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Efficient algorithm for principal eigenpair of discrete p-Laplacian

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Frontiers of Mathematics in China 2018年第3期13卷 509-524页

作者： mu-Fa CHEN School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems (Beijing Normal University) Ministry of Education Beijing 100875 China

This paper is a continuation of the author＇s previous papers [Front. Math. China, 2016, 11（6）： 1379-1418; 2017, 12（5）： 1023-1043], where the linear case was studied. A shifted inverse iteration algorithm is introduced, as an acceleration of the inverse iteration which is often used in the non-linear context （the p-Laplacian operators for instance）. Even though the algorithm is formally similar to the Rayleigh quotient iteration which is well-known in the linear situation, but they are essentially different. The point is that the standard Rayleigh quotient cannot be used as a shift in the non-linear setup. We have to employ a different quantity which has been obtained only recently. As a surprised gift, the explicit formulas for the algorithm restricted to the linear case （p = 2） is obtained, which improves the author＇s approximating procedure for the leading eigenvalues in different context, appeared in a group of publications. The paper begins with p-Laplacian, and is closed by the non-linear operators corresponding to the well-known Hardy-type inequalities.

关键词： Discrete p-Laplacian principal eigenpair shifted inverse iteration approximating procedure

Spectral Gap and Logarithmic Sobolev Constant for Continuous Spin Systems

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Acta Mathematica Sinica,English Series 2008年第5期24卷 705-736页

作者： mu Fa CHEN School of Mathematical Sciences Beijing Normal University Beijing 100875 P. R. China

The aim of this paper is to study the spectral gap and the logarithmic Sobolev constant for continuous spin systems. A simple but general result for estimating the spectral gap＇of finite dimensional systems is given by Theorem 1.1, in terms of the spectral gap for one-dimensional marginals. The study of this topic provides us a chance, and it is indeed another aim of the paper, to justify the power of the results obtained previously. The exact order in dimension one （Proposition 1.4）, and then the precise leading order and the explicit positive regions of the spectral gap and the logarithmic Sobolev constant for two typical infinite-dimensional models are presented （Theorems 6.2 and 6.3）. Since we are interested in explicit estimates, the computations become quite involved. A long section （Section 4） is devoted to the study of the spectral gap in dimension one.

关键词： spectral gap logarithmic Sobolev constant spin system principal eigenvalue

A POSITIVITY-PRESERVING FINITE ELEMENT METHOD FOR QUANTUM DRIFT-DIFFUSION MODEL

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Journal of Computational Mathematics 2023年第5期41卷 909-932页

作者： Pengcong mu Weiying Zheng School of Mathematical Science University of Chinese Academy of SciencesBeijing 100049China LSEC NCMISInstitute of Computational Mathematics and Scientific ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

In this paper,we propose a positivity-preserving finite element method for solving the three-dimensional quantum drift-diffusion *** model consists of five nonlinear elliptic equations,and two of them describe quantum corrections for quasi-Fermi *** propose an interpolated-exponential finite element(IEFE)method for solving the two quantum-correction *** IEFE method always yields positive carrier densities and preserves the positivity of second-order differential operators in the Newton linearization of quantum-correction ***,we solve the two continuity equations with the edge-averaged finite element(EAFE)method to reduce numerical oscillations of quasi-Fermi *** Poisson equation of electrical potential is solved with standard Lagrangian finite *** prove the existence of solution to the nonlinear discrete problem by using a fixed-point iteration and solving the minimum problem of a new discrete functional.A Newton method is proposed to solve the nonlinear discrete *** experiments for a three-dimensional nano-scale FinFET device show that the Newton method is robust for source-to-gate bias voltages up to 9V and source-to-drain bias voltages up to 10V.

关键词： Quantum drift-diffusion model Positivity-preserving finite element method Newton method FinFET device High bias voltage

Global algorithms for maximal eigenpair

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Frontiers of Mathematics in China 2017年第5期12卷 1023-1043页

作者： mu-Fa CHEN School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics andComplex Systems (Beijing Normal University) Ministry of Education Beijing 100875 China

This paper is a continuation of our previous work [Front. Math. China, 2016, 11（6）： 1379-1418] where an efficient algorithm for computing the maximal eigenpalr was introduced first for tridiagonal matrices and then extended to the irreducible matrices with nonnegative off-diagonal elements. This paper introduces mainly two global algorithms for computing the maximal eigenpair in a rather general setup, including even a class of real （with some negative off-diagonal elements） or complex matrices.

