检索结果-南通市图书馆

A theoretical analysis on efficiency of some Newton-PCG methods

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2005年第8期48卷 1046-1064页

作者： DENG Naiyang, ZHANG Jianzhong & ZHONG Ping China Agricultural university, Beijing 100083, China city university of Hong Kong, Hong Kong, China 1. China Agricultural university 100083 Beijing China 2. city university of Hong Kong Hong Kong China

In this paper, we study the efficiency issue of inexact Newton-type methods for smooth unconstrained optimization problems under standard assumptions from theoretical point of view by discussing a concrete Newton-PCG algorithm. In order to compare the algorithm with Newton's method, a ratio between the measures of their approximate efficiencies is investigated. Under mild conditions, it is shown that first, this ratio is larger than 1, which implies that the Newton-PCG algorithm is more efficient than Newton's method, and second, this ratio increases when the dimension n of the problem increases and tends to infinity at least at a rate In n/In 2 when n→∞, which implies that in theory the Newton-PCG algorithm is much more efficient for middle- and large-scale problems. These theoretical results are also supported by our preliminary numerical experiments.

关键词： unconstrained optimization, Newton's method, preconditioned conjugate gradient method, efficiency.

Aggregation and assembly of crescent foldamers

在线全文

学校读者我要写书评

暂无评论

Science China Chemistry 2010年第1期53卷 45-51页

作者： GONG Bing Department of Chemistry,university at Buffalo,The State university of New York,Buffalo,New York 14260,usa 1. Department of Chemistry University at Buffalo The State University of New York Buffalo New York 14260 USA

Recent studies have started to provide initial insights into the aggregation and assembly of two classes of back-rigidified foldamers with flat,curved backbones consisting of aromatic *** their persistent shape that presents large,well-defined aromatic surface areas,these crescent foldamers were found to undergo size-dependent aggregation in solution and pack into 1D assemblies in the solid *** aromatic oligoamides undergo stacking interactions not only in polar solvents but also in nonpolar ones,a unique property that is not associated with many other molecules that associate via π-π stacking *** stacking of oligo(m-phenylene ethynylenes) is similar to aromatic hydrocarbons,being promoted in polar solvents such as methanol while being discouraged in nonpolar solvents such as *** ready synthetic availability of crescent foldamers makes it possible to directly control the intermolecular interaction by tuning surface ***,the columnar assembly of these cavity-containing molecules provides a new strategy for constructing supramolecular nanotubular structures.

关键词： foldamer folding hydrogen bond π-π stacking aggregation assembly

ADVANCED SYNTHESIS OF LIGHT METALS

在线全文

学校读者我要写书评

暂无评论

Acta Metallurgica Sinica(English Letters) 1996年第6期9卷 531-536页

作者： F.H. Froes(IMAP, university of Idaho, Moscow, ID 838443026, usa ) Univ of Idaho Moscow United States

The synthesis, processing and mechanical properties of the light metals, aluminum,magnesium and titanium Produced by advanced techniques are reviewed. Synthesis techniques to be addressed will include rapid solidifica... 详细信息

关键词： synthesis/processing powder metallurgy lightweight metals,aluminum magnesium,titanium rapid solidification spray depositin mechanical alloying Plasma processing,vapor deposition

Discrete Calderón-type Reproducing Formula

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2000年第2期16卷 277-294页

作者： Yongsheng Han Department of Mathematics,Auburn university,Auburn,Alabama 36849-5310,usa Department of Mathematics Auburn University Auburn Alabama 36849-5310 USA

In this paper we use the Calderón-Zygmund operator theory to provide a discrete Calderón- type reproducing *** translation,dilation and,in particular,the Fourier transform are never used in the proofs,all results still hold on spaces of homogeneous type introduced by Coifman and Weiss. As a consequence,we obtain a class of frames with the minimum regularity properties.

关键词： Spaces of homogeneous type Calderón reproducing formula Frame

Boundary Layer Theory and the Zero-Viscosity Limit of the Navier-Stokes Equation

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2000年第2期16卷 207-218页

作者： Weinan E Department of Mathematics and Program in Applied and Computational Mathematics,Princeton university,usa Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton USA

A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to *** is particularly important when boundaries are present since vorticitv is typically generated at the boundary as a result of boundary layer *** boundary laver theory,developed by Prandtl about a hundred years ago,has become a standard tool in addressing these *** at the mathematical level,there is still a lack of fundamental understanding of these questions and the validity of the boundary layer *** this article,we review recent progresses on the analysis of Prandtl’s equation and the related issue of the zero-viscosity limit for the solutions of the Navier-Stokes *** also discuss some directions where progress is expected in the near future.

