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Convergence of one-leg methods for singular perturbation problems with delays

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Science China Mathematics 2002年第3期45卷 280-289页

作者：甘四清孙耿 Dept. of Comp. Sci. and Technology Tsinghua University Beijing 100084 China Institute of Mathematics Chinese Academy of Sciences Beijing 100080 China

This paper is concerned with the error behaviour of one-leg methods applied to some classes of one-parameter multiple stiff singularly perturbed problems with delays. We obtain convergence results of A-stable one-leg ... 详细信息

关键词： singular perturbation problems with delays, interpolation, one-leg methods, convergence.

Analysis on the problems of Innovation and Entrepreneurship Education in Colleges and Universities

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Journal of Contemporary Educational Research 2023年第8期7卷 80-85页

作者： Zerun Lin The Education University of Hong Kong Hong Kong 999077China

With the acceleration of economic globalization and the deepening of China’s reform and opening-up,the demand for various talents is showing a trend of diversification.In this context,colleges and universities should make full use of their own advantages and characteristics,actively carry out innovation and entrepreneurship education,and cultivate more high-quality compound talents for the society.However,judging from the current situation,there are still some colleges and universities that lack the attention to and understanding of the importance of innovation and entrepreneurship education.

关键词： Colleges and universities Innovation and entrepreneurship education problems

Initial-irregular oblique derivative problems for nonlinear parabolic systems of second order equations with measurable coefficients

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Science China Mathematics 1999年第7期42卷 681-690页

作者：闻国椿 Department of Mathematics Peking University Beijing China

The initial-irregular oblique derivative boundary value problems for nonlinear and nondivergence parabolic systems of second order equations in multiply connected domains are dealt with where coefficients of systems of equations are meaurable. The uniqueness theorem of solutions for the above problems and some a priori estimates of solutions for the problems are given. And by using the above estimates of solutions and the Leray-Schauder theorem, the existence of solutions of the initial-boundary value problems is proved. The results are generalizations of corresponding theorems in literature.

关键词： initial-irregular oblique derivative problems nonlinear parabolic systems measurable coefficients uniqueness and existence of solutions.

Uniqueness to Some Inverse Source problems for the Wave Equation in Unbounded Domains

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Acta Mathematicae Applicatae Sinica 2020年第1期36卷 134-150页

作者： Guang-hui HU Yavar KIAN Yue ZHAO Beijing Computational Science Research Center Beijing 100193China Aix Marseille Univ Universit’e de ToulonCNRSCPTMarseilleFrance School of Mathematics and Statistics Central China Normal UniversityWuhan 430079China

This paper is concerned with inverse acoustic source problems in an unbounded domain with dynamical boundary surface data of Dirichlet kind.The measurement data are taken at a surface far away from the source support.We prove uniqueness in recovering source terms of the form f(x)g(t)and f(x1,x2,t)h(x3),where g(t)and h(x3)are given and x=(x1,x2,x3)is the spatial variable in three dimensions.Without these a priori information,we prove that the boundary data of a family of solutions can be used to recover general source terms depending on both time and spatial variables.For moving point sources radiating periodic signals,the data recorded at four receivers are prove sufficient to uniquely recover the orbit function.Simultaneous determination of embedded obstacles and source terms was verified in an inhomogeneous background medium using the observation data of infinite time period.Our approach depends heavily on the Laplace transform.

关键词： Inverse source problems Laplace transform moving point source uniqueness

Analysis of problems in urban green space system planning in China

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Journal of Forestry Research 2009年第1期20卷 79-82页

作者： WANG Xiao-Jun College of Architecture Southeast University Nanjing 210096 P. R. China

This paper discusses the major problems in urban green space system （UGSS） planning at both general and special planning levels in China. At general planning level, the problems of the UGSS are mainly from the ignorance in the characteristics of urban nature spaces and the limitation factors of the urban planning system. Great importance is attached to the green spaces in the built area of city, but the green spaces in surrounding areas of the city is unnoticed. Furthermore, because the area of UGSS planning is strictly limited by the administrative zoning, the green space system loses its integrity and rationality in spatial patterns. The schedules of urban development planning mismatched the paces and progresses of the ecological restoration cycles. At special plan level, the problem of the UGSS in China is that the green spaces quantity was over emphasized but the rationality of their layouts is neglected.. Meanwhile, the requirement of the spatial structures and the green spaces layouts to balance between the urban development and the natural ecological environments is often ignored. With regard to the layouts in the UGSS planning practices, the existing problems are the compromising to the existing land-uses, the ＇filling in＇ approach to plan green spaces and an over-emphasis on the layout patterns.

