Fen - Edebiyat Fakültesi

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Novel precise solutions and bifurcation of traveling wave solutions for the nonlinear fractional (3 + 1) -dimensional WBBM equation
(20) Jarad, Fahd; Mehdi, Khush Bukht; Jarad, Fahd; Elbrolosy, Mamdouh E.; Elmandouh, Adel A.; 234808; Matematik
The nonlinear fractional differential equations (FDEs) are composed by mathematical modeling through nonlinear corporeal structures. The study of these kinds of models has an energetic position in different fields of applied sciences. In this study, we observe the dynamical behavior of nonlinear traveling waves for the M-fractional (3 + 1)-dimensional Wazwaz-Benjamin-Bona-Mohany (WBBM) equation. Novel exact traveling wave solutions in the form of trigonometric, hyperbolic and rational functions are derived using (1/G′), modified (G′/G2) and new extended direct algebraic methods with the help of symbolic soft computation. We guarantee that all the obtained results are new and verified the main equation. To promote the essential propagated features, some investigated solutions are exhibited in the form of 2D and 3D graphics by passing on the precise values to the parameters under the constrain conditions, and this provides useful information about the dynamical behavior. Further, bifurcation behavior of nonlinear traveling waves of the proposed equation is studied with the help of bifurcation theory of planar dynamical systems. It is also observed that the proposed equation support the nonlinear solitary wave, periodic wave, kink and antikink waves and most important supernonlinear periodic wave. © 2023 World Scientific Publishing Company.
Citation - Scopus: 3
The confined system approximation for solving non-separable potentials in three dimensions
(1998) Taşeli, H.; Eid, R.
The Hubert space L2(ℝ3), to which the wavefunction of the three-dimensional Schrödinger equation belongs, has been replaced by L2(Ω), where Ω is a bounded region. The energy spectrum of the usual unbounded system is then determined by showing that the Dirichlet and Neumann problems in L2(Ω) generate upper and lower bounds, respectively, to the eigenvalues required. Highly accurate numerical results for the quartic and sextic oscillators are presented for a wide range of the coupling constants.
Citation - WoS: 7
Citation - Scopus: 5
Hamilton-Jacobi quantization of the finite-dimensional systems with constraints
(Editrice Compositori Bologna, 1999) Baleanu, Dumitru; Baleanu, D; Güler, Y; Güler, Yurdahan; 56389; Matematik
The Hamiltonian treatment of constrained systems in Guler's formalism leads us to the total differential equations in many variables. These equations are integrable if the corresponding system of partial differential equations is a Jacobi system. The main aim of this paper is to investigate the quantization of the finite-dimensional systems with constraints using the canonical formalism introduced by Guler. This approach is applied for two systems with constraints and the results are in agreement with those obtained by Dirac's canonical quatization method and path integral quantization method.
Citation - WoS: 9
Quantization of Floreanini-Jackiw chiral harmonic oscillator
(Editrice Compositori Bologna, 1999) Baleanu, Dumitru; Baleanu, D; Güler, Y; Güler, Yurdahan; 56389; Matematik
The Floreanini-Jackiw formulation for the chiral quantum mechanical system oscillator is a model of constrained theory with only second-class constraints in Dirac's classification. The covariant quantization needs an infinite number of auxiliary variables and a Wess-Zumino term. In this paper we investigate the path integral quatization of this model using Guler's canonical formalism. All variables are gauge variables in Guler's formalism. Siegel's action is obtained using Hamilton-Jacobi formulation of the systems with constraints.
Citation - WoS: 0
Citation - Scopus: 0
Lax tensors and separable coordinates in (2+1) dimensions
(inst Physics Acad Sci Czech Republic, 2000) Baleanu, D; Baleanu, Dumitru; Baskal, S; 56389; Matematik
We study the Lax tensors of the separable coordinates in (2+1) dimensions. The Lax tensors of the dual manifolds are investigated.
Citation - WoS: 10
Citation - Scopus: 6
Geometrization of the Lax pair tensors
(World Scientific Publ Co Pte Ltd, 2000) Baleanu, D; Baleanu, Dumitru; Baskal, S; 56389; Matematik
The tensorial form of the Lax pair equations are given in a compact and geometrically transparent form in the presence of Cartan's torsion tensor. Three-dimensional space-times admitting Lax tensors are analyzed in detail. Solutions to Lax tensor equations include interesting examples as separable coordinates and the Toda lattice.
Citation - WoS: 16
A general treatment of singular Lagrangians with linear velocities
(Editrice Compositori Bologna, 2000) Baleanu, D; Baleanu, Dumitru; Güler, Y; 56389; Matematik
The Hamilton-Jacobi treatment of singular systems with linear velocities is investigated. Since the rank of Hessian matrix is zero, all the generalized coordinates are independent parameters. Integrability conditions reduce the degrees of freedom. Path integral quantization is analyzed.
