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A SUPERLINEARLY CONVERGENT TRUST REGION ALGORITHM FOR LC^1 CONSTRAINED OPTIMIZATION PROBLEMS

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Acta Mathematica Scientia 2005年第1期25卷 67-80页

作者：欧宜贵侯定丕 department of Applied mathematics Hainan university Haikou 570228 China department of mathematics university of Science and {3. of china Hefei 230026 China

In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view.

关键词： LC1 optimization ODE methods trust region methods superlinear convergence

Robustness and breakup of the spiral wave in a two-dimensional lattice network of neurons

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Science china(Physics,Mechanics & Astronomy) 2010年第4期53卷 672-679页

作者： MA Jun 1,2, TANG Jun 2 , ZHANG AiHua 3.& JIA Ya 2 1 department of Physics, Lanzhou university of technology, Lanzhou 73.050, {3. 2 department of Physics, Central {3. Normal university, Wuhan 43.079, {3. 3.College of Electrical and Information Engineering, Lanzhou university of technology, Lanzhou 73.050, {3. department of Physics Lanzhou University of Technology Lanzhou China department of Physics Central China Normal University Wuhan China College of Electrical and Information Engineering Lanzhou University of Technology Lanzhou China

The robustness and breakup of spiral wave in a two-dimensional lattice networks of neurons are investigated. The effect of small- world type connection is often simplified with local regular connection and the long-range connection with certain probability. The network effect on the development of spiral wave can be better described by local regular connection and changeable long-range connection probability than fixed long-range connection probability because the long-range probability could be changeable in realistic biological system. The effect from the changeable probability for long-range connection is simplified by multiplicative noise. At first, a stable rotating spiral wave is developed by using appropriate initial values, parameters and no-flux boundary conditions, and then the effect of networks is investigated. Extensive numerical studies show that spiral wave keeps its alive and robust when the intensity of multiplicative noise is below a certain threshold, otherwise, the breakup of spiral wave occurs. A statistical factor of synchronization in two-dimensional array is defined to study the phase transition of spiral wave by checking the membrane potentials of all neurons corresponding to the critical parameters(the intensity of noise or forcing current)in the curve for factor of synchronization. The Hindmarsh-Rose model is investigated, the Hodgkin-Huxley neuron model in the presence of the channel noise is also studied to check the model independence of our conclusions. And it is found that breakup of spiral wave is easier to be induced by the multiplicative noise in presence of channel noise.

关键词： spiral wave factor of synchronization breakup multiplicative noise robustness

Comprehensive evaluation of mechanism of "chimney effect" using principles of magnetism, geochemistry and mineralogy

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Chinese Science Bulletin 1998年第9期43卷 743-748页

作者： LIU Qingsheng 1, CHENG Tongjin 2 and LIU Shugen 3.1. department of Applied Geophysics, china university of Geosciences, Wuhan 43.074, china 2. Center of Petroleum Geochemistry, china National Star Petroleum Corporation, hefei 23.022, china 3. The St department of Applied Geophysics China University of Geosciences Wuhan China Center of Petroleum Geochemistry China National Star Petroleum Corporation Hefei China The State Key Laboratory of Oil/Gas Reservoir Geology and Exploitation of china Chengdu Institute of Technology Chengdu China

Study of forming mechanism of "chimney-effect" (CE) has important significance for basic theory and applications of non-seismic geophysical and geochemical methods locating oil/gas reservoirs. The theoretical basis of comprehensive evaluation of mechanism of CE using principles of magnetism, geochemistry and mineralogy has been reviewed, with the problems to be solved: (ⅰ) study for the relationship between process of oil/gas migration and geochemical field; (ⅱ) analysis of genesis of magnetic, geochemical and mineralogical anomaly; (ⅲ) interpretation of surface soil magnetism and geochemical anomaly combined with seismic data.

关键词： chimney effect (CE) hydrocarbon microseepage oil/gas accumulation.

Gerbes and twisted orbifold quantum cohomology

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Science china mathematics 2008年第6期51卷 995-1016页

作者： PAN JianZhong~1 RUAN YongBin~(2,3. YIN XiaoQin~(1,3.) 1 Institute of mathematics,Academy of mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,china 2 {3. of mathematics,university of Wisconsin-Madison,WI 53.06,USA 3.department of mathematics,The Hong Kong university of Science and technology,Hong Kong,china Institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China department of mathematics University of Wisconsin-Madison Madison USA department of mathematics The Hong Kong University of Science and Technology Hong Kong China

In this paper,we construct an orbifold quantum cohomology twisted by a flat gerbe. Then we compute these invariants in the case of a smooth manifold and a discrete torsion on a global quotient orbifold.

