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A NEW STEPSIZE FOR THE STEEPEST DESCENT METHOD

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Journal of Computational Mathematics 2006年第2期24卷 149-156页

作者： ya-xiang Yuan LSEC ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China

The steepest descent method is the simplest gradient method for optimization. It is well known that exact line searches along each steepest descent direction may converge very slowly. An important result was given by Barzilar and Borwein, which is proved to be superlinearly convergent for convex quadratic in two dimensional space, and performs quite well for high dimensional problems. The BB method is not monotone, thus it is not easy to be generalized for general nonlinear functions unless certain non-monotone techniques being applied. Therefore, it is very desirable to find stepsize formulae which enable fast convergence and possess the monotone property. Such a stepsize αk for the steepest descent method is suggested in this paper. An algorithm with this new stepsize in even iterations and exact line search in odd iterations is proposed. Numerical results are presented, which confirm that the new method can find the exact solution within 3 iteration for two dimensional problems. The new method is very efficient for small scale problems. A modified version of the new method is also presented, where the new technique for selecting the stepsize is used after every two exact line searches. The modified algorithm is comparable to the Barzilar-Borwein method for large scale problems and better for small scale problems.

关键词： Steepest descent Line search Unconstrained optimization Convergence.

New Weierstrass Semi-rational Expansion Method to Doubly Periodic Solutions of Soliton Equations

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Communications in Theoretical Physics 2005年第3期43卷 391-396页

作者： yaNZhen-ya KeyLaboratoryofMathematicsMechanization InstituteofSystemsScienceAMSStheChineseAcademyofSciencesBeijing100080China

Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem solving soliton equations into another one solving the corresponding set of nonlinear algebraic equations. With the aid of Maple, we choose the modified KdV equation, (2+ 1)-dimensional KP equation, and (3+1)-dimensional Jimbo-Miwa equation to illustrate our algorithm. As a consequence, many types of new doubly periodic solutions are obtained in terms of the Weierstrass elliptic *** the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented as simple limits of doubly periodic solutions.

关键词： soliton equations Weierstrass elliptic function doubly periodic solution symbolic computation

generalized-Type Synchronization of Hyperchaotic Oscillators Using a Vector Signal

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Communications in Theoretical Physics 2005年第1X期44卷 72-78页

作者： yaNZhen-ya KeyLaboratoryofMathematicsMechanization InstituteofSystemsScienceAMSStheChineseAcademyofSciencesBeijing100080China

In this paper, a systematic and powerful scheme is proposed to address a generalized-type synchronization of a class of continuous-time systems, which includes generalized lag synchronization, generalized anticipated synchronization, and generalized synchronization. The presented scheme is used to investigate the generalized-type synchronization of the 4D hyperchaotic oscillator and the hyperchaotic oscillator with gyrators. Numerical simulations are used to verify the effectiveness of the proposed scheme. The scheme is more powerful than the scalar signal scheme due to grassi and Mascolo.

关键词：混沌系统广义同步性 4D混沌振荡器振荡回旋器数字仿真

Microstructure evolution and precipitation behavior of Al-Mg-Si alloy during initial aging

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China Foundry 2023年第1期20卷 57-62页

作者： ya-ya Zheng Bing-hui Luo Wei Xie Wang Li Department of Materials Engineering Hunan University of HumanitiesScience and TechnologyLoudi 417000HunanChina College of Materials Science and Engineering Central South UniversityChangsha 410083China Key Laboratory of Safety Design and Reliability Technology for Engineering Vehicle Changsha University of Science&TechnologyChangsha 410114China

The microstructure evolution and precipitation behavior of Al-Mg-Si alloy during initial aging were studied using hardness testing, conductivity testing, differential scanning calorimetry(DSC), and high resolution transmission electron microscopy(HRTEM). The results show that the precipitation sequence of the Al-Mg-Si alloy during initial aging can be represented as: supersaturated solid solution → spherical Mg/Si clusters → needle-like guinier Preston(gP) zone → β″. Clusters are completely coherent with the Al matrix. The gP zone with relatively complete independent lattice parameters that differ slightly from the Al matrix parameters, is oriented along the direction of Aland lying on {111}Alplane. The strength of the Al-Mg-Si alloy is greatly enhanced by the threedimensional strain field that exists between the β″ phase and the two {200}Alplanes. After aging at 170 ℃ for 6 h, the hardness reaches the peak of 127 HV and remains for a long time. At this stage, the electrical conductivity keeps relatively stable due to the formation of coherent precipitates(Mg/Si clusters/gP zones) and the reduction in solute atom concentration in the Al matrix. The severe coarsening and decreased number density of the β″ phase during the over-aging stage result in a significant decrease in the hardness.

