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Generalized gradient projection neural networks for nonsmooth optimization problems

Science china(Information Sciences) 2010年第5期53卷 990-1005页

作者： LI GuoCheng 1 , SONG ShiJi 2.? & WU Cheng 2.1 department of Mathematics, beijing Information Science and {2. University, beijing 100192. china 2.department of Automation, Tsinghua University, beijing 100084, china 1. department of Mathematics Beijing Information Science and Technology University Beijing 100192 China2. Department of Automation Tsinghua University Beijing 100084 China

Generalized gradient projection neural network models are proposed to solve nonsmooth convex and nonconvex nonlinear programming problems over a closed convex subset of R n . By using Clarke’s generalized gradient, the neural network modeled by a differential inclusion is developed, and its dynamical behavior and optimization capabilities both for convex and nonconvex problems are rigorously analyzed in the framework of nonsmooth analysis and the differential inclusion theory. First for nonconvex optimization problems, the quasi convergence results similar to those achieved by previous work are proved. For convex optimization problems, the global convergence results are proved, i.e. any trajectory of the neural network converges to an asymptotically stable equilibrium point, which is an optimal solution of the primal problem whenever it exists. This result remains valid even if the initial condition is chosen outside the feasible set. In addition, an asymptotic control result involving a Tykhonov like regularization shows that any trajectory of the revised neural network can be forced to converge toward a particular optimal solution of the primal problem. Finally, two simulation optimization algorithms for solving the optimization and control problems are designed respectively, and three typical simulation experiments are illustrated to present the accuracy and efficiency of theoretical convergence results of this paper.

关键词： nonsmooth optimization problem generalized gradient projection networks differential inclu sions convergence

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Serving High-Level Opening up with "TaxExpress"

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Belt and Road Initiative Tax Journal 2024年第1期 97-105页

作者： International Taxation department, State Taxation Administration,the People's Republic of china International Taxation department State Taxation Administrationthe People's Republic of China

Over the past decade,the Chinese tax authorities have been actively supporting the development of the Belt and Road Initiative,by creating a unique cross-border tax and fee service model with Chinese characteristics,which has laid a solid foundation for the establishment of the "TaxExpress" cross-border service *** October 2.2.,the State Taxation Administration of china(STA) officially launched the "TaxExpress" brand,focusing on one service matrix,two service teams,three service mechanisms,and four knowledge *** brand aims to enhance cooperation between ministries and commissions,promote international exchanges,and establish a framework for effective cross-border tax and fee *** forward,the STA will continue to leverage existing resources to support high-level opening up,by enhancing brand value,improving measures for international tax and fee services,expanding cross-border tax and fee services,strengthening professional talent teams,so as to develop a cross-border tax and fee service system that combines Chinese characteristics with international best practices.

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Software Simulation in GSM Environment and Hardware Implementation of Improved Multi-band Excitation Vocoder

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通信学报 1998年第5期 19-28页

作者： Kuang Jingming Li Feng Liu Botao (Electronic Engineering department, beijing {2. of technology, beijing 100081)

ＳｏｆｔｗａｒｅＳｉｍｕｌａｔｉｏｎｉｎＧＳＭＥｎｖｉｒｏｎｍｅｎｔａｎｄＨａｒｄｗａｒｅＩｍｐｌｅｍｅｎｔａｔｉｏｎｏｆＩｍｐｒｏｖｅｄＭｕｌｔｉｂａｎｄＥｘｃｉｔａｔｉｏｎＶｏｃｏｄｅｒＫｕａｎｇＪｉｎｇｍｉｎ... 详细信息

ＳｏｆｔｗａｒｅＳｉｍｕｌａｔｉｏｎｉｎＧＳＭＥｎｖｉｒｏｎｍｅｎｔａｎｄＨａｒｄｗａｒｅＩｍｐｌｅｍｅｎｔａｔｉｏｎｏｆＩｍｐｒｏｖｅｄＭｕｌｔｉｂａｎｄＥｘｃｉｔａｔｉｏｎＶｏｃｏｄｅｒＫｕａｎｇＪｉｎｇｍｉｎｇＬｉＦｅｎｇＬｉｕＢｏｔａｏ（Ｅ...

关键词： vocoder IMBE improved multi band excitation GSM software simulation

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Planar cubic hybrid hyperbolic polynomial curve and its shape classification

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Progress in Natural Science:Materials International 2004年第1期14卷 42-47页

作者： WANG Guozhao 1,2. * and YANG Qinmin 1,2. (1. institute of computer Graphics and Image Processing, 2. {2. of Mathematics, Zhejiang University, Hangzhou 31002., china) Zhejiang Univ Inst Comp Graph & Image Proc Hangzhou 310027 Peoples R China Zhejiang Univ Dept Math Hangzhou 310027 Peoples R China

The planar cubic hybrid hyperbolic polynomial curves and cubic H Bézier curves are presented. The conditions leading to inflection points and singularities (cusps and loops) are investigated and the shape of these curves is classified. The conclusions enable us to detect inflection points and singularities and get an idea of how to preserve the fair shape when designing such curves.

