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SUFFICIENCY AND DUALITY FOR NONSMOOTH MULTIOBJECTIVE PROGRAMMING PROBLEMS INVOLVING GENERALIZED UNIVEX FUNCTIONS

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Journal of Systems Science & Complexity 2013年第6期26卷 1002-1018页

作者： LONG Xianjun college of Mathematics and statistics Chongqing Technology and Business University

In this paper, nonsmooth univex, nonsmooth quasiunivex, and nonsmooth pseudounivex functions are introduced. By utilizing these new concepts, sufficient optimality conditions for a weakly efficient solution of the nonsmooth multiobjective programming problem are established. Weak and strong duality theorems axe also derived for Mond-Weir type multiobjective dual programs.

关键词： Duality multiobjective programming nonsmooth pseudounivexity nonsmooth quasiuni-vexity nonsmooth univexity sufficient optimality condition weakly efficient solution.

Convergence analysis on Browder-Tikhonov regularization for second-order evolution hemivariational inequality

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Applied Mathematics and Mechanics(English Edition) 2015年第10期36卷 1371-1382页

作者： Yibin XIAO Guoji TANG Xianjun LONG Nanjing HUANG School of mathematical Sciences University of Electronic Science and Technology of China School of Science Guangxi University for Nationalities college of Mathematics and statistics Chongqing Technology and Business University Department of Mathematics Sichuan University

This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality （SOEHVI） with non-coercive operators. With duality mapping, the regularized formulations and a derived first-order evolution hemivariational inequality （FOEHVI） for the problem considered are presented. By applying the Browder-Tikhonov regularization method to the derived FOEHVI, a sequence of regularized solutions to the regularized SOEHVI is constructed, and the strong convergence of the whole sequence of regularized solutions to a solution to the problem is proved.

关键词： second-order evolution hemivariational inequality (SOEHVI) Browder-Tikhonov regularization Clarke's generalized gradient

Single-cell technologies: current and near future

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Science China Life Sciences 2025年第1期68卷 1-4页

作者： Chenfei Wang Qi Liu Xiaohui Fan Tieliu Shi Key Laboratory of Spine and Spinal Cord Injury Repair and Regeneration Ministry of EducationOrthopedics DepartmentTongji HospitalBioinformatics DepartmentSchool of Life Sciences and TechnologyTongji University Frontier Science Center for Stem Cells School of Life Sciences and TechnologyTongji University Translational Medical Center for Stem Cell Therapy and Institute for Regenerative Medicine Shanghai East HospitalBioinformatics DepartmentSchool of Life Sciences and TechnologyTongji University Research Institute of Intelligent Computing Zhejiang Lab Pharmaceutical Informatics Institute College of Pharmaceutical SciencesZhejiang University National Key Laboratory of Chinese Medicine Modernization Innovation Center of Yangtze River DeltaZhejiang University Center for Bioinformatics and Computational Biology Shanghai Key Laboratory of Regulatory Biologythe Institute of Biomedical Sciences and School of Life SciencesEast China Normal University Key Laboratory of Advanced Theory and Application in statistics and Data Science (MOE) School of StatisticsEast China Normal University

Single-cell technologies enable the indepth exploration of multiple biological hierarchies at the scale of individual cells,which have deepened our knowledge of cellular diversity, tissue organization, and overall organism function(Sun et al.,2024). In 2009, single-cell RNA sequencing(sc RNA-seq) was first developed as a powerful tool to dissect gene expression and uncover transcriptional *** the rapid advancement of technology, single-cell approaches have expanded to encompass other omics, such as genomics, epigenomics, proteomics,and metabolomics.

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ON THE EXPECTED DISCOUNTED PENALTY FUNCTION IN A MARKOV-DEPENDENT RISK MODEL WITH CONSTANT DIVIDEND BARRIER

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Acta Mathematica Scientia 2010年第5期30卷 1481-1491页

作者：刘娟徐建成胡亦钧 college of Mathematics and statistics Hubei Normal University School of Mathematics and statistics Wuhan University

This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given.

