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A New Approach to Nonlinear Partial Differential Equations

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Communications in Nonlinear Science and Numerical Simulation 1997年第4期2卷 230-235页

作者： Jihuan HE (Shanghai University,Shanghai Institute of Applied Mathematics and Mechanics,Shanghai 2 0 0 0 72 ,China) Shanghai University Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

In this paper,a novel method called variational iteration method is proposed to solve nonlinear partial differential equations without linearization or small *** this method,a correction functional is constructed by a general Lagrange multiplier,which can be identified via variational *** analytical solution can be obtained from its trial- function with possible unknown constants,which can be identified by imposing the boundary conditions,by successively iteration.

关键词： Nonlinear Problems Partial Differential Equations Variational Iteration Method Variational Theory

Valued Gabriel quiver of a wedge product and semiprime coalgebras

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Frontiers of Mathematics in China 2013年第5期8卷 1157-1183页

作者： Gabriel NAVARR0 Department of Computer Sciences and AI University of Granada E1 Greco s/n E-51002Ceuta Spain

We describe the valued Gabriel quiver of a wedge product of coalgebras and study the category of comodules of a semiprime coalgebra. In particular, we prove that any monomial semiprime k-tame fc-tame coalgebra is string. We also prove a version of Eisenbud-Griffith theorem for coalgebras, namely, any hereditary semiprime strictly quasi-finite coalgebra is serial.

关键词： Wedge product semiprime coalgebras representation theory,valued Gabriel quiver

Variational Iteration Method for Delay Differential Equations

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Communications in Nonlinear Science and Numerical Simulation 1997年第4期2卷 235-236页

The variational iteration method is shown to be applicable to delay differential equations for analytical approximate solutions

关键词： Variational Iteration Method for Delay Differential Equations

Numerical simulations for G-Brownian motion

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Frontiers of Mathematics in China 2016年第6期11卷 1625-1643页

作者： Jie YANG Weidong ZHA0 School of Mathematics & Finance Institute Shandong University Jinan 250100 China

This paper is concerned with numerical simulations for the G- Brownian motion （defined by S. Peng in Stochastic Analysis and Applications, 2007, 541-567）. By the definition of the G-normal distribution, we first show that the G-Brownian motions can be simulated by solving a certain kind of Hamilton-Jacobi-Bellman （HJB） equations. Then, some finite difference methods are designed for the corresponding HJB equations. Numerical simulation results of the G-normal distribution, the G-Brownian motion, and the corresponding quadratic variation process are provided, which characterize basic properties of the G-Brownian motion. We believe that the algorithms in this work serve as a fundamental tool for future studies, e.g., for solving stochastic differential equations （SDEs）/stochastic partial differential equations （SPDEs） driven by the G-Brownian motions.

关键词： Nonlinear expectation G-Brownian motion G-normal distribu- tion Hamilton-Jacobi-Bellman (HJB) equation

Projected area and drag coefficient of high velocity irregular fragments that rotate or tumble

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Defence Technology（防务技术） 2017年第4期13卷 269-280页

作者： John F. Moxnes 0yvind Fr0 yland Ivar J. 0ye Tom I. Brate Eva Friis Gard 0degardstuen Tallak H. Risdal Norwegian Defence Research Establishment Land Systems Division P.O. Box 25 2027 Kjeller Norway Nammo Raufoss AS P.O. Box 162 2831 Raufoss Norway HPVisTech AS Bj0rnstadgutua 21 2092 Minnesund Norway

3 degrees of freedom(DOF)exterior ballistic computer models are used in fragment studies to calculate individual trajectories of each fragment based on drag coefficient and the projected(presented)area in the direction of velocity of center of *** expectation of a randomly distributed projected area is commonly used for fragments that tumble(random rotation)during *** forecast a model where the expected drag coefficient is dependent of shape and Mach *** or tumbling only affects the expected projected *** of projected areas during tumbling and rotation are *** examination of the data by Mc Cleskey(1988)indicates that the volume of the fragment to the power of2/3 is a better parameter to characterize the drag coefficient of the fragments than the maximum projected *** simulations are used to verify results and to study projected area and drag coefficient of fragments.