关键词： Maximal eigenpair shifted inverse iteration global algorithm

Effects of Organic Matter-Rich Amendments on Selenium Mobility in Soils

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Pedosphere 2019年第6期29卷 740-751页

作者： Petra SMAZíková Luká? PRAUS Jirina SZáková Jana TREMLOVá Ale? HANC Pavel TLUSTOS Department of Agro-Environmental Chemistry and Plant Nutrition Faculty of Agrobiology Food and Natural Resources Czech University of Life Sciences Prague

Soil organic matter (SOM) plays an important role in the Se dynamics in soil. The potential effects of vermicompost and digestate as important sources of SOM on selenium (Se) mobility were assessed in this study. Three soils differing in their physicochemical parameters, fluvisol, chernozem, and luvisol, were chosen, and three types of vermicomposts based on various bio-waste materials as digestate (vermicompost 1), kitchen waste with woodchips (vermicompost 2), and garden bio-waste (vermicompost 3) were used due to their high organic matter content. Additionally, digestate samples alone were applied. To evaluate the potential effect of vermicompost application on sorption characteristics of soils, batch sorption experiments were performed. The results showed a predominant effect on Se species in the soils, where selenite sorbed more intensively compared to selenate, regardless of the soil and ameliorative material applied. In the control, the soil sorption ability of selenite tended to decrease in the order: fluvisol > luvisol > chernozem. However, these differences were not significant. Moreover, the effects of the ameliorative materials depended on both soil and amendment used. In fluvisol, all the amendment applications resulted in a decrease in distribution coefficient ( K d values) of Se, whereas in chernozem, this effect was observed only for the digestate-based vermicompost 1. Increasing K d levels were reported in luvisol treated with digestate;the application of garden bio-waste-based vermicompost 3 tended to decrease the K d values. Further studies are required on long-term effects of these amendments on Se mobility in soils and the role of individual organic matter fractions in this context.

关键词： Batch sorption experiments Bio-waste material Selenite Selenate Sorption isotherms Vermicompost

Analysis of liquid bridge between spherical particles

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China Particuology 2007年第6期5卷 420-424页

作者： Fusheng mu Xubin Su College of Mechanical and Electrical Engineering Central South University Changsha 410083 China

A pair of central moving spherical particles connected by a pendular liquid bridge with interstitial Newtonlan fluid is otten encountered in particulate coalescence process. In this paper, by assuming perfect-wet condition, the effects of liquid volume and separation distance on static liquid bridge are analyzed, and the relation between rupture energy and liquid bridge volume is also studied. These points would be of significance in industrial processes related to adhesive particles.

关键词： Surface-wet Liquid bridge force Rupture energy Viscous force

The Optimal Constant in Hardy-type Inequalities

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Acta Mathematica Sinica,English Series 2015年第5期31卷 731-754页

作者： mu-Fa CHEN School of Mathematical Sciences Beijing Normal University

To estimate the optimal constant in Hardy-type inequalities, some variational formulas and approximating procedures are introduced. The known basic estimates are improved considerably. The results are illustrated by typical examples. It is shown that the sharp factor is meaningful for each finite interval and a classical sharp model is re-examined.

关键词： Hardy-type inequality optimal constant variational formulas approximating procedure

Developing nonlinear adaptive optimal regulators through an improved neural learning mechanism

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Science China(Information Sciences) 2017年第5期60卷 252-254页

作者： Ding WANG Chaoxu mu The State Key Laboratory of Management and Control for Complex Systems Institute of AutomationChinese Academy of Sciences Tianjin Key Laboratory of Process Measurement and Control School of Electrical and Information EngineeringTianjin University

Optimal feedback design of dynamical systems is a significant topic in automatic control community and information *** for nonlinear systems,optimal control design always leads to coping with the nonlinear Hamilton-Jacobi-Bellman ***,it is intractable to acquire the analytic solution of the nonlinear Hamilton-JacobiBellman equation for general nonlinear systems.

关键词： Developing nonlinear adaptive optimal regulators through an improved neural learning mechanism

Recent advances in drug delivery applications of cubosomes,hexosomes,and solid lipid nanoparticles

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Acta Pharmaceutica Sinica B 2021年第4期11卷 871-885页

作者： Anan Yaghmur Huiling mu Department of Pharmacy Faculty of Health and Medical SciencesUniversity of CopenhagenUniversitetsparken 2CopenhagenФ2100Denmark

The use of lipid nanocarriers for drug delivery applications is an active research area,and a great interest has particularly been shown in the past two *** different lipid nanocarriers,ISAsomes(Internally self-assembled somes or particles),including cubosomes and hexosomes,and solid lipid nanoparticles(SLNs)have unique structural features,making them attractive as nanocarriers for drug *** this contribution,we focus exclusively on recent advances in formation and characterization of ISAsomes,mainly cubosomes and hexosomes,and their use as versatile nanocarriers for different drug delivery ***,the advantages of SLNs and their application in oral and pulmonary drug delivery are discussed with focus on the biological fates of these lipid nanocarriers in *** the demonstrated advantages in in vitro and in vivo evaluations including preclinical studies,further investigations on improved understanding of the interactions of these nanoparticles with biological fuids and tissues of the target sites is necessary for effcient designing of drug nanocarriers and exploring potential clinical applications.

关键词： Biological fate Cubosomes Drug delivery Hexosomes Inverse non-lamellar liquid crystalline phases Nano-self-assemblies Solid crystalline phases Solid lipid nanoparticles