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Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations

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Science China(Physics,Mechanics & Astronomy) 2006年第6期49卷 716-728页

作者： WANG Shunjin ZHANG Hua Center of Theoretical Physics Sichuan UniversityChengdu610064China Center of Theoretical PhysicsSichuan UniversityChengdu610064China

The problem of preserving fidelity in numerical computation of nonlinear or-dinary differential equations is studied in terms of preserving local differential structure and approximating global integration structure of the dynamical system. The ordinary differen-tial equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics,and a new algorithm——algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential equations by the alge-braic dynamics method. In the new algorithm,the time evolution of the ordinary differential system is described locally by the time translation operator and globally by the time evo-lution operator. The exact analytical piece-like solution of the ordinary differential equa-tions is expressd in terms of Taylor series with a local convergent radius,and its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm and Symplectic Geometric Algorithm.

关键词： exact algebraic dynamics solutions of ordinary differential equations,algebraic dynamics algorithm,preserving fidelity geometrically and dynamically.

Computational uncertainty principle in nonlinear ordinary differential equations (I)——Numerical results

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Science China(Technological Sciences) 2000年第5期43卷 449-460,561页

作者：李建平曾庆存丑纪范 State Key Laboratory of Numerical Modelling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG) Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China Department of Atmospheric Sciences Lanzhou University Lanzhou 730000 China

In a majority of cases of long-time numerical integration for initial-value problems, roundoff error has received little attention. Using twenty-nine numerical methods, the influence of round-off error on numerical solutions is generally studied through a large number of numerical experiments. Here we find that there exists a strong dependence on machine precision (which is a new kind of dependence different from the sensitive dependence on initial conditions), maximally effective computation time (MECT) and optimal stepsize (OS) in solving nonlinear ordinary differential equations (ODEs) in finite machine precision. And an optimal searching method for evaluating MECT and OS under finite machine precision is presented. The relationships between MECT, OS, the order of numerical method and machine precision are found. Numerical results show that round-off error plays a significant role in the above phenomena. Moreover, we find two universal relations which are independent of the types of ODEs, initial values and numerical schemes. Based on the results of numerical experiments, we present a computational uncertainty principle, which is a great challenge to the reliability of long-time numerical integration for nonlinear ODEs.

关键词： ordinary differential equations (ODEs) computational uncertainty principle round-off error discretization error strong dependence on machine precision maximally effective computation time (MECT) optimal stepsize (OS) universal relation no

Homophily Exclusion or Homophily Preference? The Influence of the Executive Identity of Nonexecutive Directors on the Focal Firm Executive Pay and ordinary Employee Pay

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Journal of Systems Science and Information 2019年第6期10卷 550-567页

作者： Shuai FANG Guanghua School of Management Peking UniversityBeijing 100871China

The occupational identity of nonexecutive directors exerts a considerable influence on their way of designing and distributing executive pay as well as ordinary employee pay in the focal *** the status characteristics theory into the corporate governance literature,I theorize that status contest effect comes into play in the process of setting executive pay in the focal firm,specifically when its nonexecutive directors serve as executives on *** often than not,such executive identity triggers the status competition with focal firm executives,which motivates nonexecutive directors to reduce the focal firm executive pay so as to secure and aggrandize their own status within the focal ***,since ordinary employees pose no threat to nonexecutive directors in the focal firm,they tend to increase ordinary employee *** upon the empirical test which adopts the data of China’s Shanghai and Shenzhen A-share listed firms,I find that the greater the focal firm’s nonexecutive director ratio,the less will be the top executives’pay in the focal firm;the greater the focal firm’s nonexecutive director ratio,the greater will be ordinary employees’pay in the focal firm;the greater the focal firm’s nonexecutive director ratio,the smaller will be the pay gap between top executives and ordinary employees in the focal *** addition,I also find that ownership power and gender can moderate the relationship between nonexecutive director ratio and executive pay:top executive ownership can alleviate the negative relationship between focal firm’s nonexecutive directors and top executives’pay;female nonexecutive directors are more likely to increase focal firm’s ordinary employee pay than their male counterparts.

关键词： nonexecutive director status contest executive pay ordinary employee pay

NEW PROGRESS IN THEORY OF SURFACES DEFINED BY ordinary DIFFERENTIAL EQUATIONS~*

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Chinese Science Bulletin 1989年第10期34卷 800-803页

作者：秦元勋 Institute of Applied Mathematics Academia Sinica Beijing Department of MathematiesUniversity of Florida GainesuilleUSA

Here singular points of the system (E_n~*) includes both finite and infinite singular points defined by H. Poincare, but extended to complex domain.

关键词： nonlinear ordinary differential equations strong rooted theorem general integral representation theorem Hilbert number N(n).