关键词： Boundary layer Blow-up Zero-viscosity limit Prandtl’s equation

Dispersion of ultrafine alumina in modifier solution ——the role of polar interfacial interaction

在线全文

学校读者我要写书评

暂无评论

Journal of Central South university of Technology 2001年第1期8卷 18-23页

作者： HU Yue hua 1,QIU Guan zhou 1,J.D.Miller 2 (1.Department of Mineral Engineering, Central South university, Changsha 410083, China 2.Department of Metallurgical Engineering, university of Utah, 412 WBB, Salt Lake city, UT 84112, usa) 1. Department of Mineral Engineering Central South University 410083 Changsha China 2. Department of Metallurgical Engineering University of Utah 412 WBB 84112 Salt Lake City UT USA

Dispersion of ultrafine alumina suspension is examined by using particle size analyzer. The zeta potential and contact angle measurements were used to discuss the electrokinetic behavior and surface wettability of alumina in modifier solution, and to calculate the electrostatic interaction forces and interfacial interaction forces between alumina particles. The aggregation of ultrafine alumina occurs near its PZC. Addition of modifier increases the zeta potential of alumina and its surface hydrophilicity, resulting in increase of electrostatic and hydration repulsion. It makes the suspension of ultrafine alumina completely dispersed. The average particle size of the suspension is decreased from 1.73 μm in absence of modifier to 0.8 μm in the presence of tripolyphosphate. According to polar interfacial interaction approach, the hydration forces responsible for the stability of alumina suspension in the presence of modifier have also been obtained. The extended DLVO theory is successful to describe the dispersion behavior of ultrafine alumina in modifier solution.

关键词： dispersion alumina modifier polar interfacial interaction extended DLVO theory

SYMPLECTIC SCHEMES FOR QUASILINEAR WAVE EQUATIONS OF KLEIN-GORDON AND SINE-GORDON TYPE

在线全文

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2001年第5期19卷 475-488页

作者： Xiao-wu Lu (Department of Mathematics and Computer Science, Emory university, Atlanta, GA 30322, usa) Emory university 美国 30322

Presents a class of finite difference methods of first and second order accuracy for the computation of solutions to the quasilinear wave equations. Overview of general symplectic schemes and generating functional; Nu... 详细信息

关键词： Symplectic integration Sine-Gordon equations Finite difference method.

Polynomials,Higher Order Sobolev Extension Theorems and Interpolation Inequalities on Weighted Folland-Stein Spaces on Stratified Groups

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2000年第3期16卷 405-444页

作者： Guozhen Lu Department of Mathematics,Wayne State university,Detroit,MI 482.2.usa Department of Mathematics Wayne State University Detroit USA

This paper consists of three main *** of them is to develop local and global Sobolev interpolation inequalities of any higher order for the nonisotropic Sobolev spaces on stratified nilpotent Lie *** the extensive research after Jerison’s work[3]on Poincaré-type inequalities for Hrmander’s vector fields over the years,our results given here even in the nonweighted case appear to be *** interpolation inequalities have crucial applications to subelliptic or parabolic PDE’s involving vector *** main tools to prove such inequalities are approximating the Sobolev func- tions by polynomials associated with the left invariant vector fields on *** very useful properties for polynomials associated with the functions are given here and they appear to have independent interests in their own *** the existence of such polynomials is the second main part of this *** results of these two parts have been announced in the author’s paper in Mathematical Research Letters[38]. The third main part of this paper contains extension theorems on anisotropic Sobolev spaces on stratified groups and their applications to proving Sobolev interpolation inequalities on(εδ)domains. Some results of weighted Sobolev spaces are also given *** construct a linear extension operator which is bounded on different Sobolev spaces *** particular,we are able to construct a bounded linear extension operator such that the derivatives of the extended function can be controlled by the same order of derivatives of the given Sobolev *** are stated and proved for weighted anisotropic Sobolev spaces on stratified groups.

关键词： Poincaré inequalities Extension theorems Interpolation inequalities Anisotropic Sobolev spaces A_p weights (ε,δ)domains Vector fields Polynomials on stratified groups

CONVERGENCE RATES OF MARKOV CHAIN APPROXIMATION METHODS FOR CONTROLLED DIFFUSIONS WITH STOPPING

在线全文

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2010年第3期23卷 600-621页

作者： Qingshuo SONG Gang George YIN Department of Mathematics City University of Hong Kong 83 Tat Chee Avenue Kowloon Tong Hong Kong China Department of Mathematics Wayne State University Detroit Michigan 48202 USA

This work is concerned with rates of convergence of numerical methods using Markov chainapproximation for controlled diffusions with stopping (the first exit time from a bounded region).In lieuof considering the associated finite difference schemes for Hamilton-Jacobi-Bellman (HJB) equations,a purely probabilistic approach is *** is an added difficulty due to the boundary condition,which requires the continuity of the first exit time with respect to the discrete *** prove theconvergence of the algorithm by Markov chain approximation method,a tangency problem might arise.A common approach uses certain conditions to avoid the tangency ***,by modifying thevalue function,it is demonstrated that the tangency problem will not arise in the sense of convergencein probability and in L^*** addition,controlled diffusions with a discount factor is also treated.

关键词： Controlled diffusion dynamic programming equation Markov chain approximation rate of convergence.