关键词： Al-Mg-Si alloy precipitation behavior strengthening mechanism strain field β″

Energy Estimates on Existence of Extremals for Trudinger–Moser Inequalities

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Acta Mathematica Sinica,English Series 2020年第7期36卷 829-841页

作者： ya Min WANg School of Mathematics Renmin University of ChinaBeijing 100872P.R.China

LetΩbe a smooth bounded domain in R2,W01,2(Ω)be the standard Sobolev *** the method of energy estimate developed by Malchiodi–Martinazzi(***.,16,893–908(2014)),Mancini–Martinazzi(*** Differential Equations,56,94(2017))and Mancini–Thizy(*** Equations,266,1051–1072(2019)),we reprove the results of Carleson–Chang(***.,110,113–127(1986)),Flucher(***.,67,471–497(1992)),Li(Acta ***.,22,545–550(2006))and Su(***.,in press).Namely,for any real numberα≤1,the supremum■can be achieved by some function v∈W01,2(Ω)with║?v║22≤4π.

关键词： space. Existence 1,2

Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第10期8卷 1691-1694页

作者： WANg ya-qin Mathematics and Sciences College Shanghai Normal University Shanghai 200234 China

Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.

关键词： Viscosity approximation methods Weakly contractive mapping Fixed point Weakly sequentially continuous duality mapping

Weak and strong convergence of an explicit iteration scheme with perturbed mapping for nonexpansive mappings

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第12期8卷 2032-2036页

作者： WANg ya-qin Mathematics and Sciences College Shanghai Normal University Shanghai 200234 China

In this paper, we consider an explicit iteration scheme with perturbed mapping for nonexpansive mappings in real q-uniformly smooth Banach spaces. Some weak and strong convergence theorems for this explicit iteration scheme are established. In particular, necessary and sufficient conditions for strong convergence of this explicit iteration scheme are obtained. At last, some useful corollaries for strong convergence of this explicit iteration scheme are given.

关键词： Nonexpansive mapping Iteration scheme with perturbed mapping Opial condition Completely continuous

Synthesis and Crystal Structure of a Ternary Complex:[Ni(phen)_2(pmal)]·8H_2O

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Chinese Journal of Structural Chemistry 2006年第10期25卷 1265-1269页

作者： SNN ya-guang Laboratory of Coordination Chemistry Shenyang Institute of Chemical TechnologyShenyang 110142 China

A new ternary complex [Ni（phen）（pmal）]·8H2O （phen = 1,10-phenanthroline, pmal^2- = phenethyl malonic acid） has been synthesized by the reaction of nickel acetate, phen and phenethyl malonic acid. Elemental analysis, IR spectra and X-ray single-crystal diffraction were carried out to determine the composition and crystal structure. Crystal data for this complex： triclinic system, space group PI^-, a = 10.387（5）, b = 13.112（6）, c = 14.229（6） °A, α= 76.176（7）, β = 83.778（8）, γ = 71.770（6）°, C35H42N4O12Ni, Mr= 769.44, Z = 2, F（000） = 808, V = 1786.1°A^3, Dc = 1.431 g/cm^3,μ= 0.612 mm^-1, the final R = 0.0653 and wR = 0.1033 for 9379 （Rint = 0.0244） independent reflections and 4730 observed reflections （I〉 2σ（I））. Structural analysis shows that the coordination geometry of Ni（Ⅱ） is a distorted octahedron. A novel two-dimensional structure is constructed from （H2O）4 and （H2O）12 water clusters, and the complex forms a 3-D network supramolecular structure by hydrogen bonds and π-π stacking of neighboring phens.

关键词： Ni(Ⅱ) phenethyl malonic acid crystal structure water cluster

ground State Density Distribution of Bose-Fermi Mixture in a One-Dimensional Harmonic Trap

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Chinese Physics Letters 2011年第1期28卷 16-19页

作者： HAO ya- Jiang Department of Physics University of Science and Technology Beijing Beijing 100083

By the density-functional calculation we investigate the ground-state properties of Bose-Fermi mixture confined in one-dimensional harmonic traps. The homogeneous mixture of bosons and polarized fermions with contact interaction can be exactly solved by the Bethe-ansatz method. After giving the exact formula of ground state en- ergy density, we employ the local-density approximation to determine the density distribution of each component. It is shown that with the increase in interaction, the total density distribution evolves to Fermi-like distribution and the system exhibits phase separation between finite. While in the infinite interaction limit both distributions and phase separation disappears. two components when the interaction is strong enough but bosons and fermions display the completely same Fermi-like

关键词： Quantum gases liquids and solids Mathematical physics Statistical physics and nonlinear systems