Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Conference Object Continuous wavelet analysis for the ratio signals of the absorption spectra of binary mixtures(Springer, 2007) Dinç, Erdal; Baleanu, Dumitru; Taş, KenanWavelet analysis is successfully applied to the quantitative determination of the components in the binary mixture. This mathematical application is based on the use of the division of the absorption signals by the standard absorption signal and the transformation of the ratio signals. Calibration functions are obtained by measuring the continuous wavelet amplitudes corresponding to the minimum points of the wavelengths. The method is validated and applied to one example of binary mixture analysis.Article Dualisation of the D=7 heterotic string(Springer, 2004) Yılmaz, N. T.The dualisation and the first-order formulation of the D = 7 abelian Yang-Mills supergravity which is the low energy effective limit of the D = 7 fully Higssed heterotic string is discussed. The non-linear coset formulation of the scalars is enlarged to include the entire bosonic sector by introducing dual fields and by constructing the Lie superalgebra which generates the dualized coset element.Article Citation - WoS: 5Citation - Scopus: 2Dualisation of the D = 9 Matter Coupled Supergravity(Springer, 2005) Yilmaz, NTWe perform the bosonic dualisation of the matter coupled N ≤ 1, D ≤ 9 supergravity. We derive the Lie superalgebra which parameterizes the coset map whose Cartan form realizes the second-order bosonic field equations. Following the non-linear coset construction we present the first-order formulation of the bosonic field equations as a twisted self-duality condition. © SISSA 2005.Conference Object Citation - WoS: 9Citation - Scopus: 11On Fractional Variational Principles(Springer, 2007) Muslih, Sami I.; Baleanu, DumitruThe paper provides the fractional Lagrangian and Hamiltonian formulations of mechanical and field systems. The fractional treatment of constrained system is investigated together with the fractional path integral analysis. Fractional Schrodinger and Dirac fields are analyzed in details.Article Citation - WoS: 102Citation - Scopus: 120On Exact Solutions of a Class of Fractional Euler-Lagrange Equations(Springer, 2008) Trujillo, Juan J.; Baleanu, DumitruIn this paper, first a class of fractional differential equations are obtained by using the fractional variational principles. We find a fractional Lagrangian L(x(t), where D-c(a)t(alpha) x(t)) and 0 < alpha < 1, such that the following is the corresponding Euler-Lagrange D-t(b)alpha(D-c(a)t(alpha))x(t) + b(t, x(t)) ((c)(a)D(t)(alpha)x(t)) + f(t, x(t)) = 0. (1) At last, exact solutions for some Euler-Lagrange equations are presented. In particular, we consider the following equations D-t(b)alpha(D-c(a)t(alpha))x(t) = lambda x(t) (lambda is an element of R), (2) D-t(b)alpha(D-c(a)t(alpha))x(t) + g(t) D-c(a)t(alpha) x(t) = f(t), (3) where g(t) and f (t) are suitable functions.Article Citation - WoS: 88Citation - Scopus: 98On Fractional Euler-Lagrange and Hamilton Equations and the Fractional Generalization of Total Time Derivative(Springer, 2008) Muslih, Sami I.; Rabei, Eqab M.; Baleanu, DumitruFractional mechanics describe both conservative and nonconservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics, the equivalent Lagrangians play an important role because they admit the same Euler-Lagrange equations. By adding a total time derivative of a suitable function to a given classical Lagrangian or by multiplying with a constant, the Lagrangian we obtain are the same equations of motion. In this study, the fractional discrete Lagrangians which differs by a fractional derivative are analyzed within Riemann-Liouville fractional derivatives. As a consequence of applying this procedure, the classical results are reobtained as a special case. The fractional generalization of Faa di Bruno formula is used in order to obtain the concrete expression of the fractional Lagrangians which differs from a given fractional Lagrangian by adding a fractional derivative. The fractional Euler-Lagrange and Hamilton equations corresponding to the obtained fractional Lagrangians are investigated, and two examples are analyzed in detail.Book Part Citation - WoS: 4Citation - Scopus: 5Solving Technological Change Model by Using Fractional Calculus(Springer, 2009) Omay, Tolga; Baleanu, DumitruFractional calculus is a generalization of classical calculus, which is a generalization of ordinary differentiation and integration to arbitrary order, and has recently been used in various fields like physics, engineering, biology, and finance. By applying fractional calculus to Romer's Technological Change Model, we introduce this new method to the field of economics and obtain a generalized solution for the model.Article Citation - WoS: 20Citation - Scopus: 26Vartiational Optimal-Control Problems With Delayed Arguments on Time Scales(Springer, 2009) Abdeljawad (Maraaba), Thabet; Jarad, Fahd; Baleanu, Dumitru; Abdeljawad , ThabetThis paper deals with variational optimal-control problems on time scales in the presence of delay in the state variables. The problem is considered on a time scale unifying the discrete, the continuous, and the quantum cases. Two examples in the discrete and quantum cases are analyzed to illustrate our results. Copyright (C) 2009 Thabet Abdeljawad (Maraaba) et al.Article Citation - WoS: 57Citation - Scopus: 64Intensity Fluctuations in J-Bessel Beams of All Orders Propagating in Turbulent Atmosphere(Springer, 2008) Sermutlu, E.; Baykal, Y.; Cai, Y.; Korotkova, O.; Eyyuboglu, H. T.The scintillation index of a J (n) -Bessel-Gaussian beam of any order propagating in turbulent atmosphere is derived and numerically evaluated at transverse cross-sections with the aid of a specially designed triple integral routine. The graphical outputs indicate that, just like the previously investigated J (0)-Bessel-Gaussian beam, higher-order members of the family also offer favorable scintillation characteristics at large source sizes. This advantage is maintained against rising beam orders. Viewed along the propagation axis, beams with lower orders and smaller widths exhibit smaller values of the scintillation index at shorter propagation distances and large values at longer propagation distances. Further, it is shown that the scintillation index of the J (n) -Bessel-Gaussian beams (n > 0) is larger than that of the fundamental Gaussian and the J (0)-Bessel-Gaussian beams only near the on-axis points, while remaining smaller towards the edges of the beam.Article Citation - WoS: 70Citation - Scopus: 80Fractional-Order Euler-Lagrange Equations and Formulation of Hamiltonian Equations(Springer, 2009) Baleanu, Dumitru; Herzallah, Mohamed A. E.This paper presents the fractional order Euler-Lagrange equations and the transversality conditions for fractional variational problems with fractional integral and fractional derivatives defined in the sense of Caputo and Riemann-Liouville. A fractional Hamiltonian formulation was developed and some illustrative examples were treated in detail.