关键词： hybrid hyperbolic polynomial curve H-Bézier curve shape classification inflection points singularities

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Analysis on ignition and extinction of n-heptane in homogeneous systems

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Science china(Technological Sciences) 2005年第5期48卷 556-569页

作者： LIU Yongfeng1 & PEI Pucheng2.1. Mechanical and Electrical Engineering department, beijing {2. of Civil Engineering and Architec-ture, beijing 100044, china 2. State Key Laboratory of Automotive Safety and Energy, Tsinghua University, beijing 100084, china 1. Mechanical and Electrical Engineering department Beijing Institute of Civil Engineering and Architecture 100044 Beijing China 2. State Key Laboratory of Automotive Safety and Energy Tsinghua University 100084 Beijing China

To calculate ignition delay times, the governing equations about species and temperature, which are in a closed volume based on the theory of thermal explosion and in a continuously stirred flow reactor, are deducted. The method referred to steady state assumptions is based on the observation that due to very fast chemical processes in combustion problems many chemical species and reactions are in a quasi-steady state or partial equilibrium. When a species is assumed to be in the steady state, the corresponding differential equation can be replaced by an algebraic relation, which reduces the computational costs. The steady state solution of the reactor equations describes the three ignition temperature regimes and get “S-shaped curve”. The reduced simplified 4-step mechanism for n-heptane from 1011 elementary reactions leads with the steady state assumptions to linear differential equations, which is solved. The simulation results of the 4-step reduced mechanism for n-heptane are fitted well with the experiment data. At last, two important parameters are discussed thoroughly and the temperature perturbation is given. It reduces the computational efforts considerably without losing too much accuracy and further supplies numerical methods for turbulent combustion in the diesel engine.

关键词： ignition delay times, thermal runaway, steady state assumptions, continuously stirred flow reactor.

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Three-dimensional configurations of organic/inorganic hybrid nanostructural blocks (I).A quantum mechanical investigation for ladder-like structure of vinylsilsesquioxane

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Science china Chemistry 2004年第5期47卷 388-395页

作者： ZHANG Xingwen1,2. HU Lijiang1, HUANG Yudong1, SUN Dezhi2.& SUN Yi3 1. department of Applied Chemistry,Harbin institute of {2., HUANG Yudong, Harbin 150001, china 2. department of Environmental Engineering, Harbin institute of {2., Harbin 150001, china 3. department of Experimental Mechanics,Harbin institute of {2., Harbin 150001, china 1. department of Applied Chemistry Harbin Institute of Technology HUANG Yudong 150001 Harbin China 2. department of Environmental Engineering Harbin Institute of Technology 150001 Harbin China 3. department of Experimental Mechanics Harbin Institute of Technology 150001 Harbin China

The organic/inorganic hybrid nanostructural vinylsilsesquioxanes (VSSO) were prepared from the hydrolytic condensation of vinyltrimethoxysilane (VMS). The proposed formu- las of VSSO were assigned with standard spectroscopic techniques, FTIR, NMR (1H, C and 13 2.Si) and MALDI-TOF MS, and a generic formula of the SSO, Tn(OH)x(OR’)y(x, y = 0, 1, 2.; n = 1, 2.; T = RSiO1.5 ?(x+y)/2.). Geometric parameters (Si-O and Si-C bond lengths, Si-O-Si and O-Si-O bond angles) and total energies of the multi-structures of VSSO were calculated by a quantum mechanical investigation and molecular symmetries. According to the results of the calculation, most molecules had stabler ladder structures than the cage isomers, therefore, the most probably reasonable and optimum structure of the VSSO system was the ladder type.

关键词： vinyltrimethoxysilane (VMS), silsesquioxanes (SSO), sol-gel process, quantum mechanical calculation, MNDO.

