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Chinese Physics Letters 2013年第12期30卷 62-66页

作者：郭亮刘国强夏慧陈晶 Institute of Electrical Engineering Chinese Academy of SciencesBeijing 100190 University of Chinese Academy of Sciences Beijing 100190 College of Control Theory and Engineering China University of PetroleumQingdao 266555

Magneto-acousto-electric tomography(MAET)is known as a method of impedance tomography,with the procedure of acoustic waves propagating in a static magnetic field and producing the electric signal attributing to Lorentz force.We analyze the method of calculating the electric signal with given sound sources and magnetic field in the radially stratified medium of conductivity.It consists of finding an analytic solution of the sound propagating in homogeneous acoustic medium and applying to the data one of the algorithms(the FD method)for the electric scalar potential field.The ideal well logging model is considered in our algorithm,which is very different from the ordinary one in arrangement of the sound sources and electrodes in medical tomography.Combining the analytical and numerical methods in coupled fields for the well logging model is a stable algorithm in forward procedure of MAET.

关键词： field propagating ordinary

Heat Transfer in a Moving Fluid over a Moving Non-Isothermal Flat Surface

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Chinese Physics Letters 2011年第12期28卷 183-186页

作者： Swati Mukhopadhyay Department of Mathematics The University of BurdwanBurdwan-713104W.B.India

Boundary layer forced convective flow and heat transfer passing a moving flat surface parallel to a moving stream are presented.The power-law surface temperature of the second degree at the boundary is described.The similarity solutions for the problem are obtained and the reduced ordinary differential equations are solved numerically.The numerical results are compared with the known results from the literature for some special cases of the present study to support their validity.It is found that dual solutions exist when the surface and the fluid move in opposite directions.

关键词： moving ordinary directions

Cavitating Flow over a Mini Hydrofoil

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Chinese Physics Letters 2012年第1期29卷 198-201页

作者：罗先武季斌张瑶许洪元 State Key Laboratory for Hydroscience and Engineering Tsinghua UniversityBeijing 100084 China Ship Development and Design Center Wuhan 430064

We consider a cavitating flow over a mini hydrofoil (foil profile:Clark-Y-11.7) having a 14mm chord length in a cavitation tunnel at various cavitation numbers.Experimental observations show that cavitating flows over a miniature hydrofoil display several types of cavitation behavior,such as cavitation inception,sheet cavitation,cloud cavitation and super cavitation with the decreasing cavitation number.Under the same cavitation conditions,cavitation over a mini hydrofoil would be suppressed in comparison to cavitation over an ordinary hydrofoil.This cavitation scale effect is suspected to be caused by the Reynolds number.

关键词： number cavitation ordinary

Wearing Face Masks--the Simple and Effective Way to Block the Infection Source of COVID-19

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China CDC weekly 2020年第16期2卷 268-269页

作者： Tianxing Jiang Hao Wang George F.Gao Xiaoming Jiang China University of Geosciences BeijingChina National Center for Nanoscience and Technology CASBeijingChina Chinese Center for Disease Control and Prevention BeijingChina Beijing Advanced Science and Innovation Center CASBeijingChina Institute of High Energy Physics CASBeijingChina.

The key difference between the coronavirus disease 2019(COVID-19)and previous coronaviruses such as SARS and MERS is that some infected people do not display obvious symptoms but are contagious during the incubation period for 14 days(1)or longer.Recently,there are many discussions about whether all persons should wear masks when they go out during the COVID-19 pandemic.The main reasons for the opposition are that the effectiveness of masks in preventing infection is not clear,ordinary people rarely wear masks correctly,everyone wearing masks may cause social panic,there are not enough masks,etc.(2–3).

关键词： everyone discussions ordinary

Nonlinear versus linearised model on stand density model fitting and stand density index calculation: analysis of coefficients estimation via simulation

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Journal of Forestry Research 2019年第5期30卷 1595-1602页

作者： Maurizio Marchi CREA-Research Centre for Forestry and Wood geoLAB-Laboratory of Forest Geomatics Department of Agriculture Food Environment and Forestry Università degli Studi di Firenze

The stand density index,one of the most important metrics for managing site occupancy,is generally calculated from empirical data by means of a coefficient derived from the“self-thinning rule”or stand density model.I undertook an exploratory analysis of model fitting based on simulated data.I discuss the use of the logarithmic transformation(i.e.,linearisation)of the relationship between the total number of trees per hectare(N)and the quadratic mean diameter of the stand(QMD).I compare the classic method used by Reineke(J Agric Res 46:627–638,1933),i.e.,linear OLS model fitting after logarithmic transformation of data,with the“pure”powerlaw model,which represents the native mathematical structure of this relationship.I evaluated the results according to the correlation between N and QMD.Linear OLS and nonlinear fitting agreed in the estimation of coefficients only for highly correlated(between-1 and-0.85)or poorly correlated([-0.39)datasets.At average correlation values(i.e.,between-0.75 and-0.4),it is probable that for practical applications,the differences were relevant,especially concerning the key coefficient for Reineke’s stand density index calculation.This introduced a non-negligible bias in SDI calculation.The linearised log–log model always estimated a lower slope term than did the exponent of the nonlinear function except at the extremes of the correlation range.While the logarithmic transformation is mathematically correct and always equivalent to a nonlinear model in case of prediction of the dependent variable,the difference detected in my studies between the two methods(i.e.,coefficient estimation)was directly related to the correlation between N and QMD in each simulated/disturbed dataset.In general,given the power law as the“natural”structure of the N versus QMD relationship,the nonlinear model is preferred,with a logarithmic transformation used only in the case of violation of parametric assumptions(e.***.data distributed non-normally).

