The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Delfim F. M. Torres - One of the best experts on this subject based on the ideXlab platform.
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a survey on fractional Variational Calculus
arXiv: Optimization and Control, 2018Co-Authors: Ricardo Almeida, Delfim F. M. TorresAbstract:Main results and techniques of the fractional Calculus of variations are surveyed. We consider Variational problems containing Caputo derivatives and study them using both indirect and direct methods. In particular, we provide necessary optimality conditions of Euler-Lagrange type for the fundamental, higher-order, and isoperimetric problems, and compute approximated solutions based on truncated Grunwald--Letnikov approximations of Caputo derivatives.
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hahn s symmetric quantum Variational Calculus
Numerical Algebra Control and Optimization, 2013Co-Authors: Artur Brito M C Da Cruz, Natalia Martins, Delfim F. M. TorresAbstract:We introduce and develop the Hahn symmetric quantum Calculus with applications to the Calculus of variations. Namely, we obtain a necessary optimality condition of Euler--Lagrange type and a sufficient optimality condition for Variational problems within the context of Hahn's symmetric Calculus. Moreover, we show the effectiveness of Leitmann's direct method when applied to Hahn's symmetric Variational Calculus. Illustrative examples are provided.
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variable order fractional Variational Calculus for double integrals
Conference on Decision and Control, 2012Co-Authors: Tatiana Odzijewicz, Agnieszka B Malinowska, Delfim F. M. TorresAbstract:We introduce three types of partial fractional operators of variable order. An integration by parts formula for partial fractional integrals of variable order and an extension of Green's theorem are proved. These results allow us to obtain a fractional Euler-Lagrange necessary optimality condition for variable order two-dimensional fractional Variational problems.
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higher order hahn s quantum Variational Calculus
Nonlinear Analysis-theory Methods & Applications, 2012Co-Authors: Artur Brito M C Da Cruz, Natalia Martins, Delfim F. M. TorresAbstract:Abstract We prove a necessary optimality condition of Euler–Lagrange type for quantum Variational problems involving Hahn’s derivatives of higher-order.
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Fractional Variational Calculus with Classical and Combined Caputo Derivatives
Nonlinear Analysis: Theory Methods and Applications, 2012Co-Authors: Tatiana Odzijewicz, Agnieszka B Malinowska, Delfim F. M. TorresAbstract:We give a proper fractional extension of the classical Calculus of variations by considering Variational functionals with a Lagrangian depending on a combined Caputo fractional derivative and the classical derivative. Euler-Lagrange equations to the basic and isoperimetric problems are proved, as well as transversality conditions.
X Hernandez - One of the best experts on this subject based on the ideXlab platform.
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deriving star formation histories inverting hertzsprung russell diagrams through a Variational Calculus maximum likelihood method
Monthly Notices of the Royal Astronomical Society, 1999Co-Authors: X Hernandez, D Vallsgabaud, Gerard GilmoreAbstract:We introduce a new method for solving maximum likelihood problems through Variational Calculus, and apply it to the case of recovering an unknown star formation history, SFR(t), from the resulting Hertzsprung--Russell (HR) diagram. This approach allows a totally non-parametric solution, which has the advantage of requiring no initial assumptions about SFR(t). As a full maximum likelihood statistical model is used, and we take advantage of all the information available in the HR diagram, rather than concentrating on particular features such as turn-off points or luminosity functions. We test the method using a series of synthetic HR diagrams produced from known SFR(t), and find it to be quite successful under noise conditions comparable to those present in current observations. At this point we restrict the analysis to situations in which the metallicity of the system is known, as is the case with the resolved population of dwarf spheroidal companions to the Milky Way or the solar neighbourhood Hipparcos data. We also include tests to quantify the way uncertainties in the assumed metallicity, binary fraction and initial mass function (IMF) affect our inferences.
