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Moment bounds for IID sequences under sublinear expectations

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Science china mathematics 2011年第10期54卷 2155-2160页

作者： HU Feng1,2 1Department of mathematics,Qufu Normal university,Qufu 273165,china 2school of mathematics,shandong university,jinan 250100,china Department of mathematics Qufu Normal University Qufu China school of mathematics Shandong University Jinan China

With the notion of independent identically distributed(IID) random variables under sublinear expectations introduced by Peng,we investigate moment bounds for IID sequences under sublinear expectations. We obtain a moment inequality for a sequence of IID random variables under sublinear expectations. As an application of this inequality,we get the following result:For any continuous functionsatisfying the growth condition |(x) | C(1 + |x|p) for some C > 0,p 1 depending on ,the central limit theorem under sublinear expectations obtained by Peng still holds.

关键词： moment bound sublinear expectation IID random variables G-normal distribution central limit theorem

MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

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Acta Mathematica Scientia 2010年第5期30卷 1819-1836页

作者：吴臻消华 school of mathematics Shandong University school of mathematics and Statistics Shandong University at Weihai

In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth.

关键词： backward stochastic differential equations comparison theorem local time

Total coloring of embedded graphs of maximum degree at least ten

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Science china mathematics 2010年第8期53卷 2127-2133页

作者： HOU JianFeng 1,2,WU JianLiang 2,LIU GuiZhen 2 & LIU Bin 2 1 Center for Discrete mathematics,Fuzhou university,Fuzhou 350002,china 2 school of mathematics,shandong university,jinan 250100,china Center for Discrete mathematics Fuzhou University Fuzhou China school of mathematics Shandong University Jinan China

A total k-coloring of a graph G is a coloring of V(G) ∪ E(G) using k colors such that no two adjacent or incident elements receive the same *** total chromatic number χ〃(G) is the smallest integer k such that G has a total *** this paper,it is proved that the total chromatic number of any graph G embedded in a surface Σ of Euler characteristic χ(Σ)≥0 is Δ(G) + 1 if Δ(G)≥10,where Δ(G) denotes the maximum degree of G.

关键词： surface Euler characteristic total coloring total chromatic number

Error analysis of the semi-discrete local discontinuous Galerkin method for semiconductor device simulation models

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Science china mathematics 2010年第12期53卷 3255-3278页

作者： LIU YunXian 1, & SHU Chi-Wang 2 1 school of mathematics, shandong university, jinan 250100, china 2 Division of Applied mathematics, Brown university, Providence, RI 02912, USA school of mathematics Shandong University Jinan China Division of Applied mathematics Brown University Providence USA

In this paper we continue our effort in Liu-Shu (2004) and Liu-Shu (2007) for developing local discontinuous Galerkin (LDG) finite element methods to discretize moment models in semiconductor device simulations. We consider drift-diffusion (DD) and high-field (HF) models of one-dimensional devices, which involve not only first derivative convection terms but also second derivative diffusion terms, as well as a coupled Poisson potential equation. Error estimates are obtained for both models with smooth solutions. The main technical difficulties in the analysis include the treatment of the inter-element jump terms which arise from the discontinuous nature of the numerical method, the nonlinearity, and the coupling of the models. A simulation is also performed to validate the analysis.

关键词： local discontinuous Galerkin method error estimate semiconductor

Note on the number of integral ideals in Galois extensions

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Science china mathematics 2010年第9期53卷 2417-2424页

作者： L GuangShi1,& WANG YongHui2 1school of mathematics,shandong university,jinan 250100,china 2Department of mathematics,Capital Normal university,Beijing 100048,china school of mathematics Shandong University Jinan China Department of mathematics Capital Normal University Beijing China

Let K be an algebraic number field of finite degree over the rational filed *** ak be the number of integral ideals in K with norm *** this paper we study the l-th integral power sum of ak,i.e.,∑k≤ x akl(l = 2,3,...).We are able to improve the classical result of Chandrasekharan and *** an application we consider the number of solutions of polynomial congruences.

