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Approximation Properties of Vectorial Exponential Functions
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作者 Christophe Buet Bruno Despres Guillaume Morel 《Communications on Applied Mathematics and Computation》 EI 2024年第3期1801-1831,共31页
This contribution is dedicated to the celebration of Rémi Abgrall’s accomplishments in Applied Mathematics and Scientific Computing during the conference“Essentially Hyperbolic Problems:Unconventional Numerics,... This contribution is dedicated to the celebration of Rémi Abgrall’s accomplishments in Applied Mathematics and Scientific Computing during the conference“Essentially Hyperbolic Problems:Unconventional Numerics,and Applications”.With respect to classical Finite Elements Methods,Trefftz methods are unconventional methods because of the way the basis functions are generated.Trefftz discontinuous Galerkin(TDG)methods have recently shown potential for numerical approximation of transport equations[6,26]with vectorial exponential modes.This paper focuses on a proof of the approximation properties of these exponential solutions.We show that vectorial exponential functions can achieve high order convergence.The fundamental part of the proof consists in proving that a certain rectangular matrix has maximal rank. 展开更多
关键词 Trefftz method Transport equation Vectorial exponential functions
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Exponentially Convergent Multiscale Finite Element Method
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作者 Yifan Chen Thomas Y.Hou Yixuan Wang 《Communications on Applied Mathematics and Computation》 EI 2024年第2期862-878,共17页
We provide a concise review of the exponentially convergent multiscale finite element method(ExpMsFEM)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave pr... We provide a concise review of the exponentially convergent multiscale finite element method(ExpMsFEM)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation.The ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis functions.Unlike most generalizations of the MsFEM in the literature,the ExpMsFEM does not rely on any partition of unity functions.In general,it is necessary to use function representations dependent on the right-hand side to break the algebraic Kolmogorov n-width barrier to achieve exponential convergence.Indeed,there are online and offline parts in the function representation provided by the ExpMsFEM.The online part depends on the right-hand side locally and can be computed in parallel efficiently.The offline part contains basis functions that are used in the Galerkin method to assemble the stiffness matrix;they are all independent of the right-hand side,so the stiffness matrix can be used repeatedly in multi-query scenarios. 展开更多
关键词 Multiscale method exponential convergence Helmholtz's equation Domain decomposition Nonlinear model reduction
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The Maximum and Minimum Value of Exponential RandićIndices of Quasi-Tree Graph
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作者 Lei Qiu Xijie Ruan Yan Zhu 《Journal of Applied Mathematics and Physics》 2024年第5期1804-1818,共15页
The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, whe... The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, where d( u ) denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved. 展开更多
关键词 exponential Randić Index Quasi-Tree Graph Extremal Value Extremal Graphs
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THE GROWTH OF SOLUTIONS TO HIGHER ORDER DIFFERENTIAL EQUATIONS WITH EXPONENTIAL POLYNOMIALS AS ITS COEFFICIENTS 被引量:1
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作者 黄志波 罗敏伟 陈宗煊 《Acta Mathematica Scientia》 SCIE CSCD 2023年第1期439-449,共11页
By looking at the situation when the coefficients Pj(z)(j=1,2,…,n-1)(or most of them) are exponential polynomials,we investigate the fact that all nontrivial solutions to higher order differential equations f((n))+Pn... By looking at the situation when the coefficients Pj(z)(j=1,2,…,n-1)(or most of them) are exponential polynomials,we investigate the fact that all nontrivial solutions to higher order differential equations f((n))+Pn-1(z)f((n-1))+…+P0(z)f=0 are of infinite order.An exponential polynomial coefficient plays a key role in these results. 展开更多
关键词 differential equations entire solution exponential polynomial GROWTH
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A Numerical Investigation Based on Exponential Collocation Method for Nonlinear SITR Model of COVID-19 被引量:1
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作者 Mohammad Aslefallah Suayip Yüzbasi Saeid Abbasbandy 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第8期1687-1706,共20页