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deriving star formation histories inverting hr diagrams through a Variational Calculus maximum likelihood method
arXiv: Astrophysics, 1998Co-Authors: X Hernandez, D Vallsgabaud, Gerard GilmoreAbstract:We introduce a new method for solving maximum likelihood problems through Variational Calculus, and apply it to the case of recovering an unknown star formation history, $SFR(t)$, from a resulting HR diagram. This approach allows a totally non-parametric solution which has the advantage of requiring no initial assumptions on the $SFR(t)$. As a full maximum likelihood statistical model is used, we take advantage of all the information available in the HR diagram, rather than concentrating on particular features such as turn off points or luminosity functions. We test the method using a series of synthetic HR diagrams produced from known $SFR(t)$, and find it to be quite successful under noise conditions comparable to those present in current observations. At this point we restrict the analysis to situations where the metallicity of the system is known, as is the case with the resolved populations of the dwarf spheroidal companions to the Milky Way or the solar neighbourhood Hipparcos data. We also include tests to quantify the way uncertainties in the assumed metallicity, binary fraction and IMF affect our inferences.
Gerard Gilmore - One of the best experts on this subject based on the ideXlab platform.
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deriving star formation histories inverting hertzsprung russell diagrams through a Variational Calculus maximum likelihood method
Monthly Notices of the Royal Astronomical Society, 1999Co-Authors: X Hernandez, D Vallsgabaud, Gerard GilmoreAbstract:We introduce a new method for solving maximum likelihood problems through Variational Calculus, and apply it to the case of recovering an unknown star formation history, SFR(t), from the resulting Hertzsprung--Russell (HR) diagram. This approach allows a totally non-parametric solution, which has the advantage of requiring no initial assumptions about SFR(t). As a full maximum likelihood statistical model is used, and we take advantage of all the information available in the HR diagram, rather than concentrating on particular features such as turn-off points or luminosity functions. We test the method using a series of synthetic HR diagrams produced from known SFR(t), and find it to be quite successful under noise conditions comparable to those present in current observations. At this point we restrict the analysis to situations in which the metallicity of the system is known, as is the case with the resolved population of dwarf spheroidal companions to the Milky Way or the solar neighbourhood Hipparcos data. We also include tests to quantify the way uncertainties in the assumed metallicity, binary fraction and initial mass function (IMF) affect our inferences.
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deriving star formation histories inverting hr diagrams through a Variational Calculus maximum likelihood method
arXiv: Astrophysics, 1998Co-Authors: X Hernandez, D Vallsgabaud, Gerard GilmoreAbstract:We introduce a new method for solving maximum likelihood problems through Variational Calculus, and apply it to the case of recovering an unknown star formation history, $SFR(t)$, from a resulting HR diagram. This approach allows a totally non-parametric solution which has the advantage of requiring no initial assumptions on the $SFR(t)$. As a full maximum likelihood statistical model is used, we take advantage of all the information available in the HR diagram, rather than concentrating on particular features such as turn off points or luminosity functions. We test the method using a series of synthetic HR diagrams produced from known $SFR(t)$, and find it to be quite successful under noise conditions comparable to those present in current observations. At this point we restrict the analysis to situations where the metallicity of the system is known, as is the case with the resolved populations of the dwarf spheroidal companions to the Milky Way or the solar neighbourhood Hipparcos data. We also include tests to quantify the way uncertainties in the assumed metallicity, binary fraction and IMF affect our inferences.
D Vallsgabaud - One of the best experts on this subject based on the ideXlab platform.
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deriving star formation histories inverting hertzsprung russell diagrams through a Variational Calculus maximum likelihood method
Monthly Notices of the Royal Astronomical Society, 1999Co-Authors: X Hernandez, D Vallsgabaud, Gerard GilmoreAbstract:We introduce a new method for solving maximum likelihood problems through Variational Calculus, and apply it to the case of recovering an unknown star formation history, SFR(t), from the resulting Hertzsprung--Russell (HR) diagram. This approach allows a totally non-parametric solution, which has the advantage of requiring no initial assumptions about SFR(t). As a full maximum likelihood statistical model is used, and we take advantage of all the information available in the HR diagram, rather than concentrating on particular features such as turn-off points or luminosity functions. We test the method using a series of synthetic HR diagrams produced from known SFR(t), and find it to be quite successful under noise conditions comparable to those present in current observations. At this point we restrict the analysis to situations in which the metallicity of the system is known, as is the case with the resolved population of dwarf spheroidal companions to the Milky Way or the solar neighbourhood Hipparcos data. We also include tests to quantify the way uncertainties in the assumed metallicity, binary fraction and initial mass function (IMF) affect our inferences.
