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WEAK ORLICZ SPACE AND ITS convergence theoremS

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Acta Mathematica Scientia 2010年第5期30卷 1492-1500页

作者：刘宁叶永刚 School of Economics and Managements Wuhan University Finance School Hubei University of Economics

In this article, a class of weak Orlicz function spaces is defined and their basic properties are discused. In particular, for the sequences in weak Orlicz space, we establish several basic convergence theorems including bounded convergence theorem, control convergence theorem and Vitali-type convergence theorem and so on. Moreover, the conditional compactness of its subsets is also discussed.

关键词： weak Orlicz space convergence theorem conditional compactness

Optimal design study of high order FIR digital filters based on neural network algorithm

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Journal of Systems Engineering and Electronics 2004年第2期15卷 115-119,130页

作者： Wang Xiaohua & He YigangCollege of Electrical and Information Engineering, Hunan University, Changsha 410082, P. R. China College of Electrical and Information Engineering, Changsha University of Science and Technology,Changsha 410077, P. R. China College of Electrical and Information Engineering Hunan University Changsha 410082 P. R. China College of Electrical and Information Engineering Changsha University of Science and Technology Changsha 410077 P. R. China

An optimal design approach of high order FIR digital filter is developed based on the algorithm of neural networks with cosine basis function . The main idea is to minimize the sum of the square errors between the amplitude response of the desired FIR filter and that of the designed by training the weights of neural networks, then obtains the impulse response of FIR digital filter . The convergence theorem of the neural networks algorithm is presented and proved, and the optimal design method is introduced by designing four kinds of FIR digital filters , i.e., low-pass, high-pass, bandpass , and band-stop FIR digital filter. The results of the amplitude responses show that attenuation in stop-bands is more than 60 dB with no ripple and pulse existing in pass-bands, and cutoff frequency of passband and stop-band is easily controlled precisely .The presented optimal design approach of high order FIR digital filter is significantly effective.

关键词： high order FIR digital filters amplitude-frequency response neural network convergence theorem optimal design.

Design of twodimensional digital filters using neural networks

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Journal of Systems Engineering and Electronics 2005年第4期16卷 767-771页

作者： Wang Xiaohua He Yigang Electrical and Information Engineering Coll. Changsha Univ. of Science & Technology Changsha 410077 P. R. China Electrical and Information Engineering Coll. Hunan Univ. Changsha 410082 P. R. China

A new approach for the design of two-dimensional （2-D） linear phase FIR digital filters based on a new neural networks algorithm （NNA） is provided. A compact expression for the transfer function of a 2-D linear phase FIR filter is derived based on its frequency response characteristic, and the NNA, based on minimizing the square-error in the frequency-domain, is established according to the compact expression. To illustrate the stability of the NNA, the convergence theorem is presented and proved. Design examples are also given, and the results show that the ripple is considerably small in passband and stopband, and the NNA-based method is of powerful stability and requires quite little amount of computations.

关键词： 2-D linear-phase FIR digital filters neural network convergence theorem stability.

A Positive Solution for Some Critical p-Laplacian Systems

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Acta Mathematica Sinica,English Series 2015年第3期31卷 479-500页

作者： Xiao Zhi WANG College of Science University of Shanghai for Science and Technology

This paper deals with the existence of a positive solution for two classes of critical quasilinear system. We prove these results by a variant of mountain pass lemma, combining two convergence theorems and two estimate results. Here we avoid the usual compactness arguments（e.g., Palais-Smale condition or Cerami condition） and reveal the potential of some energy level estimates for the existence of nontrivial solutions.

关键词： p-Laplacian system critical growth convergence theorem estimate result

Mean Curvature Flow of Arbitrary Codimension in Complex Projective Spaces

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Chinese Annals of Mathematics,Series B 2023年第6期44卷 857-892页

作者： Li LEI Hongwei XU School of Mathematical Sciences Chongqing Normal UniversityChongqing 401331China. Center of Mathematical Sciences Zhejiang UniversityHangzhou 310027China

Recently,Pipoli and Sinestrari[Pipoli,*** Sinestrari,C.,Mean curvature flow of pinched submanifolds of CPn,***.,25,2017,799-846]initiated the study of convergence problem for the mean curvature flow of small codimension in the complex projective space *** purpose of this paper is to develop the work due to Pipoli and Sinestrari,and verify a new convergence theorem for the mean curvature flow of arbitrary codimension in the complex projective ***,the authors prove that if the initial submanifold in CPm satisfies a suitable pinching condition,then the mean curvature flow converges to a round point in finite time,or converges to a totally geodesic submanifold as t→∞.Consequently,they obtain a differentiable sphere theorem for submanifolds in the complex projective space.