In this work,the exponential approximation is used for the numerical simulation of a nonlinear SITR model as a system of differential equations that shows the dynamics of the new coronavirus(COVID-19).The SITR mathema... In this work,the exponential approximation is used for the numerical simulation of a nonlinear SITR model as a system of differential equations that shows the dynamics of the new coronavirus(COVID-19).The SITR mathematical model is divided into four classes using fractal parameters for COVID-19 dynamics,namely,susceptible(S),infected(I),treatment(T),and recovered(R).The main idea of the presented method is based on the matrix representations of the exponential functions and their derivatives using collocation points.To indicate the usefulness of this method,we employ it in some cases.For error analysis of the method,the residual of the solutions is reviewed.The reported examples show that the method is reasonably efficient and accurate. 展开更多
关键词 Coronavirus(COVID-19) SITR model exponential approximation differential equations system collocation method operational matrix
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The Modi Exponentiated Exponential Distribution
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作者 Antoine Dieudonné Ndayisaba Leo Odiwuor Odongo Anthony Ngunyi 《Journal of Data Analysis and Information Processing》 2023年第4期341-359,共19页
In this study, a new four-parameter distribution called the Modi Exponentiated Exponential distribution was proposed and studied. The new distribution has three shape and one scale parameters. Its mathematical and sta... In this study, a new four-parameter distribution called the Modi Exponentiated Exponential distribution was proposed and studied. The new distribution has three shape and one scale parameters. Its mathematical and statistical properties were investigated. The parameters of the new model were estimated using the method of Maximum Likelihood Estimation. Monte Carlo simulation was used to evaluate the performance of the MLEs through average bias and RMSE. The flexibility and goodness-of-fit of the proposed distribution were demonstrated by applying it to two real data sets and comparing it with some existing distributions. 展开更多
关键词 Modi Family exponentiated exponential Distribution Maximum Likelihood Estimation Order Statistics MOMENTS Quantile Function
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Vertical deformation model on postseismic phase using exponential and logarithmic function based on InSAR
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作者 Irma Yusiyanti Tattyana Wening Kalbuadi Prajardi +1 位作者 Yofita Indah Saputri Cecep Pratama 《Geodesy and Geodynamics》 EI CSCD 2023年第4期392-400,共9页
The Palu MW7.4 earthquake occurred on September 28, 2018, with the epicenter at 119.86°, 0.72°. The severe shaking caused severe damage in Central Sulawesi, especially in Palu. We conducted a postseismic def... The Palu MW7.4 earthquake occurred on September 28, 2018, with the epicenter at 119.86°, 0.72°. The severe shaking caused severe damage in Central Sulawesi, especially in Palu. We conducted a postseismic deformation study to determine the deformation pattern and reduce future earthquakes’ impact.Interferometric Synthetic Aperture Radar(In SAR) data were processed using Li CSBAS to get the time series. The time series data were fitted to exponential and logarithmic functions to determine the mechanism of postseismic deformation. The exponential model identified the influence of the viscoelastic mechanism, and the logarithm identified the afterslip mechanism. The Palu earthquake was fitted to logarithmic and exponential, but the logarithmic was more significant than an exponential function.Afterslip mechanism predominates, and viscoelastic mechanisms play a minor role in this postseismic deformation. 展开更多
关键词 EARTHQUAKE DEFORMATION POSTSEISMIC Physical mechanism exponential Logarithmic
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Improved population mean estimator with exponential function under non-response
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作者 CerenUnal Cem Kadilar 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第4期562-580,共19页
In this article,we consider a new family of exponential type estimators for estimating the unknown population mean of the study variable.We propose estimators taking advantage of the auxiliary variable information und... In this article,we consider a new family of exponential type estimators for estimating the unknown population mean of the study variable.We propose estimators taking advantage of the auxiliary variable information under the first and second non-response cases separately.The required theoretical comparisons are obtained and the numerical studies are conducted.In conclusion,the results show that the proposed family of estimators is the most efficient estimator with respect to the estimators in literature under the obtained conditions for both cases. 展开更多
关键词 NON-RESPONSE exponential estimators sub-sampling method population mean
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Trimmable bandgap reference circuit with exponential curvature compensation
