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Schauder Estimates for Elliptic and Parabolic Equations

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Chinese Annals of Mathematics,Series B 2006年第6期27卷 637-642页

作者： Xu-Jia WANG centre for Mathematics and its applications Australian National University Canberra ACT 0200 Australia

In this note the author gives an elementary and simple proof for the Schauder estimates for elliptic and parabolic equations. The proof also applies to nonlinear equations.

关键词： Schauder estimate Elliptic equation Parabolic equation

Strong stability of Nash equilibria in load balancing games

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Science China Mathematics 2014年第7期57卷 1361-1374页

作者： CHEN Bo LI SongSong ZHANG YuZhong centre for Discrete Mathematics and its applications Warwick Business SchoolUniversity of Warwick School of Management Qufu Normal University

We study strong stability of Nash equilibria in load balancing games of m(m 2)identical servers,in which every job chooses one of the m servers and each job wishes to minimize its cost,given by the workload of the server it chooses.A Nash equilibrium(NE)is a strategy profile that is resilient to unilateral *** an NE in such a game is ***,an NE assignment is not stable against coordinated deviations of several jobs,while a strong Nash equilibrium(SNE)*** study how well an NE approximates an *** any job assignment in a load balancing game,the improvement ratio(IR)of a deviation of a job is defined as the ratio between the pre-and post-deviation *** NE is said to be aρ-approximate SNE(ρ1)if there is no coalition of jobs such that each job of the coalition will have an IR more thanρfrom coordinated deviations of the *** it is already known that NEs are the same as SNEs in the 2-server load balancing game,we prove that,in the m-server load balancing game for any given m 3,any NE is a(5/4)-approximate SNE,which together with the lower bound already established in the literature yields a tight approximation *** closes the final gap in the literature on the study of approximation of general NEs to SNEs in load balancing *** establish our upper bound,we make a novel use of a graph-theoretic tool.

关键词： load balancing game Nash equilibrium strong Nash equilibrium approximate strong Nash equilibrium

Coverage optimization for Defect-Tolerance Logic Mapping on Nanoelectronic Crossbar Architectures

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Journal of Computer Science & Technology 2012年第5期27卷 979-988页

作者：袁博李斌 Natural Inspired Computation and applications Lab Joint USTC-Birmingham Research Institute in Intelligent Computation and Its Applications University of Science and Technology of China

Emerging nano-devices with the corresponding nano-architectures are expected to supplement or even replace conventional lithography-based CMOS integrated circuits, while, they are also facing the serious challenge of high defect rates. In this paper, a new weighted coverage is defined as one of the most important evaluation criteria of various defecttolerance logic mapping algorithms for nanoelectronic crossbar architectures functional design. This new criterion is proved by experiments that it can calculate the number of crossbar modules required by the given logic function more accurately than the previous one presented by Yellambalase et al. Based on the new criterion, a new effective mapping algorithm based on genetic algorithm （GA） is proposed. Compared with the state-of-the-art greedy mapping algorithm, the proposed algorithm shows pretty good effectiveness and robustness in experiments on testing problems of various scales and defect rates, and superior performances are observed on problems of large scales and high defect rates.

关键词： coverage optimization defect-tolerance nanoelectronic crossbar logic mapping evolutionary algorithm

Duality Theorems on Multi-objective Programming of Generalized Functions

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Acta Mathematicae Applicatae Sinica 2006年第1期22卷 49-58页

作者： Li-ping Pang Wei Wang Zun-quan Xia centre for optimization Hesearch and applications Department of Applied Mathematics Dalian University of Technology Dalian 116024 China Department of Physics Dalian University of Technology China Mathcmat ics school Liaoning Normal University Dalian 116029 China centre for optimization Research and applications Department of Applied Mathematics Dalian University of Techaology Dalian 116024 China

The form of a dual problem of Mond-Weir type for multi-objective programming problems of generalized functions is defined and theorems of the weak duality, direct duality and inverse duality are proven.

关键词： Nonlinear optimization multiobjective optimization duality theory schwartz distribution

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

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

On Self-Adjointness of the Product of Two Second-Order Differential Operators

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Acta Mathematica Sinica,English Series 1999年第3期15卷 375-383,385-386页

作者： D. E. Edmunds Department of Mathematics Inner Mongolia University Huhhot 010021 P. R. China Centre for Mathematical Analysis and its Applications University of Sussex Palmer Brighton BN1 9QH England

In this paper, the problem of self-adjointness of the product of two differential operators is considered. A number of results concerning self-adjointness of the product L2L1 of two second-order self-adjoint differential operators are obtained by using the general construction theory of self-adjoint extensions of ordinary differential operators.

关键词： Self-adjoint operator Differential operator Product of two differential operators

Global regularity of optimal mappings in non-convex domains

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Science China Mathematics 2019年第11期62卷 2057-2072页

作者： Shibing Chen Jiakun Liu Xu-Jia Wang School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026China School of Mathematics and Applied Statistics University of WollongongWollongongNSW 2522Australia centre for Mathematics and its applications The Australian National UniversityCanberraACT 0200Australia

In this paper, we establish a global regularity result for the optimal transport problem with the quadratic cost, where the domains may not be convex. This result is obtained by a perturbation argument,using a recent ... 详细信息

关键词： Monge-Ampère equation optimal transportation global regularity

Mapping of quantitative trait loci using the skew-normal distribution

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Journal of Zhejiang University-Science B(Biomedicine & Biotechnology) 2007年第11期8卷 792-801页

作者： FERNANDES Elisabete PACHECO António PENHA-GONALVES Carlos centre for Mathematics and its applications IST-Technical University of Lisbon1049-001 LisboaPortugal Department of Statistics and Operational ResearchFaculty of SciencesUniversity of Lisbon1749-016 LisboaPortugal Gulbenkian Institute of ScienceP-2781-901 OeirasPortugal Department of Mathematics and centre for Mathematics and its applications IST-Technical University of Lisbon1049-001 LisboaPortugal Gulbenkian Institute of Science P-2781-901 OeirasPortugal

In standard interval mapping (IM) of quantitative trait loci (QTL), the QTL effect is described by a normal mixture model. When this assumption of normality is violated, the most commonly adopted strategy is to use the previous model after data transformation. However, an appropriate transformation may not exist or may be difficult to find. Also this approach can raise interpretation issues. An interesting alternative is to consider a skew-normal mixture model in standard IM, and the resulting method is here denoted as skew-normal IM. This flexible model that includes the usual symmetric normal distribution as a special case is important, allowing continuous variation from normality to non-normality. In this paper we briefly introduce the main peculiarities of the skew-normal distribution. The maximum likelihood estimates of parameters of the skew-normal distribution are obtained by the expectation-maximization (EM) algorithm. The proposed model is illustrated with real data from an intercross experiment that shows a significant departure from the normality assumption. The performance of the skew-normal IM is assessed via stochastic simulation. The results indicate that the skew-normal IM has higher power for QTL detection and better precision of QTL location as compared to standard IM and nonparametric IM.

关键词： Interval mapping (IM) Quantitative trait loci (QTL) Skew-normal distribution Expectation-maximization (EM)algorithm