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A MODIFIED ALGORITHM OF FINDING AN ELEMENT OF CLARKE GENERALIZED GRADIENT FOR A SMOOTH COMPOSITION OF MAX-TYPE FUNCTIONS A MODIFIED ALGORITHM OF FINDING AN ELEMENT OF CLARKE GENERALIZED GRADIENT FOR A SMOOTH COMPOSITION OF MAX-TYPE FUNCTIONS

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Journal of Computational Mathematics 2000年第5期18卷 513-520页

作者： Yan Gao (department of Basic Science, china University of Mining and {2.-beijing, beijing 100083, china) （北京）中国矿业大学北京 100083

This paper refers to Clarke generalized gradient for a smooth composition of max-type functions of the form: f(x) = g(x, maxj∈J1 f1j(x),''', maxj∈Jm fmj(x)), where x ∈Rn, Ji, i = 1,''',m are finite index sets, g and fij,j ∈ Ji, i = 1,... )m, are continuously differentiable on Rm+n and Rn, respectively. In a previous paper) we proposed an algorithm of finding an element of Clarke generalized gradient for f, at a point. In that paper, finding an element of Clarke generalized gradient for f, at a point, is implemented by determining the compatibilities of systems of linear inequalities many times. So its computational amount is very expensive. In this paper) we will modify the algorithm to reduce the times that the compatibilities of systems of linear inequalities have to be determined.

关键词： Nonsmooth optimization Clarke generalized gradient Max-type function.

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Weighted estimates for the multilinear singular integral operators with non-smooth kernels

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Science china Mathematics 2011年第3期54卷 587-602页

作者： HU GuoEn1 & LU ShanZhen2.1department of Applied Mathematics, Zhengzhou Information Science and technology {2., Zhengzhou 450002. china 2.0} of Mathematics, beijing Normal University, beijing 100875, china 1. department of Applied Mathematics Zhengzhou Information Science and Technology Institute Zhengzhou 450002 China2. Department of Mathematics Beijing Normal University Beijing 100875 China

In this paper, by sharp function estimates and certain weak type endpoint estimates, the authors establish some weighted norm inequalities with Ap weights for the multilinear singular integral operators with non-smoot... 详细信息

关键词： approximation to the identity weighted norm inequality singular integral operator non-smooth kernel Calderón-Zygmund decomposition

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Dynamic mechanisms of the post-seismic deformation following large events:Case study of the 1999 Chi-Chi earthquake in Taiwan of china

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Science china Earth Sciences 2009年第11期52卷 1813-1824页

作者： ZHU ShouBiao1,2.& CAI YongEn2.1 institute of Crustal Dynamics, china Earthquake Administration, {2. 100085, china 2.department of Geophysics, Peking University, {2. 100871, china 1. institute of Crustal Dynamics China Earthquake Administration Beijing 100085 China 2. department of Geophysics Peking University Beijing 100871 China

The mechanism of postseismic deformation related to strong earthquakes is important in geodynamics, and presumably afterslip or viscoelastic relaxation is responsible for the postsesimic deformation. The 1999 Chi-Chi, Taiwan of china, earthquake occurred in the region where GPS observation station is most densely deployed in the world. The unprecedented GPS data provides a unique opportunity to study the physical processes of postseismic deformation. Here we assume that the interactions of viscoelastic relaxation, afterslip, fault zone collapse, poroelastic rebound, flow of underground fluids, and all these combined contribute to the surface displacements following the main shock. In order to know the essence of the postseismic deformation after the strong event, fault zone collapse, poroelastic rebound, flow of underground fluids, and so on, are represented equivalently by the variations of the focal medium properties. Therefore, the viscoelastic relaxation, afterslip, and the variations of the equivalent focal medium properties are inverted by applying the GPS temporal series measurement data with viscoelastic finite element method. Both the afterslip rate distribution along the fault and the afterslip evolution with time are obtained by means of inversion. Also, the preliminary result suggests that viscosities of the lower crust and the upper mantle in Taiwan region is 2.7×1018 and 4.2.102. Pa·s, respectively. Moreover, the inversion results indicate that the afterslip contributing to postseismic deformation of 44.6% in 450 days after the Chi-Chi earthquake, with 34.7% caused by the viscous relaxation and 2..7% by other factors such as fault zone collapse, poroelastic rebound, and the flow of liquids.

关键词： mechanism of postseismic deformation viscoelastic finite element method GPS temporal series data Chi-Chi earthquake

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A Sensitivity-Based Heuristic Search for Constrained Optimization in Complex Systems

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Journal of Systems Engineering and Electronics 1999年第1期10卷 75-80页

作者： Gao Peiwang Ma Xiaoqing (department of Mechanical and Electronic Engineering, beijing {2. of technology, 100081, P. R. china)(Received September 4, 1998) department of Mechanical and Electronic Engineering Beijing Institute of Technology 100081 P. R. China

On the basis of sensitivity analysis, an algorithm presented in this paper does a multi dimensional heuristic search for the optimal solution of complex systems in the feasible intervals of components reliability. Compared with some existing methods, the algorithm both has heuristic speciality that it is modest and easy to implement, and obtains the optimal solution as exact methods do.

关键词： Complex systems Systems reliability Sensitivity Heuristic methods.

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