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作者 Hong-Zhuan Chen Fei Chu +3 位作者 Wen-Tao Lu Tie-Liang Zhang Wen-Chang Li Wei Gao 《Journal of Electronic Science and Technology》 EI CAS CSCD 2023年第3期52-62,共11页
This paper proposes an improved exponential curvature-compensated bandgap reference circuit to exploit the exponential relationship between the current gainβof the bipolar junction transistor(BJT)and the temperature ... This paper proposes an improved exponential curvature-compensated bandgap reference circuit to exploit the exponential relationship between the current gainβof the bipolar junction transistor(BJT)and the temperature as well as reduce the influence of resistance-temperature dependency.Considering the degraded circuit performance caused by the process deviation,the trimmable module of the temperature coefficient(TC)is introduced to improve the circuit stability.The circuit has the advantages of simple structure,high linear stability,high TC accuracy,and trimmable TC.It consumes an area of 0.09 mm^(2)when fabricated by using the 0.25-μm complementary metal-oxide-semiconductor(CMOS)process.The proposed circuit achieves the simulated power supply rejection(PSR)of about-78.7 dB@1 kHz,the measured TC of~4.7 ppm/℃over a wide temperature range from-55℃to 125℃with the 2.5-V single-supply voltage,and the tested line regulation of 0.10 mV/V.Such a high-performance bandgap reference circuit can be widely applied in high-precision and high-reliability electronic systems. 展开更多
关键词 Bandgap reference exponential curvature compensation Temperature coefficient(TC) Trimmable
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The Class of Atomic Exponential Basis Functions EFup_(n)(x,ω)-Development and Application
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作者 Nives Brajcic Kurbasa Blaz Gotovac Vedrana Kozulic 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第4期65-90,共26页
The purpose of this paper is to present the class of atomic basis functions(ABFs)which are of exponential type and are denoted by EFupn(x,ω).While ABFs of the algebraic type are already represented in the numerical m... The purpose of this paper is to present the class of atomic basis functions(ABFs)which are of exponential type and are denoted by EFupn(x,ω).While ABFs of the algebraic type are already represented in the numerical modeling of various problems inmathematical physics and computationalmechanics,ABFs of the exponential type have not yet been sufficiently researched.These functions,unlike the ABFs of the algebraic type Fupn(x),contain the tension parameterω,which gives them additional approximation properties.Exponential monomials up to the nth degree can be described exactly by the linear combination of the functions EFupn(x,ω).The function EFupn for n=0 is called the“mother”ABF of the exponential type,i.e.,EFup0(x,ω)≡Eup(x,ω).In other words,the functions EFupn(x,ω)are elements of the linear vector space EUPn and retain all the properties of their“mother”function Eup(x,ω).Thus,this paper,in terms of its content and purpose,can be understood as a sequel of the article by Brajcic Kurbasa et al.,which shows the basic properties and application of the basis function Eup(x,ω).This paper presents,in an analogous way,the development and application of the exponential basis functions EFupn(x,ω).Here,for the first time,expressions for calculating the values of the functions EFupn(x,ω)and their derivatives are given in a form suitable for application in numerical analyses,which is shown in the verification examples of the approximations of known functions. 展开更多
关键词 exponential atomic basis functions Fourier transform compact support tension parameter
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On the Fractional Derivatives with an Exponential Kernel
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作者 Enyu Fan Jingshu Wu Shaoying Zeng 《Communications on Applied Mathematics and Computation》 EI 2023年第4期1655-1673,共19页
The present article mainly focuses on the fractional derivatives with an exponential kernel(“exponential fractional derivatives”for brevity).First,several extended integral transforms of the exponential fractional d... The present article mainly focuses on the fractional derivatives with an exponential kernel(“exponential fractional derivatives”for brevity).First,several extended integral transforms of the exponential fractional derivatives are proposed,including the Fourier transform and the Laplace transform.Then,the L2 discretisation for the exponential Caputo derivative with a∈(1,2)is established.The estimation of the truncation error and the properties of the coefficients are discussed.In addition,a numerical example is given to verify the correctness of the derived L2 discrete formula. 展开更多
关键词 exponential fractional derivative Integral transform L2 discretisation Truncation error
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Finite Element Implementation of the Exponential Drucker-Prager Plasticity Model for Adhesive Joints
