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Hardy spaces on Lie groups of polynomial growth

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Science China Mathematics 2010年第1期53卷 23-40页

作者： ter ELST A F M ROBINSON Derek W Department of Mathematics University of Auckland Center for Mathematics and its applications Mathematical Science Institute

We give several characterizations of Hardy spaces associated with complex, second-order,subelliptic operators on Lie groups with polynomial growth.

关键词： Lie groups Hardy spaces heat kernel

A Multi-Objective Particle Swarm optimization Algorithm Based on Decomposition and Multi-Selection Strategy

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Computers, Materials & Continua 2025年第1期82卷 997-1026页

作者： Li Ma Cai Dai Xingsi Xue Cheng Peng School of Computer Science Shaanxi Normal UniversityXi’an710119China Fujian Provincial Key Laboratory of Big Data Mining and applications Fujian University of TechnologyFuzhou350118China Information Construction and Management Center and Institute of Artificial Intelligence and Educational New Productivity Ningxia Normal UniversityGuyuan756099China

The multi-objective particle swarm optimization algorithm(MOPSO)is widely used to solve multi-objective optimization *** the article,amulti-objective particle swarm optimization algorithmbased on decomposition and multi-selection strategy is proposed to improve the search ***,two update strategies based on decomposition are used to update the evolving population and external archive,***,a multiselection strategy is *** first strategy is for the subspace without a non-dominated *** the neighbor particles,the particle with the smallest penalty-based boundary intersection value is selected as the global optimal solution and the particle far away fromthe search particle and the global optimal solution is selected as the personal optimal solution to enhance global *** second strategy is for the subspace with a non-dominated *** the neighbor particles,two particles are randomly selected,one as the global optimal solution and the other as the personal optimal solution,to enhance local *** third strategy is for Pareto optimal front(PF)discontinuity,which is identified by the cumulative number of iterations of the subspace without non-dominated *** the subsequent iteration,a new probability distribution is used to select from the remaining subspaces to ***,an adaptive inertia weight update strategy based on the dominated degree is designed to further improve the search ***,the proposed algorithmis compared with fivemulti-objective particle swarm optimization algorithms and five multi-objective evolutionary algorithms on 22 test *** results show that the proposed algorithm has better performance.

关键词： Multi-objective optimization multi-objective particle swarm optimization decomposition multi-selection strategy

The drying of liquid droplets

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Chinese Physics B 2020年第9期29卷 435-442页

作者： Zechao Jiang Xiuyuan Yang Mengmeng Wu Xingkun Man Center of Soft Matter Physics and its applications Beihang UniversityBeijing 100191China School of Physics Beihang UniversityBeijing 100191China

The drying of liquid droplets is a common phenomenon in daily life,and has long attracted special interest in scientific *** propose a simple model to quantify the shape evolution of drying *** model takes into account the friction constant between the contact line(CL)and the substrate,the capillary forces,and the evaporation *** typical evaporation processes observed in experiments,i.e.,the constant contact radius(CCR)and the constant contact angle(CCA),are demonstrated by the ***,the simple model shows complicated evaporation dynamics,for example,the CL first spreads and then recedes during *** models of no evaporation,CCR,and CCA cases are given,*** scaling law of the CL or the contact angle as a function of time obtained by analytical model is consistent with the full numerical model,and they are all subjected to experimental *** general model facilitates a quantitative understanding of the physical mechanism underlying the drying of liquid droplets.

关键词： evaporation droplets Onsager variational principle contact line motion

A NUMERICAL STUDY OF UNIFORM SUPERCONVERGENCE OF LDG METHOD FOR SOLVING SINGULARLY PERTURBED PROBLEMS

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Journal of Computational Mathematics 2009年第2期27卷 280-298页

作者： Ziqing Xie Zuozheng Zhang Zhimin Zhang Key Laboratory of Computational and Stochastic Mathematics and its applications Universities of Hunan Province Hunan Normal University Changsha 410081 China

In this paper, we consider the local discontinuous Galerkin method （LDG） for solving singularly perturbed convection-diffusion problems in one- and two-dimensional settings. The existence and uniqueness of the LDG solutions are verified. Numerical experiments demonstrate that it seems impossible to obtain uniform superconvergence for numerical fluxes under uniform meshes. Thanks to the implementation of two-type different anisotropic meshes, i.e., the Shishkin and an improved grade meshes, the uniform 2p ＋ i-order superconvergence is observed numerically for both one-dimensional and twodimensional cases.

关键词： Singularly perturbed problems Local discontinuous Galerkin method Numerical fluxes Uniform superconvergence

LINEARIZATION OF A NONLINEAR PERIODIC BOUNDARY CONDITION RELATED TO CORROSION MODELING

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Journal of Computational Mathematics 2007年第6期25卷 645-660页

作者： Y. S. Bhat S. Moskow Institute for Mathematics and its applications Univ. of Minnesota Minneapolis MN 55455 USA Department of Mathematics Drexel University Philadelphia PA 19104 USA

We study galvanic currents on a heterogeneous surface. In electrochemistry, the oxidation-reduction reaction producing the current is commonly modeled by a nonlinear elliptic boundary value problem. The boundary condition is of exponential type with periodically varying parameters. We construct an approximation by first homogenizing the problem, and then linearizing about the homogenized solution. This approximation is far more accurate than both previous approximations or direct linearization. We establish convergence estimates for both the two and three-dimensional case and provide two-dimensional numerical experiments.

