期53卷 2973-2992页

作者： LUAN NaNa school of Mathematical sciences, Beijing normal university, Beijing 100875, china 1. school of Mathematical sciences Beijing Normal University Beijing 100875 China

Let BH,K = {BH,K(t), t ∈ R+} be a bifractional Brownian motion in Rd. This process is a selfsimilar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brownian motion (which is obtained for K = 1). The exact Hausdorff measures of the image, graph and the level set of BH,K are investigated. The results extend the corresponding results proved by Talagrand and Xiao for fractional Brownian motion.

关键词： bifractional Brownian motion self-similar Gaussian processes image graph level set local time Hausdorff dimension Hausdorff measure

Multipliers and Herz type spaces

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Science china mathematics 2008年第10期51卷 1919-1936页

作者： LU ShanZhen school of Mathematical sciences, Beijing normal university, Beijing 100875, china school of Mathematical sciences Beijing Normal University Beijing 100875 China

Hrmander condition for boundedness of multiplier operators will be replaced by a weaker condition described by certain weighted or non-weighted Herz spaces. Some results on boundedness of multiplier operators are then established. As direct corollaries of main theorems in this paper, several celebrated results on boundedness of multiplier operators will be improved or deduced.

关键词： multiplier Herz space Herz type Hardy space 42B15 42B30 42B35