关键词： Markov-dependent risk model dividend barrier Cerber-Shiu function integro-differential equation Laplace transform

Asymptotic Optimality of the Nonnegative Garrote Estimator Under Heteroscedastic Errors

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Journal of Systems Science & Complexity 2020年第2期33卷 545-562页

作者： CHEN Xiuping CAI Guanghui GAO Yan ZHAO Shangwei college of statistics and Mathematics Zhejiang Gongshang UniversityHangzhou 310018China Department of statistics College of ScienceMinzu University of ChinaBeijing 100081China

This paper proposes the Nonnegative Garrote(NG)estimator for linear model with heteroscedastic *** the other hand,under some regularity conditions,the authors show the asymptotic optimality of the NG estimator by referring to the idea of the asymptotic optimality of the model average *** results and a real data analysis are reported for testing the results obtained *** results provide a stronger theoretical basis for the use of NG estimator by strengthening existing findings.

关键词： Asymptotic optimality coefficient shrinkage heteroscedastic errors Nonnegative Garrote

Parameter Dependence of Stable Manifolds for Nonuniform (μ, ν)-dichotomies

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Acta Mathematica Sinica,English Series 2013年第6期29卷 1111-1130页

作者： Ji Min ZHANG Meng FAN Xiao Yuan CHANG college of Mathematics Jilin University School of mathematical Sciences Heilongjiang University School of Mathematics and statistics Northeast Normal University School of Applied Sciences Harbin University of Science and Technology

We construct stable invariant manifolds for semiflows generated by the nonlinear impulsive differential equation with parameters x＇= A（t）x ＋ f（t, x, λ）, t≠τi and x（τ＋i） = Bix（τi）＋ gi（x（τi）, λ）, i ∈ N in Banach spaces, assuming that the linear impulsive differential equation x＇= A（t）x, t≠τi and x（τ＋i） = Bix（τi）, i ∈ N admits a nonuniform （μ, ν）-dichotomy. It is shown that the stable invariant manifolds are Lipschitz continuous in the parameter λ and the initial values provided that the nonlinear perturbations f, g are sufficiently small Lipschitz perturbations.

关键词： Stable invariant manifolds nonuniform ( μ ν )-dichotomies impulsive differential equations

AN INTEGRAL ESTIMATE AND THE EQUIVALENT NORMS ON F(p, q, s, k) SPACES IN THE UNIT BALL

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Acta Mathematica Scientia 2018年第6期38卷 1861-1880页

作者：张学军黎深莲尚清丽郭雨婷 college of Mathematics and statistics Hunan Normal University

In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.

关键词： F(p q s k) space integral estimate equivalent norm unit ball

Applications of Burr Ⅲ-Weibull quantile function in reliability analysis

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Statistical Theory and Related Fields 2023年第4期7卷 296-308页

作者： G.S.Deepthy Nicy Sebastian N.Chandra Department of statistics St.Thomas College(Autonomous)Thrissur affiliated to University of CalicutKeralaIndia Department of statistics Ramanujan School of Mathematical SciencesPondicherry UniversityPuducherryIndia

This paper introduces a new family of distributions defined in terms of quantile *** quantile function introduced here is the sum of quantile functions of life time distributions called Burr Ⅲ and *** distributional characteristics and reliability properties are included in the *** of Least Square and Method of L-moments are applied to estimate the parameters of the *** real life data sets are used to illustrate the performance of the model.

关键词： Weibull distribution Burr III distribution quantile density function quantile function hazard quantile function L-moments

Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems

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Chinese Physics B 2017年第3期26卷 215-225页

作者：唐耀宗李小林 college of Mathematics and statistics Kashgar University college of Mathematics Science Chongqing Normal University

We first give a stabilized improved moving least squares （IMLS） approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin method is provided theoretically for both linear and nonlinear elliptic boundary value problems. Finally, numerical examples are given to verify the theoretical analysis.

关键词： meshless method moving least squares approximation element-free Galerkin method error esti-mate