关键词： Fragments Form factor Mach number Drag coefficient Cauchy area Tumbling

Lattice-Boltzmann Models for Heat Transfer

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Communications in Nonlinear Science and Numerical Simulation 1997年第4期2卷 212-216页

作者： Chenghai SUN,Zujun XU,Baoguo WANG &Mengyu SHEN (Dept. of Engineering Mechanics,Tsing- hua University,Beijing,1 0 0 0 84) Department of Engineering Mechanics Tsinghua University Beijing 100084 China

A multispeed heat transfer lattice Boltzmann model is presented. The model possesses the perfect gas state equation with arbitrary special heat ratio. The macroscopic conservation equations are derived by the Chapman- Enskog *** one dimensional simulation for the sinusoidal energy distributions are compared with the theoretical results, showing good *** theoretical conductivity in the energy equation is in accordance with the simulations.

关键词： Lattice Boltzmann heat transfer perfect gas

Classification of hypersurfaces with two distinct principal curvatures and closed Mbius form in S^(m+1)

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Science China Mathematics 2012年第7期55卷 1463-1478页

作者： LINLiMiao GU0Zhen DepartmentofMathematics EastChinaNormalUniversityShanghai200241China DepartmentofMathematics YunnanNormalUniversityKunming650092China

Let x be an m-dimensional umbilic-free hypersurface in an （m＋1）-dimensional unit sphere Sm＋l （m≥3）. In this paper, we classify and explicitly express the hypersurfaces with two distinct princi- pal curvatures and closed MSbius form, and then we characterize and classify conformally flat hypersurfaces of dimension larger than 3.

关键词： moebius geometry principal curvature conformally fiat MSbius form

SOFTWARE-CONTROLLED SYSTEM OF ULTRA-PRECISION MACHINING AXISYMMETRIC ASPHERIC MIRROR

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Chinese Journal of Mechanical Engineering 2006年第2期19卷 256-259页

作者： GU0 Yinbiao　 WEI Lizhen Department of Mechanical and Electrical Engineering Xiamen UniversityXiamen 361005 China

In order to improve machining accuracy and efficiency, a software-controlled system of ultra-precision machining for axisymmetric aspheric mirror, using techniques of error compensation, remote transmission and modularization, is designed based on industrial PC, Windows 2000 work platform and Visual Basic 6.0. By experiments, this system realizes functions of ultra-precision machining, machining error compensation, remote data transmission and automatic data transformation among first machining, compensation machining and accuracy measurement. The actual application shows that error compensation improves machining accuracy, remote transmission improves machining efficiency while modularization avoids repeated work and improves design efficiency. Therefore, the system has met ultra-precision machining need for aspheric mirror.

关键词： Aspheric surface machining Error compensation Remote transmission Visual Basic

Effects of Bentonite,Hydrogel and Biochar Amendments on Soil Hydraulic Properties from Saturation to Oven Dryness

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Pedosphere 2019年第5期29卷 598-607页

作者： Osama M0HAWESH Wolfgang DURNER Department of Plant Production Faculty of AgricultureMutah UniversityKarak 61710 (Jordan) Division of Environmental Science and Technology Graduate School of AgricultureKyoto UniversityKyoto 6110011 (Japan) Institute of Geoecology Technical University of BraunschweigLanger Kamp 19cBraunschweig 38106 (Germany)

Effects of hydrogel, bentonite, and biochar as soil amendments on soil hydraulic properties and improving water availability from saturation to oven dryness were investigated. Soils were mixed with hydrogel (0.10%, 0.25%, and 0.50%), bentonite (0.5%, 1.0%, and 2.5%), and biochar (1.0%, 2.5%, and 5.0%) as soil amendments (weight:weight). Three methods (extended multistep outflow (XMSO), evaporation (EVA), and WP4 dewpoint potentiometer) were used to measure soil hydraulic properties from saturation to oven dryness. The cumulative XMSO results were more uniform across all the applied pressure steps for the amended soils. The EVA exhibited a shorter linear decrease during the first evaporation stage and a lower evaporation rate during the second evaporation stage. The WP4 results also exhibited that soil amendments increased the soil water content of the amended soils at low matric potentials. The results of soil water retention curves revealed that the unamended soil retained less water at any matric potential compared to the amended soils. Soil hydraulic conductivity decreased with increasing amount of soil amendments. The saturated hydraulic conductivity was higher for the unamended soil than the soils amended w计h 2.5% bentonite, 0.50% hydrogel, and 5.0% biochar by 11, 3, and 18 times, respectively. These results suggested that soil amendments improved soil water retentivity, which confirmed the appropriateness of these soil amendments for potential use in sandy soil improvements. However, field experiments and economical perception studies should be considered for further investigation.

关键词： evaporation extended multistep outflow soil amendment soil matric potential soil moisture soil water retentivity water availability WP4 dewpoint potentiometer