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作者 Kerati Suwanpakpraek Baramee Patamaprohm +1 位作者 Sacharuck Pornpeerakeat Arisara Chaikittiratana 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第6期1765-1778,共14页
This paper deals with the numerical implementation of the exponential Drucker-Parger plasticitymodel in the commercial finite element software,ABAQUS,via user subroutine UMAT for adhesive joint simulations.The influen... This paper deals with the numerical implementation of the exponential Drucker-Parger plasticitymodel in the commercial finite element software,ABAQUS,via user subroutine UMAT for adhesive joint simulations.The influence of hydrostatic pressure on adhesive strength was investigated by a modified Arcan fixture designed particularly to induce a different state of hydrostatic pressure within an adhesive layer.The developed user subroutine UMAT,which utilizes an associated plastic flow during a plastic deformation,can provide a good agreement between the simulations and the experimental data.Better numerical stability at highly positive hydrostatic pressure loads for a very high order of exponential function can also be achieved compared to when a non-associated flow is used. 展开更多
关键词 exponential Drucker-Prager model modified-Arcan test finite element analysis plastic potential function
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Non-harmonic resonance of viscoelastic structures subjected to time-dependent exponentially decreasing transverse distributed loads
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作者 Nasrin Jafari 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2023年第3期825-840,共16页
In this paper,the non-harmonic resonance of Bernoulli viscoelastic beams,Kirchhoff viscoelastic plates,Timoshenko viscoelastic beams,and Mindlin viscoelastic plates subjected to time-dependent exponentially decreasing... In this paper,the non-harmonic resonance of Bernoulli viscoelastic beams,Kirchhoff viscoelastic plates,Timoshenko viscoelastic beams,and Mindlin viscoelastic plates subjected to time-dependent exponentially decreasing transverse distributed load is investigated for the first time.The constitutive equations are expressed utilizing Boltzmann integral law with a constant bulk modulus.The displacement vector is approximated by employing the separation of variables method.The Laplace transformation is used to transfer equations from the time domain to the Laplace domain and vice versa.The novel point of the proposed method is to express,prove and calculate the critical time in which the displacement will be several times the displacement at time zero.In addition,this new method calculates the maximum deflection at the critical time,explicitly and exactly,without any need to follow the time-displacement curve with a low computational cost.Additionally,the proposed method introduces the critical range of time so that the responses are greater than the responses at time zero. 展开更多
关键词 Bernoulli and Timoshenko viscoelastic beams critical time non-harmonic resonance time-dependent decreasing exponential load Kirchhoff and Mindlin viscoelastic plates
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Exponential stability criteria on neural networks with continuously distributed delays 被引量:2
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作者 李涛 费树岷 朱清 《Journal of Southeast University(English Edition)》 EI CAS 2007年第4期529-533,共5页
The exponential stability of a class of neural networks with continuously distributed delays is investigated by employing a novel Lyapunov-Krasovskii functional. Through introducing some free-weighting matrices and th... The exponential stability of a class of neural networks with continuously distributed delays is investigated by employing a novel Lyapunov-Krasovskii functional. Through introducing some free-weighting matrices and the equivalent descriptor form, a delay-dependent stability criterion is established for the addressed systems. The condition is expressed in terms of a linear matrix inequality (LMI), and it can be checked by resorting to the LMI in the Matlab toolbox. In addition, the proposed stability criteria do not require the monotonicity of the activation functions and the derivative of a time-varying delay being less than 1, which generalize and improve earlier methods. Finally, numerical examples are given to show the effectiveness of the obtained methods. 展开更多
关键词 exponential stability neural networks free-weighting matrix continuously distributed delay linear matrix inequality
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Exponential stability and existence of periodic solutions for a class of recurrent neural networks with delays 被引量:1
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作者 戴志娟 《Journal of Southeast University(English Edition)》 EI CAS 2006年第2期286-293,共8页
Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays (RNNs) are studied. By employing the inequality α∏k=1^m ... Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays (RNNs) are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r+1/rα^r(α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications. 展开更多