关键词： gerbe orbifold quantum cohomology 53.45

SYNTHESIS AND CHARACTERIZATION OF FOUR-ARMED BLOCK POLY(STYRENE-b-p-NITROPHENYL METHACRYLATE)PREPARED BY THE ATRP METHOD

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Chinese Journal of Polymer Science 2002年第4期20卷 353-360页

作者： Cai-yuan Pan Lei Tao Ye Liu department of Polymer Science and Engineering university of Science and technology of {3., hefei 23.026 {3. department of Polymer Science and Engineering University of Science and Technology of China Hefei 230026

A novel tetrafunctional initiator, C [CH_2O (CH_2)_3.OOCCH(Br)CH_3._4 (1), was synthesized through the reaction oftetraol with α-bromopropionyl chloride, and then was used as initiator of atom transfer radical polymerization (ATRP) in thepreparation of 4-armed polystyrene (PSt) with narrow polydispersity. The structure, molecular weight and molecular weightdistribution (MWD) of each arm were studied by ~1H-NMR and GPC data of hydrolyzed products of the 4-armed PSt. TheATRP of St using 1/CuBr/bpy as initiator system is of 'living' character based on the following evidence: narrow MWD,constant concentration of chain radical during the polymerization, control of molecular weight by the molar ratio of monomerconsumed to 1. The 4-armed poly(St-b-p-nitrophenyl methacrylate) [poly(St-b-NPMA)] was prepared by the ATRP ofNPMA using 4-armed PSt with terminal bromine as the initiator, and characterized by FT-IR, ~1H-NMR spectra and GPCcurves. The micelles with PSt as core, and PNPMA as shell were formed by dropping DMSO into a solution of 4-armedpoly(St-b-NPMA) in DMF, as proved by laser light scatter (LLS) method.

关键词： Tetrafunctional initiator Atom transfer radical polymerization 4-Armed polystyrene 4-Armed poly(styrene-b-pnitrophenyl methacrylate) Unimolecular micelles

Sharp Estimates in Bergman and Besov Spaces on Bounded Symmetric Domains

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Acta Mathematica Sinica,English Series 2002年第3期18卷 499-504页

作者： Guang Bin REN Ji Huai SHI department of mathematics. university of Science and {3. of china. hefei 23.026. P. R. china department of mathematics University of Science and Technology of China Hefei P. R. China

Sharp estimates of the point-evaluation functional in weighted Bergman spaces L_~p(Ω, dv_) and for the point-evaluation derivalive functional in Besov spaces B^p(Ω) are obtained for bounded symmetric domains Ω in C^n.

关键词： Bergman spaces Besov spaces Bounded svmmetric domains

Generic modules for tilted algebras

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Chinese Science Bulletin 1997年第3期42卷 177-180页

作者： DU Xiannengdepartment of mathematics, Anhui university, {3. 23.03., china department of mathematics Anhui University Hefei China

IN the theory of infinite abelian groups, the concepts of torsion-free groups and divisible groups are well known. We know that there exists, up to isomorphism, one and only one abelian group which is both torsion-free and divisible at the same time. This is the additive group Q of the rational numbers. Q plays an important role in the study of infinite-abelian groups. The theory of infinite-dirnensional modules over a finite-dimensional algebra runs similarly to the theory of infinite abelian groups but there are also some substantial differences.

关键词： tilting modules tilted algebras tame hereditary algebras generic modules.

EXISTENCE OF FAST-DECM GROUNDSTATE OF P-LAPLACIAN EQUATION

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Acta Mathematica Scientia 1999年第4期19卷 382-390页

作者：宣本金陈祖墀 department of mathematics University of Science and Technology of China Hefei 230026 China

Using the shooting argument and an approximating method, this paper isconcerncd with the existence of fast-decay ground state of p-Laplacian equation: Apu＋f(u)=0, in Rn, where f(u) behaves just like f(u) = uq - us, a... 详细信息

关键词： fast-decay ground state p-Laplacian equation shooting method

ON F-z-SUPPLEMENTED SUBGROUPS OF FINITE GROUPS

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Acta Mathematica Scientia 2011年第1期31卷 22-28页

作者：郭文彬唐娜李保军 department of mathematics University of Science and Technology of China department of mathematics Xuzhou Normal University department of mathematics Huaiyin Teachers College School of mathematics Chengdu University of Information Technology

A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F（G）, where Z∞F（G） is the F-hypercenter of G. We obtain some results about the F-z-suppl... 详细信息

关键词： Finite groups local formations F-z-supplemented subgroups supersoluble groups p-nilpotent groups