The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform
Chiihuei Yu - One of the best experts on this subject based on the ideXlab platform.
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some Improper Integral problems
International Journal of Research, 2017Co-Authors: Chiihuei YuAbstract:This paper takes advantage of the mathematical software Maple to study two types of Improper Integrals . T he infinite series form s of these two types of Improper Integrals can be obtained by using differentiation with respect to a parameter and differentiation term by term theorem. In addition , two examples of Improper Integrals are proposed and we actually find their infinite series forms . T he research method adopted in this article is to obtain the answer s by manual calculation , and then use s Maple to verify the answers . This research method not only allows us to find the c alculation error s , but also help s us to amend the original thinking direction because we can verify the correctness of our theory from the consistency of manual and Maple calculations .
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techniques for evaluating some type of multiple Improper Integral
International Journal of Research, 2016Co-Authors: Chiihuei YuAbstract:This paper considers some type of multiple Improper Integral. We can obtain the closed form of this multiple Improper Integral using differentiation with respect to a parameter and Leibniz rule. On the other hand, some examples are proposed to demonstrate the calculations. The method adopted in this study is to find solutions through manual calculations and verify our answers using Maple. This method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking. Key Words: multiple Improper Integral; closed form; differentiation with respect to a parameter; Leibniz rule; Maple
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a study on the multiple Improper Integral problems with maple
Applied Mechanics and Materials, 2013Co-Authors: Chiihuei YuAbstract:This paper uses the mathematical software Maple for the auxiliary tool to study the evaluation of two types of multiple Improper Integrals. We can obtain the infinite series forms of these two types of multiple Improper Integrals, and we propose four examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding problem-solving methods.
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using maple to study the multiple Improper Integral problem
2013Co-Authors: Chiihuei YuAbstract:Multiple Improper Integral problem is closely related with probability theory and quantum field theory. Therefore, the evaluation and numerical calculation of multiple Improper Integrals is an important issue. This paper takes the mathematical software Maple as the auxiliary tool to study some types of multiple Improper Integrals. We can obtain the infinite series forms of these types of multiple Improper Integrals by using integration term by term theorem. On the other hand, we propose some examples to do calculation practically. Our research way is to count the answers by hand, and then use Maple to verify our results. This research way can not only let us find the calculation errors but also help us to revise the original thinking direction because we can verify the correctness of our theory from the consistency of hand count and Maple calculations. Therefore, Maple can bring us inspiration and guide us to find the problem-solving method, this is not an exaggeration.
Marcus Wagner - One of the best experts on this subject based on the ideXlab platform.
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different interpretations of the Improper Integral objective in an infinite horizon control problem
Journal of Mathematical Analysis and Applications, 2008Co-Authors: Valeriya Lykina, Sabine Pickenhain, Marcus WagnerAbstract:Abstract We provide an example of a convex infinite horizon problem with a linear objective functional where the different interpretations of the Improper Integral ∫ 0 ∞ f ( t , x ( t ) , u ( t ) ) d t in either Lebesgue or Riemann sense lead to different but finite optimal values.
Robert Mcgough - One of the best experts on this subject based on the ideXlab platform.
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time domain analysis of power law attenuation in space fractional wave equations
Journal of the Acoustical Society of America, 2018Co-Authors: Xiaofeng Zhao, Robert McgoughAbstract:Ultrasound attenuation in soft tissue follows a power law as a function of the ultrasound frequency, and in medical ultrasound, power law attenuation is often described by fractional calculus models that contain one or more time- or space-fractional derivatives. For certain time-fractional models, exact and approximate time-domain Green's functions are known, but similar expressions are not available for the space-fractional models that describe power law attenuation. To address this deficiency, a numerical approach for calculating time-domain Green's functions for the Chen–Holm space-fractional wave equation and Treeby–Cox space-fractional wave equation is introduced, where challenges associated with the numerical evaluation of a highly oscillatory Improper Integral are addressed with the Filon integration formula combined with the Pantis method. Numerical results are computed for both of these space-fractional wave equations at different distances in breast and liver with power law exponents of 1.5 and 1.139, respectively. The results show that these two space-fractional wave equations are causal and that away from the origin, the time-domain Green's function for the Treeby–Cox space-fractional wave equation is very similar to the time-domain Green's function for the time-fractional power law wave equation.Ultrasound attenuation in soft tissue follows a power law as a function of the ultrasound frequency, and in medical ultrasound, power law attenuation is often described by fractional calculus models that contain one or more time- or space-fractional derivatives. For certain time-fractional models, exact and approximate time-domain Green's functions are known, but similar expressions are not available for the space-fractional models that describe power law attenuation. To address this deficiency, a numerical approach for calculating time-domain Green's functions for the Chen–Holm space-fractional wave equation and Treeby–Cox space-fractional wave equation is introduced, where challenges associated with the numerical evaluation of a highly oscillatory Improper Integral are addressed with the Filon integration formula combined with the Pantis method. Numerical results are computed for both of these space-fractional wave equations at different distances in breast and liver with power law exponents of 1.5 and ...
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Numerical computation of time-domain Green's functions for the Treeby-Cox space-fractional wave equation
2017 IEEE International Ultrasonics Symposium (IUS), 2017Co-Authors: Xiaofeng Zhao, Robert McgoughAbstract:The attenuation of ultrasound in soft tissue follows a frequency-dependent power law. As an alternative to the time-fractional partial differential equations that describe power law attenuation and dispersion, Treeby and Cox derived a space-fractional model that accounts for both power law attenuation and dispersion. The Treeby-Cox space-fractional wave equation is convenient for simulations with the pseudo-spectral approach; however, numerical calculations of the time-domain Green's function for the Treeby-Cox wave equation are more challenging because numerical evaluation of a highly oscillatory Improper Integral is required. When applied to this problem, most standard numerical integration techniques perform poorly, so an alternative approach is required.
Mihailo P Lazarevic - One of the best experts on this subject based on the ideXlab platform.
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damped vibration of a nonlocal nanobeam resting on viscoelastic foundation fractional derivative model with two retardation times and fractional parameters
Meccanica, 2017Co-Authors: Milan Cajic, Danilo Karlicic, Mihailo P LazarevicAbstract:In this paper, we investigate the free damped vibration of a nanobeam resting on viscoelastic foundation. Nanobeam and viscoelastic foundation are modeled using nonlocal elasticity and fractional order viscoelasticity theories. Motion equation is derived using D’Alambert’s principle and involves two retardation times and fractional order derivative parameters regarding to a nanobeam and viscoelastic foundation. The analytical solution is obtained using the Laplace transform method and it is given as a sum of two terms. First term denoting the drift of the system’s equilibrium position is given as an Improper Integral taken along two sides of the cut of complex plane. Two complex conjugate roots located in the left half-plane of the complex plane determine the second term describing the damped vibration around equilibrium position. Results for complex roots of characteristic equation obtained for a single nanobeam without viscoelastic foundation, where imaginary parts represent damped frequencies, are validated with the results found in the literature for natural frequencies of a single-walled carbon nanotube obtained from molecular dynamics simulations. In order to examine the effects of nonlocal parameter, fractional order parameters and retardation times on the behavior of characteristic equation roots in the complex plane and the time-response of nanobeam, several numerical examples are given.
Jiang Xue-yuan - One of the best experts on this subject based on the ideXlab platform.
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On Mean Value Theorem for Improper Integral
Journal of Southwest China Normal University, 2020Co-Authors: Jiang Xue-yuanAbstract:In this paper,the mean value theorem has been given for Improper Integral.Some results of the mean value theorem have been extended and improved.