关键词： Urban Green Space System （UGSS） planning problems quantity layout

Investigating the problems and Proposing Solutions for Rural Residential Buildings in Northwest China

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Journal of Architectural Research and Development 2022年第2期6卷 8-14页

作者： Zhaobo Zhang Jianqiang Wang Mao Hu Department of Civil Engineering Gansu Agricultural UniversityLanzhou 730070Gansu ProvinceChina Gansu Wande Green Building Co. Ltd.Pingliang 743400Gansu ProvinceChina Pingliang Mechanical and Electrical Engineering School Pingliang 743400Gansu ProvinceChina

With the increasing income of the rural population in Northwest China,people’s sense of happiness and gain is also increasing.However,the improvement of housing conditions is lagging behind the increasing income levels.In recent years,the government and owners have paid much attention to this issue.The local government has successively issued relevant guidelines and policies to encourage owners to reconstruct their houses and improve their housing conditions.Before improving housing conditions,the existing housing problems must be identified.In order to have a comprehensive and in-depth understanding of the problems of rural residential buildings in Northwest China and to propose corresponding solutions,90 representative rural residential buildings of three provinces in Northwest China have been selected for investigation,and mass data have been obtained.Upon analyzing these data,it has been found that there are problems in five aspects of rural residential buildings in Northwest China:architectural style and functional space layout,energy utilization and dissipation,design,construction,as well as structural safety and seismic measures.Valid solutions are proposed to address these problems,which can also provide a reference for the government and enterprises engaged in the architecture,engineering,and construction(AEC)industry in rural areas.

关键词： Investigation problems Rural residential buildings Solutions

Fast Solvers of Fredholm Optimal Control problems

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Numerical Mathematics(Theory,Methods and Applications) 2010年第4期3卷 431-448页

作者： Mario Annunziato Alfio Borzi Universita degli Studi di Salerno Dipartimento di Matematica e InformaticaVia Ponte Don Melillo84084 Fisciano(SA)Italia Universita degli Studi del Sannio Dipartimento e Facolta di IngegneriaPalazzo Dell'Aquila Bosco LucarelliCorso Garibaldi 10782100 BeneventoItalia Institutfr Mathematik und Wissenschaftliches Rechnen Karl-Franzens-Universitt GrazHeinrichstr.368010 GrazAustria.

The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.

关键词： Control problems control problems Fredholm integral equations Existence and uniqueness optimal solutions Fourier analysis performance framework results kind

An Efficient Approach to a Class of Non-smooth Optimization problems

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Science China Mathematics 1994年第3期37卷 323-330页

作者：李兴斯 Research Institute of Engineering Mechanics Dalian University of TechnologyDalian 116023PRChis paper presents an entropy-based smoothing technique for solving a class of non-smooth optimization problems that are in some way related to the maximum function.Basic ideas concerning this approach are that we replace the non-smooth maximum function by a smooth onecalled aggregate functionwhich is derived by employing the maximum entropy principle and its useful properties are proved.Wilh this smoothing techniqueboth unconstrained and constrained mimma.x problems are transformed into unconstrained optimization problems of smooth functions such that this class of non-smooth optimization problems can be solved by some existing unconstrained optimization softwares for smooth functions The present approach can be very easily implemented on computers with very fast and -.Inhie convergence.

This paper presents an entropy-based smoothing technique for solving a class of non-smooth optimization problems that are in some way related to the maximum function.Basic ideas concerning this approach are that we replace the non-smooth maximum function by a smooth one,called aggregate function,which is derived by employing the maximum entropy principle and its useful properties are proved.Wilh this smoothing technique,both unconstrained and constrained mimma.x problems are transformed into unconstrained optimization problems of smooth functions such that this class of non-smooth optimization problems can be solved by some existing unconstrained optimization softwares for smooth functions The present approach can be very easily implemented on computers with very fast and -.Inhie convergence.

关键词： nun smooth optimization mininiax problems nonlinear programming exact penalty functions entropy

Analysis of Existing problems and Treatment Methods of Urban Environmental Monitoring

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Journal of Environmental Science and Engineering(A) 2022年第2期11卷 49-54页

作者： Zhang Qiandong Song Xin Shandong Yantai Ecological Environment Monitoring Center Yantai 264000China Shandong Deep Sea Marine Technology Co. Ltd.Fushan DistrictYantai 265500China

With the rapid development of the city,the concept of ecological environment has been integrated into everyone’s heart.In the new era,people also have higher requirements for the quality of living environment.However,at this stage,with the development of urbanization and industrialization,the problem of environmental pollution has become more and more serious.Therefore,we must do a good job in urban environmental monitoring,pay attention to the protection of urban environment,design and implement effective governance methods,so as to improve the quality of environmental governance.This article analyzes the problems in urban environmental monitoring,and formulates reasonable treatment methods and suggestions.

关键词： Urban environmental monitoring problems governance methods analysis