A variational iteration method for solving Troesch’s problem

Troesch’s problem is an inherently unstable two-point boundary value problem. A new and efficient algorithm based on the variational iteration method and variable transformation is proposed to solve Troesch’s problem. The underlying idea of the method is to convert the hyperbolic-type nonlinearity in the problem into polynomial-type nonlinearities by variable transformation, and the variational iteration method is then directly used to solve this transformed problem. Only the second-order iterative solution is required to provide a highly accurate analytical solution as compared with those obtained by other analytical and numerical methods.     

Spectral properties of continuous refinement operators

This paper studies the spectrum of continuous refinement operators and relates their spectral properties with the solutions of the corresponding continuous refinement equations.

     

实Banach空间中渐近半压缩映象的不动点

证明了Osilike和Aniagbosor最近的有关q 一致光滑实Banach空间中渐近半压缩映象的不动点的迭代逼近的一主要结果 (它本身也是 1 998年Osilike的一定理的一般化 )能被延拓至任意实Banach空间上 ,且所用证明方法比已有的简单 .     

啁啾脉冲多程放大及其逆问题的研究

利用非线性薛定谔方程和速率方程，研究了啁啾脉冲在增益介质中多程放大的特性. 在此基础上，利用分步傅里叶和迭代法对啁啾脉冲多程放大的逆问题做了研究和模拟，即在给定输出脉冲和多程放大系统参数的情况下，求出相应的输入脉冲波形. 有关结果对啁啾脉冲的多程放大及整形提供有用的理论参考. 关键词： 增益窄化 增益饱和 迭代法 逆问题     

Variant of an Analytical Shear Model for the Stress-Strain State of Heterogeneous Composite Beams

A nonclassical analytical model for the stress-strain state of composite beams with account of shear strains is suggested. It is assumed that the beam is piecewise heterogeneous across its height. Normal and tangential loads operate on its upper and lower surfaces and on interfaces. The model describes the distribution of tangential displacements across the thickness of plies by a third-degree polynomial. The corresponding system of differential equations is obtained by the variational method and contains two equations. The first one is an analog of the equation of classical theory of beams for deflections, and the second one is an analog of the equation of the theory for the bending moment from the generalized load. The solutions to test problems are compared with three-dimensional solutions and with experimental results for simply supported and clamped beams of different composite structure. An applied engineering problem is solved for a multispan statically indeterminate beam.     

A SPLITTING ITERATION METHOD FOR DOUBLE X_0-BREAKING BIFURCATION POINTS

1.IntroductionConsiderthefollowingtwo-parameterdependentnonlinearproblemwhereX=Re,^,parerealpaxameters,fEC"(r23),D.fo(=D.f(xo,^o,Po))isanedholmmapwithindexzero.Oneofourmainassumptions,whichariseinmanyapplications[1'2,5--7],isthatfsatisfiesZZ--symmetry:the…     

Banach空间中一般的强增生算子方程解的迭代逼近

设1相似文献   

Universal partial indestructibility and strong compactness

For any ordinal δ, let λ_δ be the least inaccessible cardinal above δ. We force and construct a model in which the least supercompact cardinal κ is indestructible under κ‐directed closed forcing and in which every measurable cardinal δ < κ is < λ_δ strongly compact and has its < λ_δ strong compactness indestructible under δ‐directed closed forcing of rank less than λ_δ. In this model, κ is also the least strongly compact cardinal. We also establish versions of this result in which κ is the least strongly compact cardinal but is not supercompact. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

CONVERGENCE BALL OF ITERATIONS WITH ONE PARAMETER

§1Introduction OfthevariousiterationmethodsusedtosolvetheequationF(x)=0,thefamilyof iterativemethodswithoneparameter xn+1=xn-I+12PF(I-αPF)-1F′(xn)-1F(xn),PF(x)=F′(x)-1F″(x)F′(x)-1F(x),α∈[0,1],(1)isremarkablebecauseitincludesthesuper-Halleymethod,theChebyshevmethodand Halley'smethodasitsspecialcaseswhenαisequalto1,0and1/2,respectively.Thereareanumberofpapersconcerningtheabovethreeiterations.In[1-7],Halley's methodisstudied.Amongthesereferences,[1]givestheconvergenceofHalley'sme…     

On the Existence of Fixed Points for Approximate Value Iteration and Temporal-Difference Learning

Approximate value iteration is a simple algorithm that combats the curse of dimensionality in dynamic programs by approximating iterates of the classical value iteration algorithm in a spirit reminiscent of statistical regression. Each iteration of this algorithm can be viewed as an application of a modified dynamic programming operator to the current iterate. The hope is that the iterates converge to a fixed point of this operator, which will then serve as a useful approximation of the optimal value function. In this paper, we show that, in general, the modified dynamic programming operator need not possess a fixed point; therefore, approximate value iteration should not be expected to converge. We then propose a variant of approximate value iteration for which the associated operator is guaranteed to possess at least one fixed point. This variant is motivated by studies of temporal-difference (TD) learning, and existence of fixed points implies here existence of stationary points for the ordinary differential equation approximated by a version of TD that incorporates exploration.