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Computer Modeling in Engineering & Sciences 2015年第1期104卷 69-85页

作者： Jinsheng Wang Liqing Liu Yiming Chen Lechun Liu Dayan Liu School of Continuing Education Yanshan UniversityQinhuangdao066004HebeiChina College of Science Yanshan UniversityQinhuangdao066004HebeiChina INSA Centre Val de Loire Universitéd’OrléansPRISME EA 4229Bourges 18022 France

The aim of this paper is to seek the numerical solution of a class of variable order fractional integral-differential equation in terms of Bernstein *** fractional derivative is described in the Caputo *** kinds of operational matrixes of Bernstein polynomials are introduced and are utilized to reduce the initial equation to the solution of algebraic equations after dispersing the *** solving the algebraic equations,the numerical solutions are *** method in general is easy to implement and yields good *** examples are provided to demonstrate the validity and applicability of the method.

关键词： Bernstein polynomials variable order fractional integral-differentialequation operational matrix numerical solution convergence analysis the absolute error

Properties of Complex Oscillation of Solutions of a Class of Higher order Linear Differential Equations

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Chinese Annals of Mathematics,Series B 2020年第1期41卷 27-36页

作者： Jianren LONG Yezhou LI School of Computer Science and School of Science Beijing University of Posts and TelecommunicationsBeijing 100876China School of Mathematical Science Guizhou Normal UniversityGuiyang 550001China School of Science Beijing University of Posts and TelecommunicationsBeijing 100876China

Let A(z)be an entire function withμ(A)<1/2 such that the equation f^(k)+A(z)f=0,where k≥2,has a solution f with λ(f)<μ(A),and suppose that A1=A+h,where h■0 is an entire function with ρ(h)<μ(A).Then g^(k)+A1(z)g... 详细信息

关键词： Complex differential equations Entire function order of growth Exponent of convergence of the zeros

ERA modal identification method for hydraulic structures based on order determination and noise reduction of singular entropy

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Science China(Technological Sciences) 2009年第2期52卷 400-412页

作者： LIAN JiJian LI HuoKun ZHANG JianWei School of Civil Engineering Tianjin UniversityTianjin 300072China School of Civil Engineering Nanchang UniversityNanchang 330031China

Modal parameter has been considered as one of the indices in assessing the working state of hydraulic structures. The method for obtaining the modal parameter indices is crucial for health monitoring of hydraulic structures. Traditionally, model parameters are measured from the prototype dynamic test under the excitation of special equipment. The preparation is time-consuming and the method is difficult to carry out. We propose a method in this paper to denoise, reconstruct, determine the order and identify modal parameters based on singular entropy (SE) of eigenmatrix. It can be used to solve the problem of system eigenmatrix order determination, and to identify the modal order and the characteristics of structures under the working state. Finally, this method is applied to identify the operational modal parameters of Ertan arch dam under different flood discharging states and vibration frequencies of the powerhouse with a two-row placed unit in Lijiaxia hydropower station during the unit halting process. This new method provides a simple way to identify the modal parameters of large-scale hydraulic structures under ambient excitation.

关键词： hydraulic structure eigenmatrix singular entropy order determination operational modal arch dam powerhouse with two-row placed unit

Costate estimation for dynamic systems of the second order

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Science China(Technological Sciences) 2009年第3期52卷 752-760页

作者： WEN Hao JIN DongPing HU HaiYan Institute of Vibration Engineering Research MOE Key Lab of Structure Mechanics and Control for AircraftNanjing University of Aeronautics and AstronauticsNanjing 210016China

The dynamics of a mechanical system in the Lagrange space yields a set of differential equations of the second order and involves much less variables and constraints than that described in the state space. This paper presents a so-called Legendre pseudo-spectral (PS) approach for directly estimating the costates of the Bolza problem of optimal control of a set of dynamic equations of the second order. Under a set of closure conditions, it is proved that the Karush-Kuhn-Tucker (KKT) multipliers satisfy the same conditions as those determined by collocating the costate equations of the second order. Hence, the KKT multipliers can be used to estimate the costates of the Bolza problem via a simple linear map- ping. The proposed approach can be used to check the optimality of the direct solution for a trajectory optimization problem involving the dynamic equations of the second order and to remove any conver- sion of the dynamic system from the second order to the first order. The new approach is demonstrated via two classical benchmark problems.