关键词 recurrent neural network global exponential stability periodic solution delay HOMEOMORPHISM Lyapunov function
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Absolute Exponential Stability of Generalized Dynamical Neural Networks
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作者 孙长银 费树岷 冯纯伯 《Journal of Southeast University(English Edition)》 EI CAS 2002年第2期159-163,共5页
This paper investigates the absolute exponential stability of generalized neural networks with a general class of partially Lipschitz continuous and monotone increasing activation functions. The main obtained result i... This paper investigates the absolute exponential stability of generalized neural networks with a general class of partially Lipschitz continuous and monotone increasing activation functions. The main obtained result is that if the interconnection matrix T of the neural system satisfies that - T is an H matrix with nonnegative diagonal elements, then the neural system is absolutely exponentially stable(AEST). The Hopfield network, Cellular neural network and Bidirectional associative memory network are special cases of the network model considered in this paper. So this work gives some improvements to the previous ones. 展开更多
关键词 absolute exponential stability partial Lipschitz continuity neural networks
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GLOBAL EXISTENCE, UNIFORM DECAY AND EXPONENTIAL GROWTH FOR A CLASS OF SEMI-LINEAR WAVE EQUATION WITH STRONG DAMPING 被引量:7
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作者 陈化 刘功伟 《Acta Mathematica Scientia》 SCIE CSCD 2013年第1期41-58,共18页
In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potentia... In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E(0) 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E(0) 〈 0. 展开更多
关键词 strong damping nonlinear damping global existence polynomial decay exponential decay exponential growth
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New robust chaotic system with exponential quadratic term 被引量:9
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作者 包伯成 李春彪 +1 位作者 许建平 刘中 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第11期4022-4026,共5页
This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic a... This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller. 展开更多
关键词 ATTRACTOR chaotic system exponential quadratic term constant controller
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EXPRESSION OF MEROMORPHIC SOLUTIONS OF SYSTEMS OF ALGEBRAIC DIFFERENTIAL EQUATIONS WITH EXPONENTIAL COEFFICIENTS 被引量:9
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作者 高凌云 《Acta Mathematica Scientia》 SCIE CSCD 2011年第2期541-548,共8页
Using the Nevanlinna theory of the value distribution of meromorphic functions and theory of differential algebra, we investigate the problem of the forms of meromorphic solutions of some specific systems of generaliz... Using the Nevanlinna theory of the value distribution of meromorphic functions and theory of differential algebra, we investigate the problem of the forms of meromorphic solutions of some specific systems of generalized higher order algebraic differential equations with exponential coefficients and obtain some results. 展开更多
关键词 EXPRESSION exponential coefficients systems of differential equations.
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NEW TECHNOLOGY FOR FAULT DIAGNOSIS BASED ON WAVELET DENOISING AND MODIFIED EXPONENTIAL TIME-FREQUENCY DISTRIBUTION 被引量:13
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作者 Wang Xinqing,Wang Yaohua,Qian Shuhua,Chen Liuhai (Engineering College of PLA University of Science and Technology) Xu Yanshen,Zhao Xiangsong (Tianjin University) 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2001年第3期262-265,共4页
Fast wavelet multi-resolution analysis (wavelet MRA) provides a effective tool for analyzing and canceling disturbing components in original signal. Because of its exponential frequency axis, this method isn't s... Fast wavelet multi-resolution analysis (wavelet MRA) provides a effective tool for analyzing and canceling disturbing components in original signal. Because of its exponential frequency axis, this method isn't suitable for extracting harmonic components. The modified exponential time-frequency distribution ( MED) overcomes the problems of Wigner distribution( WD) ,can suppress cross-terms and cancel noise further more. MED provides high resolution in both time and frequency domains, so it can make out weak period impulse components fmm signal with mighty harmonic components. According to the 'time' behavior, together with 'frequency' behavior in one figure,the essential structure of a signal is revealed clearly. According to the analysis of algorithm and fault diagnosis example, the joint of wavelet MRA and MED is a powerful tool for fault diagnosis. 展开更多
关键词 Wavelet multi-resolution analysis DENOISING Modified exponential distribution Fault diagnosis
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