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Evolution of three-dimensional coherent structures in compressible axisymmetric jet

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Science China(Physics,Mechanics & Astronomy) 2003年第4期46卷 348-355页

作者：刘明宇马延文傅德薰 Laboratory of Nonlinear Mechanics Institute of MechanicsChinese Academy of SciencesBeijing 100080China

A high order difference scheme is used to simulate the spatially developing compressible axisymmetric jet. The results show that the Kelvin-Helmholtz instability appears first when the jet loses its stability, and then with development of jet the increase in nonlinear effects leads to the secondary instability and the formation of the streamwise vortices. The evolution of the three-dimensional coherent structure is presented. The computed results verify that in axisymmetric jet the secondary instability and formation of the streamwise vortices are the important physical mechanism of enhancing the flow mixing and transition occurring.

关键词： jet, vortex ring, streamwise vortex

Geometry of 2×2 hermitian matrices

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Science China Mathematics 2002年第8期45卷 1025-1037页

作者：黄礼平万哲先 Institute of Mathematics Xiangtan Polytechnic University Xiangtan China Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China Center for Combinatorics Nankai University Tianjin China

LetD be a division ring which possesses an involution a → α . Assume that $F = \{ a \in D|a = \overline a \} $ is a proper subfield ofD and is contained in the center ofD. It is pointed out that ifD is of characteristic not two, D is either a separable quadratic extension of F or a division ring of generalized quaternions over F and that if D is of characteristic two,D is a separable quadratic extension ofF. Thus the trace map Tr:D → F, a → a + a is always surjective, which is formerly posed as an assumption in the fundamental theorem of n×n hermitian matrices overD when n ≥ 3 and now can be deleted. WhenD is a field, the fundamental theorem of 2 × 2 hermitian matrices overD has already been proved. This paper proves the fundamental theorem of 2×2 hermitian matrices over any division ring of generalized quaternions of characteristic not two

关键词： division ring, involution, generalized quaternion, hermitian matrix, adjacency.

Exchange rings satisfying power ideal-cancellation

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Science China Mathematics 2003年第6期46卷 804-814页

作者：陈焕艮 Department of Mathematics Zhejiang Normal University Jinhua 321004 China

In this paper, we introduce a new kind of partial power cancellations, and get a number of necessary and sufficient conditions for exchange rings satisfying power ideal-cancellation. These also extend many known results.

关键词： exchange ring, power ideal-cancellation, regularity.

The structure of a class of Z-local rings

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Science China Mathematics 2006年第10期49卷 1297-1302页

作者： WU Tongsuo & LU Dancheng Department of Mathematics , Shanghai Jiao Tong University, Shanghai 200240, China Department of Mathematics, Suzhou University, Suzhou 215006, China Department of Mathematics Shanghai Jiao Tong University Shanghai China Department of Mathematics Suzhou University Suzhou China

A local ring R is called Z-local if J(R)= Z(R) and J(R)2= 0. In this paper the structure of a class of Z-local rings is determined.

关键词： Z-local ring, structure, polynomial rings.

Complete settling of the multiplier conjecture for the case of n=3p^r

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Science China Mathematics 2002年第9期45卷 1117-1134页

作者：丘维声 School of Mathematical Science Peking University Beijing China

In this paper we improve the character approach to the multiplier conjecture that we presented after 1992, and thus we have made considerable progress in the case of n = 3n1. We prove that in the case of n = 3n1 Second multiplier theorem remains true if the assumption “n1 > λ” is replaced by “(n1, λ) = 1”. Consequentially we prove that if we let D be a (v, k, λ)-difference set in an abelian group G, and n = 3pr for some prime p, (p,v) = 1, then p is a numerical multiplier of D.

关键词： difference set, multiplier conjecture, group ring, character, inversion formula, cyclo-tomic field, CH-equations, basic equation.

Semirings which are unions of rings

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Science China Mathematics 2002年第2期45卷 172-195页

作者：郭聿琦 F.Pastijn Department of Mathematics Statistics and Computer Science Marquette University Milwaukee USA Department of Mathematics Yunnan University Kunming China

Semirings which are a disjoint union of rings form a variety S which contains the variety of all rings and the variety of all idempotent semirings, and in particular, the variety of distributive lattices. Various stru... 详细信息

关键词： semiring, ring, completely regular semigroup, lattice of varieties, band, idempotent semiring, semilattice, orthodox completely regular semigroup, bisemilattice, orthodox semiring, completely simple semigroup, Mal'cev product.