关键词： Galvanic corrosion Homogenization Nonlinear elliptic boundary value problem Butler-Volmer boundary condition Robin boundary condition.

Influence of Cell-Cell Interactions on the Population Growth Rate in a Tumor

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Communications in Theoretical Physics 2017年第12期67卷 798-802页

作者：陈勇 Center of Soft Matter Physics and its applications Beihang University School of Physics and Nuclear Energy Engineering Beihang University

The understanding of the macroscopic phenomenological models of the population growth at a microscopic level is important to predict the population behaviors emerged from the interactions between the individuals. In this work, we consider the influence of the population growth rate R on the cell-cell interaction in a tumor system and show that, in most cases especially small proliferative probabilities, the regulative role of the interaction will be strengthened with the decline of the intrinsic proliferative probabilities. For the high replication rates of an individual and the cooperative interactions, the proliferative probability almost has no effect. We compute the dependences of R on the interactions between the cells under the approximation of the nearest neighbor in the rim of an avascular tumor. Our results are helpful to qualitatively understand the influence of the interactions between the individuals on the growth rate in population systems.

关键词： population dynamics growth rate avasular tumor cell-cell interaction

The Christoffel problem by the fundamental solution of the Laplace equation

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Science China Mathematics 2021年第7期64卷 1599-1612页

作者： Qi-Rui Li Dongrui Wan Xu-Jia Wang School of Mathematical Sciences Zhejiang UniversityHangzhou 310027China centre for Mathematics and its applications The Australian National UniversityCanberraACT 2601Australia College of Mathematics and Statistics Shenzhen UniversityShenzhen 518060China

The Christoffel problem is equivalent to the existence of convex solutions to the Laplace equation on the unit sphere S^(n).Necessary and sufficient conditions have been found by Firey(1967)and Berg(1969),by using the Green function of the Laplacian on the *** the Christoffel problem as the Laplace equation on the entire space R^(n+1),we observe that the second derivatives of the solution can be given by the fundamental solutions of the Laplace *** we find new and simpler necessary and sufficient conditions for the solvability of the Christoffel *** also study the Lp extension of the Christoffel problem and provide sufficient conditions for the problem,for the case p≥2.

关键词： Christoffel problem Laplace equation fundamental solution

A Comprehensive Taxi Assessment Index Using Floating Car Data

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Journal of Harbin Institute of Technology(New Series) 2014年第1期21卷 7-16页

作者： Dao-Zheng Zhang Daniel (Jian) Sun Zhong-Ren Peng Center for UAV applications and its Research Shanghai Jiaotong University Department of Urban and Regional Planning University of Florida

With the expansion of urban area and development of taxi system,problems arise,such as low operation efficiency,high taxi idling rate,and long passenger waiting-time. Although various studies have been conducted,only limited overview of the factors towards urban taxi system has been provided. Consequently,a comprehensive evaluation of taxi system is essential for the urban planner to analyze the current situation and take effective measures. This paper,by using Floating Car Data( FCD),proposes a Comprehensive Taxi Assessment Index( CTAI) to quantify the quality of existing urban taxi system with the assistance of Geographic Information System( GIS) technology. The proposed index system extracts and classifies key factors,reflecting the taxi system from the perspectives of operation efficiency,customer and taxi-driver satisfaction. The system contributes to improving the organization and operation of urban taxi system. Based on the data obtained from the city of Shenzhen,Guangdong Province,China,for both weekday and weekends( Dec.,2011),the proposed CTAI was illustrated by using the Principal Component Analysis( PCA) with ArcGIS 10. 0 platform. The results indicate that the system provides a good multi-dimensional view to delve into the existing urban taxi operation, thus to point out the most sensitive indices towards the entire system,which consequently provides guidelines for future improvement and management of urban taxi system.

关键词： taxi evaluation system principle component analysis(PCA) floating car data(FCD) geographic information system(GIS)

Freight Vehicle Routing optimization for Sporadic Orders Using Floating Car Data

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Journal of Donghua University(English Edition) 2013年第2期30卷 96-102页

作者：常晶晶彭仲仁孙健 Center for its and UAV applications Research Shanghai Jiaotong University Department of Urban and Regional Planning University of Florida

The increasing popularity of e-commerce brings large volumes of sporadic orders from different customers,which have to be handled by freight trucks and distribution centers. To improve the level of service and reduce the total shipping cost as well as traffic congestions in urban area, flexible methods and optimal vehicle routing strategies should be adopted to improve the efficiency of distribution effort. An optimization solution for vehicle routing and scheduling problem with time window for sporadic orders (VRPTW- S) was provided based on time-dependent travel time extracted from floating car data (FCD) with ArcGIS platform. A VRPTW-S model derived from the traditional vehicle routing problem was proposed, in which uncertainty of customer orders and travel time were considered. Based on this model, an advanced vehicle routing algorithm was designed to solve the problem. A case study of Shenzhen, Guangdong province, China, was conducted to demonstrate the vehicle operation flow,in which process of FCD and efficiency of delivery systems under different situations were discussed. The final results demonstrated a good performance of application of time-dependent travel time information using FCD in solving vehicle routing problems.

关键词： freight routing and scheduling time-dependent travel time floating car data (FCD) sporadic order ArcGIS