关键词： ordinary least squares Power law Reineke function Silviculture Ecological mathematics Forest mathematics

Damped and Divergence Exact Solutions for the Duffing Equation Using Leaf Functions and Hyperbolic Leaf Functions

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Computer Modeling in Engineering & Sciences 2019年第3期118卷 599-647页

作者： Kazunori Shinohara Daido University 10-3 Takiharu-choMinami-kuNagoya 457-8530Japan

According to the wave power rule,the second derivative of a functionχ(t)with respect to the variable t is equal to negative n times the functionχ(t)raised to the power of 2n?1.Solving the ordinary differential equations numerically results in waves appearing in the figures.The ordinary differential equation is very simple;however,waves,including the regular amplitude and period,are drawn in the figure.In this study,the function for obtaining the wave is called the leaf function.Based on the leaf function,the exact solutions for the undamped and unforced Duffing equations are presented.In the ordinary differential equation,in the positive region of the variableχ(t),the second derivative d^2χ(t)/dt^2 becomes negative.Therefore,in the case that the curves vary with the time under the conditionχ(t)>0,the gradient dχ(t)/d constantly decreases as time increases.That is,the tangential vector on the curve of the graph(with the abscissa and the ordinate χ(t)changes from the upper right direction to the lower right direction as time increases.On the other hand,in the negative region of the variableχ(t),the second derivative d^2χ(t)/dt^2 becomes positive.The gradient d χ(t)/d constantly increases as time decreases.That is,the tangent vector on the curve changes from the lower right direction to the upper right direction as time increases.Since the behavior occurring in the positive region of the variable χ(t)and the behavior occurring in the negative region of the variableχ(t)alternately occur in regular intervals,waves appear by these interactions.In this paper,I present seven types of damped and divergence exact solutions by combining trigonometric functions,hyperbolic functions,hyperbolic leaf functions,leaf functions,and exponential functions.In each type,I show the derivation method and numerical examples,as well as describe the features of the waveform.

关键词： Leaf functions hyperbolic leaf functions lemniscate functions jacobi elliptic functions ordinary differential equations duffing equation nonlinear equations

Exact Solutions of the Cubic Duffing Equation by Leaf Functions under Free Vibration

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Computer Modeling in Engineering & Sciences 2018年第5期115卷 149-215页

作者： Kazunori Shinohara Daido University 10-3 Takiharu-choMinami-kuNagoya 457-8530Japan

Exact solutions of the cubic Duffing equation with the initial conditions are presented.These exact solutions are expressed in terms of leaf functions and trigonometric functions.The leaf function r=sleafn(t)or r=cleafn(t)satisfies the ordinary differential equation dx2/dt2=-nr2n-1.The second-order differential of the leaf function is equal to-n times the function raised to the(2n-1)power of the leaf function.By using the leaf functions,the exact solutions of the cubic Duffing equation can be derived under several conditions.These solutions are constructed using the integral functions of leaf functions sleaf2(t)and cleaf2(t)for the phase of a trigonometric function.Since the leaf function and the trigonometric function are used in combination,a highly accurate solution of the Duffing equation can be easily obtained based on the data of leaf functions.In this study,seven types of the exact solutions are derived from leaf functions;the derivation of the seven exact solutions is detailed in the paper.Finally,waves obtained by the exact solutions are graphically visualized with the numerical results.

关键词： Duffing equation nonlinear equations ordinary differential equation leaf functions

The double reflection on the interface of uniaxial crystals in the Savart polariscope

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Science China(Physics,Mechanics & Astronomy) 2009年第7期52卷 1003-1006页

作者： WU JunFang1,2 & ZHANG ChunMin1 1 School of Science, Xi’an Jiaotong University, Xi’an 710049, China 2 School of Science, Xi’an Polytechnic University, Xi’an 710048, China School of Science Xi’an Jiaotong University Xi’an China School of Science Xi’an Polytechnic University Xi’an China

The reflection in the Savart polariscope is different from the isotropic medium. The double reflection of rays in the Savart polariscope is analyzed and discussed on the basis of the Snell law. The double reflection formulae of the extraordinary ray and the ordinary ray are given. These results may provide a theoretical and practical guide for studying, developing and engineering polarization interference imaging spectrometers.

关键词： the Savart polariscope double reflection the Snell law extraordinary ray ordinary ray

Conjugation-uniqueness of exact Borel subalgebras

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Science China Mathematics 1999年第12期42卷 1246-1250页

作者：张跃辉 Information College of Hainan University Haikou China

It is proved that the exact Borel subalgebras of a basic quasi-hereditary algebra are conjugate to each other. Moreover, the inner automorphism group of a basic quasi-hereditary algebra acts transitively on the set of... 详细信息

关键词： quasi-hereditary algebra exact Borel subalgebra basic algebra ordinary quiver G-subalgebra.

A New Integrable (2+1)-Dimensional Generalized Breaking Soliton Equation:N-Soliton Solutions and Traveling Wave Solutions

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Communications in Theoretical Physics 2016年第10期65卷 385-388页

作者： Abdul-Majid Wazwaz Department of Mathematics Saint Xavier University

In this work,we study a new(2+1)-dimensional generalized breaking soliton equation which admits the Painleve property for one special set of parameters.We derive multiple soliton solutions,traveling wave solutions,and... 详细信息

关键词： soliton breaking simplified traveling bilinear singular earlier ordinary auxiliary chaos