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DENSITY OF INTEGERS THAT ARE THE SUM OF FOUR CUBES OF PRIMES

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Chinese Annals of mathematics,Series B 2001年第2期22卷 233-242页

作者： REN XIUMIN school of Economics, Shandong University, jinan 250100, china. school of Economics Shandong University Jinan 250100 China

Using the circle method and sieves, the author proves that a positive proportion of positive integers can be represented as the sum of four cubes of primes.

关键词： Waring-Goldbach problem Hardy-Littlewood method Sieve methods

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

The extension of the first main theorem for π-blocks

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Science china mathematics 2006年第5期49卷 620-625页

作者： HAI Jinke Department of mathematics, Qingdao University, Qingdao 266071, china College of mathematics ,Shandong University, {3., china Department of mathematics Qingdao University Qingdao 266071 China College of mathematics Shandong University Jian 250100 China

Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer's three main theorems to the π-blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π-blocks.

关键词： π-block, π-separable group, π-regular classes, defect group.

On higher analogues of Courant algebroids

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Science china mathematics 2011年第3期54卷 437-447页

作者： BI YanHui1 & SHENG YunHe2,3.1Department of mathematics and LMAM, Peking University, Beijing 100871, china 2school of mathematics, Jilin University, Changchun 13.012, china 3.4} of mathematics, Dalian University of Technology, Dalian 116024, china 1. Department of mathematics and LMAM Peking University Beijing 100871 China2. School of Mathematics Jilin University Changchun 130012 China3. School of Mathematics Dalian University of Technology Dalian 116024 China

In this paper, we study the algebraic properties of the higher analogues of Courant algebroid structures on the direct sum bundle TM ⊕∧nT*M for an m-dimensional manifold. As an application, we revisit Nambu-Poisson structures and multisymplectic structures. We prove that the graph of an (n + 1)-vector field π is closed under the higher-order Dorfman bracket iff π is a Nambu-Poisson structure. Consequently, there is an induced Leibniz algebroid structure on ∧nT*M. The graph of an (n+1)-form ω is closed under the higher-order Dorfman bracket iff ω is a premultisymplectic structure of order n, i.e., dω = 0. Furthermore, there is a Lie algebroid structure on the admissible bundle A  ∧nT*M. In particular, for a 2-plectic structure, it induces the Lie 2-algebra structure given in (Baez, Hoffnung and Rogers, 2010).

关键词： higher analogues of Courant algebroids multisymplectic structures Nambu-Poisson structures Leibniz algebroids

S-rough sets and knowledge separation

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Journal of Systems Engineering and Electronics 2005年第2期16卷 403-410页

作者： Shi Kaiquan 1,21. school of mathematics and System Sciences, Liaocheng University, Liaocheng 252059, P. R. china 2. school of mathematics and System Sciences, Shandong University, jinan 250100, P. R. china school of mathematics and System Sciences Liaocheng University Liaocheng 252059 P. R. China school of mathematics and System Sciences Shandong University Jinan 250100 P. R. China

The conceptions of the knowledge screen generated by S-rough sets are given: f- screen and - screen , and then puts forward - filter theorem, - filter theorem of knowledge. At last, the applications of knowledge separ... 详细信息

关键词： S- rough sets f- screen - screen f-filter theorem - filter theorem knowledge separation.

Jensen's Inequality for Backward Stochastic Differential Equations

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Chinese Annals of mathematics,Series B 2006年第5期27卷 553-564页

作者： Long JIANG Department of mathematics, china University of Mining and Technology, Xuzhou 221008, Jiangsu, china {3. of Mathematical Sciences, Fudan University, Shanghai 20043., china {3. of mathematics and System Sciences, Shandong University, jinan 250100, china. Department of mathematics China University of Mining Technology Xuzhou 221008 Jiangsu China school of Mathematical Sciences Fudan University Shanghai 200433 China school of mathematics System Sciences Shandong University Jinan 250100 China

Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen＇s inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g（t, 0）≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen＇s inequality for gexpectation in [4, 7-9].

关键词： Backward stochastic differential equation g-Expectation Jensen's inequality for g-expectation Jensen's inequality for BSDEs

Local derivation on triangular subalgebras of hyperfinite von Neumann algebras

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Chinese Science Bulletin 1998年第9期43卷 716-719页

作者： JI Peisheng Department of mathematics, Shandong University, jinan 250100, china Department of mathematics Shandong University Jinan China

It is proved that every σ-weakly continuous local derivation from triangular subalgebra A of hyperfinite von Neumann algebra B into A (or B) is a derivation. Morevoer, if A is also a σ-Dirichlet subalgebra, each loc... 详细信息

关键词： hyperfinite von Neumann algebra triangular algebra derivation local derivation inner derivation.

H∞ control of a class of nonlinear Hamiltonian descriptor systems

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Science china(Information Sciences) 2010年第11期53卷 2195-2204页

作者： SUN LiYing1,2 & WANG YuZhen1 1school of Control Science and Engineering, Shandong University, jinan 250061, china {3. of Science, University of jinan, jinan 250022, china 1. school of Control Science and Engineering Shandong University Jinan 250061 China2. School of Science University of Jinan Jinan 250022 China

This paper studies the stabilization and H∞ control of a class of nonlinear Hamiltonian descriptor systems. Firstly, based on the structural characteristic of the nonlinear Hamiltonian descriptor system, an equivalent nonlinear dissipative Hamiltonian differential-algebraic system is obtained by using restricted system equivalent theory. With the dissipative form, the stabilization problem is then discussed for the nonlinear Hamiltonian descriptor systems, and an H∞ controller is designed. Finally, simulations on a nonlinear circuit system are given.

关键词： nonlinear Hamiltonian descriptor systems stabilization H∞ control

Characteristic finite difference fractional step methods for three-dimensional semiconductor device of heat conduction

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Chinese Science Bulletin 2000年第2期45卷 125-131页

作者： YUAN Yirang Institute of mathematics. Shandong University, jinan 250100, china Institute of mathematics Shandong University Jinan China

The mathematical model of the semiconductor device of heat conduction has been described by a system of four equations. The optimal order estimates in L2 norm are derived for the error in the approximates solution, pu... 详细信息

关键词： semiconductor device three-dimensional heat conduction parallel characteristic tinite differences fractional steps L2 error estimate.