关键词： Mean curvature flow Submanifolds of arbitrary codimension Complex projective space convergence theorem Differentiable sphere theorem

Four optimal design approaches of high-order finite-impulse response filters based on neural network

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Journal of Central South University of Technology 2007年第1期14卷 94-99页

作者：王小华何怡刚刘美容 School of Electrical and Information Engineering Hunan University

Four optimal approaches of high-order finite-impulse response(FIR) digital filters were developed for designing four types filters using neural network algorithms. The solutions were presented as parallel algorithms to approximate the desired frequency response specification. Therefore, these methods avoid matrix inversion, and make a fast calculation of the filter’s coefficients possible. The convergence theorems of these proposed algorithms were presented and proved to illustrate them stable, and the implementation of these methods was described together with some design guidelines. The simulation results show that the ripples of the designed FIR filters are significantly little in the pass-band and stop-band, and the proposed algorithms are of fast convergence.

关键词： high-order finite-impulse response digital filter frequency response neural network convergence theorem

A REMARK ON FORMAL MODELS FOR NONLINEARLY ELASTIC MEMBRANE SHELLS

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Chinese Annals of Mathematics,Series B 2001年第3期22卷 307-324页

作者： C. COLLARD Laboratoire d’Analyse Numerique, Tour n°55, Universite Pierre et Marie Curie, 4, place Jussieu, 75005 Paris, France. Laboratoire de Mathematiques Appliquees au Calcul Scientifique, Universite de Valenciennes et du Hainaut-Cambresis, Le Mont H Labiratoire d'Analyse Numérique Tour n°55 Université Pierre et Marie Curie 4 place Jussieu 75005 Paris France Laboratoire de Mathématiques Appliquées au Calcul Scientifique Université de Valenciennes et du Hainaut-Cambresis Le Mont Houy - B.P. 311 - F 59304 Valenciennes cedex France

This paper gives all the two-dimensional membrane models obtained from formal asymptotic analysis of the three-dimensional geometrically exact nonlinear model of a thin elastic shell made with a Saint Venant-Kirchhoff material. Therefore, the other models can be quoted as flexural nonlinear ones. The author also gives the formal equations solved by the associated stress tensor and points out that only one of those models leads, by linearization, to the "classical" linear limiting membrane model, whose justification has already been established by a convergence theorem.

关键词： Nonlinear elastic shell convergence theorem Asymptotic analysis

Non-expansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces

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Acta Mathematica Sinica,English Series 2004年第5期20卷 829-836页

作者： Ha|YunZHOU Dept.ofMath. ShijiazhuangMechanicalEngineeringCollegeShijiazhuang050003P.R.China

In this article,we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach *** results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.

关键词： Non-expansive mapping Mann and lshikawa iteration schemes convergence theorem Uniformly convex Banach space

A New Approach for Solving Nonlinear Equations by Using of Integer Nonlinear Programming

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Applied Mathematics 2016年第6期7卷 473-481页

作者： Armin Ghane-Kanafi Sohrab Kordrostami Department of Mathematics Lahijan Branch Islamic Azad University Lahijan Iran

One of the most important issues in numerical calculations is finding simple roots of nonlinear equations. This topic is one of the oldest challenges in science and engineering. Many important problems in engineering, to achieve the result need to solve a nonlinear equation. Thus, the formulation of a recursive relationship with high order of convergence and low time complexity is very important. This paper provides a modification to the Weerakoon-Fernando and Parhi-Gupta methods. It is shown that, in each iterate, the improved method requires three evaluations of the function and two evaluations of the first derivatives of function. The proposed with the Kou et al., Neta, Parhi-Gupta, Thukral and Mir et al. methods have been applied to a collection of 12 test problem. The results show that proposed approach significantly reduces the number of function calls when compared to the above methods. The numerical examples show that the proposed method is more efficiency than other methods in this class, such as sixth-order method of Parhi-Gupta or eighth-order method of Mir et al. and Thukral. We show that the order of convergence the proposed method is 9 and also, the modified method has the efficiency of .

关键词： Newton Method Nonlinear Equations convergence theorem Efficiency Index