关键词： costate estimation second order pseudo-spectral method

ON CONSTRUCTION OF HIGH order EXPONENTIALLY FITTED METHODS BASED ON PARAMETERIZED RATIONAL APPROXIMATIONS TO exp

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Applied Mathematics and Mechanics(English Edition) 1999年第9期20卷 1023-1030页

作者：杨逢建张爱国陈新明 Zhongkai Agrotechnical College Guangzhou P R China Xiangtan Institute of Machinery and Electricity Xiangtan P R China Department of Mathematics and Physics Wuyi University Jiangmen P R China

By the discussion of the formula and properties of (4,4) parametric form rational approximation to function exp(q), the fourth order derivative one_step exponentially fitted method and the third order derivative hybrid one_step exponentially fitted method are presented, their order p satisfying 6≤p≤8. The necessary and sufficient conditions for the two methods to be A_ stable are given. Finally, for the fourth order derivative method, the error bound and the necessary and sufficient conditions for it to be median are discussed.

关键词： exponentially fitted method order A_ stability

First order QED processes in a spatially flat FLRW space-time with a Milne-type scale factor

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Chinese Physics C 2020年第5期44卷 140-149页

作者： Ion ICotaescu Diana Popescu West University of Timisoara V.Parvan Ave.4RO-300223 TimisoaraRomania

The quantum electrodynamics(QED)in a spatially flat(1+3)-dimensional Friedmann-Lema?tre-Robertson-Walker(FLRW)space-time with a Milne-type scale factor is outlined focusing on the amplitudes of the allowed processes in the first order *** definition of the transition rates is reconsidered such that an appropriate angular behavior of the probability for creation of an electron-positron pair from a photon is obtained,which has a similar rate as the creation of a photon and an electron-positron pair from *** is shown that these processes are allowed only in the first order perturbations,since the photon emission or absorption by an electron or positron are forbidden.

关键词： spatially flat FLRW space-time Milne-type scale factor first order amplitudes transition rates

Solutions of the nonlocal(2+1)-D breaking solitons hierarchy and the negative order AKNS hierarchy

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Communications in Theoretical Physics 2020年第4期72卷 11-22页

作者： Jing Wang Hua Wu Da-jun Zhang Department of Mathematics Shanghai UniversityShanghai 200444China

The(2+1)-dimensional nonlocal breaking solitons AKNS hierarchy and the nonlocal negative order AKNS hierarchy are *** in double Wronskian form of these two hierarchies are derived by means of a reduction technique from those of the unreduced *** advantage of our method is that we start from the known solutions of the unreduced bilinear equations,and obtain solitons and multiple-pole solutions for the variety of classical and nonlocal *** behaviors of some obtained solutions are *** is remarkable that for some real nonlocal equations,amplitudes of solutions are related to the independent variables that are reversed in the real nonlocal reductions.

关键词： nonlocal (2+1)-dimensional breaking solitons AKNS hierarchy negative order AKNS hierarchy double Wronskian solutions reduction

On a Critical Fourth order PDE with Navier Boundary Condition

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Acta Mathematica Sinica,English Series 2019年第12期35卷 1906-1916页

作者： Khadijah SHARAF Department of Mathematics King Abdulaziz University

We consider a fourth order nonlinear PDE involving the critical Sobolev exponent on a bounded domain of R^n,n≥5 with Navier condition on the *** study the lack of compactness of the problem and we provide an existenc... 详细信息

关键词： Fourth order PDE critical nonlinearity variational problem critical points at infinity

Design of Smith Predictor Based Fractional Controller for Higher order Time Delay Process

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Computer Modeling in Engineering & Sciences 2019年第6期119卷 481-498页

作者： P.R.Hemavathy Y.Mohamed Shuaib S.K.Lakshmanaprabu Department of Electronics&Instrumentation Engineering B.S.Abdur Rahman Crescent Institute of Science&TechnologyChennaiIndia Department of Electrical&Electronics Engineering B.S.Abdur Rahman Crescent Institute of Science&TechnologyChennaiIndia

Normally all real world process in a process industry will have time *** those processes with time delays,obtaining satisfactory closed loop performances becomes very *** this work,three interacting cylindrical tank process is considered for study and the objective of the work is to compensate for time delays using smith predictor structure and to maintain the level in the third ***/Output data is generated for the three interacting tank *** is approximated as Integer First order Plus Dead Time system(IFOPDT)and Fractional First order Plus Dead Time system(FFOPDT).Smith predictor based fractional order Proportional Integral controller and Integer order Proportional Integral controller is designed for the IFOPDT and FFOPDT model using frequency response technique and their closed loop performance indices are compared and *** servo and regulatory responses are simulated using Matlab/Simulink.

关键词： Fractional order proportional integral controller frequency response technique smith predictor three interacting tank process

A New Characterization of PSL(2,q) by Group order and the Set of Vanishing Element orders

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Algebra Colloquium 2019年第3期26卷 459-466页

作者： Changguo Shao Qinhui Jiang School of Mathematical Sciences University of JinanJinan 250022China

An element g in a finite group G is called a vanishing element if there exists some irreducible complex character x of G such that y(p)=*** by Vo(G)the set of orders of vanishing elements of G,and we prove that G≌PSL... 详细信息

关键词： finite simple group vanishing element order prime graph projective speciallinear group