关键词： Dedekind zeta-function integral ideal congruences

Function S-rough sets and security-authentication of hiding law

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Science in china(Series F) 2008年第7期51卷 924-935页

作者： SHI KaiQuan1,2 & ZHAO JianLi3 1 school of mathematics and Computer Sciences, Longyan university, Longyan 364000, china 2 school of mathematics and System Sciences, shandong university, jinan 250100, china 3 school of mathematics Science, Liaocheng university, Liaocheng 252059, china school of mathematics and Computer Sciences Longyan University Longyan China school of mathematics and System Sciences Shandong University Jinan China school of mathematics Science Liaocheng University Liaocheng China

Function S-rbugh sets are defined by R-function equivalence class, which have dynamic characteristic. Function S-rough sets have dynamic characteristic, law characteristic and law-hiding characteristic. Function S-rough sets can generate f-hiding law and f-hiding law. By engrafting, crossing, and penetrating between the information security theory and function S-rough sets, the security hiding and the authentication of f-hiding law and f-hiding law are given respectively in this paper. The fusion and share between function S-rough sets and information security theory is a new research direction of the application of information law in information system.

关键词： function S-rough sets law-hiding elliptic curve the security-authentication of hiding law

Correlation of zeros of automorphic L-functions

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Science china mathematics 2008年第7期51卷 1147-1166页

作者： LIU JianYa1 & YE YangBo1,2 1 school of mathematics,shandong university,jinan 250100, china 2Department of mathematics,The university of Iowa,Iowa City,IA 52242-1419,USA school of mathematics Shandong University Jinan China Department of mathematics The University of Iowa Iowa City USA

We compute the n-level correlation of normalized nontrivial zeros of a product of Lfunctions: L(s, π1) … L(s, π k ), where πj, j = 1, …, k, are automorphic cuspidal representations of GL mj (?A). Here the sizes of the groups GL mj (?A) are not necessarily the same. When these L(s, π j ) are distinct, we prove that their nontrivial zeros are uncorrelated, as predicted by random matrix theory and verified numerically. When L(s, π j ) are not necessarily distinct, our results will lead to a proof that the n-level correlation of normalized nontrivial zeros of the product L-function follows the superposition of Gaussian Unitary Ensemble (GUE) models of individual L-functions and products of lower rank GUEs. The results are unconditional when m 1, …, m k ? 4, but are under Hypothesis H in other cases.

关键词： automorphic L-function zero correlation Selberg’s orthogonality conjecture 11F70 11M26 11M41

Range inclusion of operators on non-archimedean Banach space

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Science china mathematics 2010年第12期53卷 3215-3224页

作者： WANG PengHui 1 & ZHANG Xu 2,3 1 school of mathematics, shandong university, jinan 250100, china 2 Key Laboratory of Systems and Control, Academy of mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, china 3 school of mathematics, Sichuan university, Chengdu 610064, china school of mathematics Shandong University Jinan China Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China school of mathematics Sichuan University Chengdu China

In this paper, we establish some range inclusion theorems for non-archimedean Banach spaces over general valued fields. These theorems provide close relationship among range inclusion, majorization and factorization for bounded linear operators. It is found that these results depend strongly on a continuous extension property, which is always true in the classical archimedean case, but may fail to hold for the non-archimedean setting. Several counterexamples are given to show that our results are sharp in some sense.

关键词： range inclusion majorization factorization non-archimedean Banach space continuous extension property

Resonance between automorphic forms and exponential functions

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Science china mathematics 2010年第9期53卷 2463-2472页

作者： REN XiuMin1,& YE YangBo1,2 1school of mathematics,shandong university,jinan 250100,china 2Department of mathematics,The university of Iowa,Iowa City,Iowa 52242-1419,USA school of mathematics Shandong University Jinan China Department of mathematics The University of Iowa Iowa City USA

Let f be a holomorphic cusp form of weight k for SL2(Z) and λf(n) its n-th Fourier *** this paper,the exponential sum X2X λf(n)e(αnβ) twisted by Fourier coefficients λf(n) is proved toh ave a main term of siz... 详细信息

关键词： automorphic form exponential sum resonance