SINGULAR PERTURBATIONS OF BOUNDARY VALUE PROBLEMS FOR THIRD ORDER NONLINEAR ordinary DIFFERENTIAL EQUATIONS

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Acta Mathematica Scientia 1988年第1期8卷 95-108页

作者：赵为礼 Dept. of Math. Changchun Jilin Univ.

In this paper we obtain some results about the convergence of aolutions of the boundary value problems of the third order nonlinear ordinary differential equation with a small parameter ε>0: (i=0, 1, 2) to a solution of their reduced problem as ε→0, hero z=ψ(t, x, y) is a root of the equation f(t, x, y, z, 0)=0, and about the existence of solutions of the reduced problem. In addition, under certain conditions we prove the existence of solutions of the boundary value problems (1), (2) (i=1, 2), and give their asymptotic estimations.

关键词： ordinary asymptotic proof singular nonnegative 一葵 bounds integers depen globally

EXISTENCE OF BOUNDED SOLUTIONS OF SINGULAR ordinary DIFFERENTIAL EQUATIONS

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Chinese Science Bulletin 1992年第21期37卷 1844-1845页

作者：章熙康 Department of Mathematics Nanjing University Nanjing 210008 PRC

We deal with the bounded solution problems of the ordinary differential equations with

关键词： ordinary hasbeen letter norms locally

Mapping Soil Electrical Conductivity Using ordinary Kriging Combined with Back-propagation Network

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Chinese Geographical Science 2019年第2期29卷 270-282页

作者： HUANG Yajie LI Zhen YE Huichun ZHANG Shiwen ZHUO Zhiqing XING An HUANG Yuanfang Key Laboratory of Arable Land Conservation (North China) Ministry of Agriculture/Key Laboratory of Agricultural Land Quality Monitoring Ministry of Land and Resources College of Resources and Environmental Sciences China Agricultural University Key Laboratory of Digital Earth Science Institute of Remote Sensing and Digital Earth Chinese Academy of Sciences School of Earth and Environment Anhui University of Science and Technology

Accurate mapping of soil salinity and recognition of its influencing factors are essential for sustainable crop production and soil health. Although the influencing factors have been used to improve the mapping accuracy of soil salinity, few studies have considered both aspects of spatial variation caused by the influencing factors and spatial autocorrelations for mapping. The objective of this study was to demonstrate that the ordinary kriging combined with back-propagation network(OK_BP), considering the two aspects of spatial variation, which can benefit the improvement of the mapping accuracy of soil salinity. To test the effectiveness of this approach, 70 sites were sampled at two depths(0–30 and 30–50 cm) in Ningxia Hui Autonomous Region, China. ordinary kriging(OK), back-propagation network(BP) and regression kriging(RK) were used in comparison analysis; the root mean square error(RMSE), relative improvement(RI) and the decrease in estimation imprecision(DIP) were used to judge the mapping quality. Results showed that OK_BP avoided the both underestimation and overestimation of the higher and lower values of interpolation surfaces. OK_BP revealed more details of the spatial variation responding to influencing factors, and provided more flexibility for incorporating various correlated factors in the mapping. Moreover, OK_BP obtained better results with respect to the reference methods(i.e., OK, BP, and RK) in terms of the lowest RMSE, the highest RI and DIP. Thus, it is concluded that OK_BP is an effective method for mapping soil salinity with a high accuracy.

关键词： ordinary kriging neural network soil electrical conductivity variability mapping Ningxia,China

Re-recognition of Street from the Perspective of Globalization, Localization, and Marginality: A Review of City, Street and Citizen: The Measure of the ordinary

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China City Planning Review 2019年第2期28卷 73-76页

作者： Liu Jiayan Li Caige Urban Planning Department School of Architecture Tsinghua University

City,Street and Citizen:The Measure of the ordinary Author:Suzanne Hall Year:2012Publisher:Routledge ISBN:978-0-415-68865-9(176 pages,in English)*** streets from a marginal perspective Streets are the most common space in a ***,it is these countless streets that constitute the spatial stage for the social life of the general public in a ***,socially speaking,streets also act as an essential part that builds the public sphere of a city.

关键词： The Measure of the ordinary and Marginality A Review of City Street and Citizen

ordinary and innovation: Insights from a child psychiatrist

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Pediatric Investigation 2020年第2期4卷 77-78页

作者： Yonghua Cui Yi Zheng Department of Psychiatry Beijing Children’s HospitalCapital Medical UniversityNational Center for Children’s HealthBeijingChina Beijing Anding Hospital Capital Medical UniversityBeijingChina

“ordinary and innovation”are two words that seem ***,they are well integrated from a doctor’s *** takes more years to learn as a medical student than as an ordinary college student,and the boring and mundane life of learning breed *** seemingly mundane day‐to‐day patient‐treating work is full of *** who withstand the ordinary can achieve *** shines in ordinary *** particular,for a child psychiatrist,ignorance and discrimination among others are mixed with the *** makes the flash of innovation more dazzling and valuable.

关键词： breed ordinary words