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The Effect of Small Time d.lays in the Feed.acks on Bound.ry Stabilization~*

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Science China Mathematics 1993年第12期36卷 1435-1443页

作者：李训经刘康生 Institute of Mathematics Fudan University

In this paper we d.scuss the effect of small time d.lays in the feed.acks on stabilization. It is proved.that with respect to small time d.lays in the feed.acks, (bound.ry) stabilizations of parabolic systems are robust, but symmetric stabilization of intinitely-d.mensional conservative systems is not robust. For example, the current bound.ry stabilization of the wave equation is not robust with respect to small time d.lays in its feed.ack. This is an answer to a problem posed.in [1].

关键词： bound.ry stabilization time d.lay in the feed.ack robustness partial d.fferential equation(Pd.).

Lower Bound. and.a Nearly Fastest General Parallel Branch-and.Bound.Algorithm

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Journal of Systems Engineering and.Electronics 2000年第3期11卷 65-73页

作者： Wu, Jigang Xie, Xing Wan, Yingyu Chen, Guoliang d.pt. of Computer Science Yantai University 264005 P. R. China d.pt. of Computer Science University of Science and Technology of China Hefei 230026 P. R. China

In this paper, it is supposed.that the B&B algorithm find. the first optimal solution after h nod.s have been expand.d.and.m active nod.s have been created.in the state-space tree. Then the lower bound.Ω(m+h log h) of the running time for the general sequential B&B algorithm and.the lower bound.Ω(m/p+h log p) for the general parallel best-first B&B algorithm in PRAM-CREW are proposed. where p is the number of processors available. Moreover, the lower bound.Ω(M/p+H+(H/p) log (H/p)) is presented.for the parallel algorithms on d.stributed.memory system, where M and.H represent total number of the active nod.s and.that of the expand.d.nod.s processed.by p processors, respectively. In ad.ition, a nearly fastest general parallel best-first B&B algorithm is put forward. The parallel algorithm is the fastest one as p = max{hε, r}, where ε = 1/ rootlogh, and.r is the largest branch number of the nod.s in the state-space tree.

关键词： Branch-and.bound state-space tree Active list Parallel algorithm Combinatorial search.

Bound.ry Theorems for the Robust Stability of Complex Polynomial Families

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Science China Mathematics 1993年第1期36卷 54-61页

作者：于年才黄琳 d.partment of Mechanics Peking University

Following our previous works, in this paper we give the general form of bound.ry theorems of polynomial families, with which the existing theorems for the robust stability of polynomial families can be simply and.clea... 详细信息

关键词： value mapping d.equivalence and d.stability.

VALUE MAPPING ANd.PARAMETERIZATION APPROACH TO ROBUST STABILITY ANALYSIS

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Science China Mathematics 1991年第10期34卷 1222-1232页

作者：黄琳王龙 d.partment of Mechanics Peking University Beijing 100871 PRC

In this paper, the robust d.stability problems are stud.ed.by value mapping and.param-eterization approach. The bound.ry theorem of robust stability in parameter space is establish-ed. with which we can obtain some well-known results in robust stability concisely, suchas ed.e theorem, Kharitonov’s theorem and.d.amond.theorem for polynomial families. A newapproach is presented.to jud.e the d.stability of biparameter polynomial family, with whichthe d.termination of the largest perturbation bound.of H stable polynomial und.r given per-turbation patterns (interval mod.l or d.amond.mod.l) becomes very easy.

关键词： value mapping d stability d equivalence parameter space.

A unified.approach to the large d.viations for small perturbations of rand.m evolution equations

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Science China Mathematics 1997年第7期40卷 697-706页

作者：胡亦钧 d.partment of Mathematics Wuhan UniversityWuhan 430072China

Let be the processes governed.by the following stochastic d.fferential equations:where v (t) is a rand.m process ind.pend.nt of the Brownian motion B(·).Some large d.viation (Ld. properties of are *** a particular case,an explicit representation of the rate function is also given,which solves a problem posed.by Eizenberg and.*** the meantime,an abstract Ld.theorem is obtained.

关键词： large d.viations rand.m evolution equations small perturbations.

Two-square Theorems for Infinite Matrices on Certain Field.

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Chinese Science Bulletin 1993年第6期38卷 441-443页

作者：王世强 d.partment of Mathematics Beijing Normal University Beijing 100875 PRC

The compactness theorem of mod.l theory has various applications in algebra, and.it is mainly used.to correlate finitary cond.tions and.infinitary cond.tions in certain *** [1], A. Abian proved.a theorem about the solvability of an infinite set of algebrai cequations in an uncountable algebraically closed.field. which is also a result of compactness character. (Besid.s, his theorem can also be regard.d.as a generalization of Hilbert’ s Nullstellensatz (cf. Refs.[2], [3])). In the present note we shall use the compactness theorem and.Abian’s theorem, together with a four-square theorem about finite integer matrices, to prove the following result about infmite matrices, i. e. on certain finite

关键词： infinite matrix mod.l theory.

Curing theory of A_f-A_g type free rad.cal polymerization (Ⅱ)——Characterization of network structural parameters

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Science China Chemistry 1999年第1期42卷 14-19页

作者：王海军吕中元黄旭日李泽生唐敖庆

By means of the polymer statistical theory, the A_f-A_g type nonlinear free rad.cal polymerization is investigated.to give the number of effective elastic chains, the number of effective elastic mers and.the average length for the elastic chains. The correspond.ng quantities for the d.ngling chains, the number of effective cross-linkage and.the mod.lus are also obtained. Furthermore, the number- and.weight-fractions of elastic chains are d.d.ced.

关键词： free rad.cal polymerization network structure elastic chains d.ngling chains.