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deriving star formation histories inverting hr diagrams through a Variational Calculus maximum likelihood method
arXiv: Astrophysics, 1998Co-Authors: X Hernandez, D Vallsgabaud, Gerard GilmoreAbstract:We introduce a new method for solving maximum likelihood problems through Variational Calculus, and apply it to the case of recovering an unknown star formation history, $SFR(t)$, from a resulting HR diagram. This approach allows a totally non-parametric solution which has the advantage of requiring no initial assumptions on the $SFR(t)$. As a full maximum likelihood statistical model is used, we take advantage of all the information available in the HR diagram, rather than concentrating on particular features such as turn off points or luminosity functions. We test the method using a series of synthetic HR diagrams produced from known $SFR(t)$, and find it to be quite successful under noise conditions comparable to those present in current observations. At this point we restrict the analysis to situations where the metallicity of the system is known, as is the case with the resolved populations of the dwarf spheroidal companions to the Milky Way or the solar neighbourhood Hipparcos data. We also include tests to quantify the way uncertainties in the assumed metallicity, binary fraction and IMF affect our inferences.
Natalia Martins - One of the best experts on this subject based on the ideXlab platform.
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general quantum Variational Calculus
Statistics Optimization and Information Computing, 2018Co-Authors: Artur Brito M C Da Cruz, Natalia MartinsAbstract:We develop a new Variational Calculus based in the general quantum difference operator recently introduced by Hamza et al. In particular, we obtain optimality conditions for generalized Variational problems where the Lagrangian may depend on the endpoints conditions and a real parameter, for the basic and isoperimetric problems, with and without fixed boundary conditions. Our results provide a generalization to previous results obtained for the $q$- and Hahn-Calculus.
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hahn s symmetric quantum Variational Calculus
Numerical Algebra Control and Optimization, 2013Co-Authors: Artur Brito M C Da Cruz, Natalia Martins, Delfim F. M. TorresAbstract:We introduce and develop the Hahn symmetric quantum Calculus with applications to the Calculus of variations. Namely, we obtain a necessary optimality condition of Euler--Lagrange type and a sufficient optimality condition for Variational problems within the context of Hahn's symmetric Calculus. Moreover, we show the effectiveness of Leitmann's direct method when applied to Hahn's symmetric Variational Calculus. Illustrative examples are provided.
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the q symmetric Variational Calculus
Computers & Mathematics With Applications, 2012Co-Authors: Artur Brito M C Da Cruz, Natalia MartinsAbstract:We bring a new approach to the study of quantum Calculus and introduce the q-symmetric Variational Calculus. We prove a necessary optimality condition of Euler-Lagrange type and a sufficient optimality condition for symmetric quantum Variational problems. The results are illustrated with an example.
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higher order hahn s quantum Variational Calculus
Nonlinear Analysis-theory Methods & Applications, 2012Co-Authors: Artur Brito M C Da Cruz, Natalia Martins, Delfim F. M. TorresAbstract:Abstract We prove a necessary optimality condition of Euler–Lagrange type for quantum Variational problems involving Hahn’s derivatives of higher-order.
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generalized transversality conditions for the hahn quantum Variational Calculus
arXiv: Optimization and Control, 2012Co-Authors: Agnieszka B Malinowska, Natalia MartinsAbstract:We prove optimality conditions for generalized quantum Variational problems with a Lagrangian depending on the free end-points. Problems of Calculus of variations of this type cannot be solved using the classical theory.