Citation - WoS: 4
On the construction of the phase space of a singular system
(Editrice Compositori Bologna, 2000) Baleanu, D; Baleanu, Dumitru; Güler, Y; 56389; Matematik
In this work we present a method for obtaining the true degrees of freedom for the singular systems using the canonical transformations in the Hamilton-Jacobi formalism. The validity of our proposal has been tested by two examples of singular Lagrangians and the results are in agreement with those obtained by other methods.
Citation - Scopus: 9
Hamilton-Jacobi treatment of fields with constraints
(Editrice Compositori s.r.l., 2000) Baleanu, D.; Baleanu, Dumitru; Güler, Y.; 56389; Matematik
In this paper Güler's formalism for the systems with finite degrees of freedom is applied to the field theories with constraints. The integrability conditions are investigated and the path integral quantization is performed using the action given by Hamilton-Jacobi formulation. Proca's model is investigated in details.
Citation - WoS: 3
Citation - Scopus: 2
Symmetries of NUT-Kerr-Newman dual metrics
(Soc Italiana Fisica, 2001) Baleanu, D; Baleanu, Dumitru; 56389; Matematik
The symmetries of NUT-Kerr-Newman (NUT-KN) dual metrics are analysed. The NUT-Kerr-Newman dual spinning space is constructed in the presence of torsion.
Citation - WoS: 14
Citation - Scopus: 14
The hamilton-jacobi treatment of supersymmetric quantum mechanics
(World Scientific Publ Co Pte Ltd, 2001) Baleanu, Dumitru; Baleanu, D; Güler, Y; Güler, Yurdahan; 56389; Matematik
We study the Hamilton-Jacobi quantization of supersymmetric quantum mechanics. The equations of motion of the Grassmann variables are obtained from the integrability conditions. The results are in agreement with those obtained by Dirac's procedure.
Citation - WoS: 57
Citation - Scopus: 67
Spectrophotometric multicomponent analysis of a mixture of metamizol, acetaminophen and caffeine in pharmaceutical formulations by two chemometric techniques
(Pergamon-elsevier Science Ltd, 2001) Dinç, E; Baleanu, Dumitru; Baleanu, D; Onur, F; 56389; Matematik
Inverse least squares (ILS) and factor-based (principal component analysis (PCA)) techniques were proposed for the spectrophotometric multicomponent analysis of a ternary mixture consisting of metamizol, acetaminophen and caffeine, without prior separation. In these chemometric techniques, the measurements of the absorbance values were realized in the spectral range from 225 to 285 nm in the intervals of Delta lambda = 5 nm at the 13 wavelengths in the zero-order spectra of the different ternary mixtures of these active ingredients in 0.1 M HCl. The prepared calibrations of both techniques using the absorbance data and concentration matrix data sets were used to predict the concentration of the unknown concentrations of metamizol acetaminophen and caffeine in their ternary mixture. The 'MAPLE V' software was used for the numerical calculations, Mean recoveries and relative standard deviations for ILS and PCA techniques were found to be 99.8 and 1.68%, 99.9 and 1,66% for caffeine, 99.8 and 1.84%, 100.4 and 2.85% for metamizol, and 99.7 and 1.04%, 99.6 and 1.34/ for acetaminophen, respectively, for the first and second techniques. The techniques were successfully applied to two pharmaceutical formulations marketed in Turkey and results were compared with a new high-performance liquid chromatography method. (C) 2001 Elsevier Science B.V. All rights reserved.
Citation - WoS: 0
Citation - Scopus: 0
Hamilton-Jacobi quantization of constrained systems
(inst Physics Acad Sci Czech Republic, 2001) Baleanu, D; Baleanu, Dumitru; Güler, Y; 56389; Matematik
The path integral quantization of contrained systems is analysed using Hamilton-Jacobi formalism. The integrability conditions are investigated and the results are in agreement with those obtained by Dirac's method.
Citation - WoS: 3
Citation - Scopus: 2
Hamilton-Jacobi treatment of chiral schwinger model
(Kluwer Academic/plenum Publ, 2001) Baleanu, D; Baleanu, Dumitru; Güler, Y; 56389; Matematik
We investigate the path integral quantization of the bosonic chiral Schwinger model using multi-Hamilton-Jacobi procedure. The integrability conditions require the extension of the initial phase space. The Wess-Zumino term was recovered calculating the action corresponding to the extended system.
Citation - WoS: 18
Citation - Scopus: 20
Multi-Hamilton-Jacobi quantization of O(3) nonlinear sigma model
(World Scientific Publ Co Pte Ltd, 2001) Baleanu, Dumitru; Baleanu, D; Güler, W; Güler, Yurdahan; 56389; Matematik
The O(3) nonlinear sigma model is investigated using multi-Hamilton-Jacobi formalism. The integrability conditions are investigated and the results are in agreement with those obtained by Dirac's method. By choosing an adequate extension of phase space we describe the transformed system by a set of three Hamilton-Jacobi equations and calculate the corresponding action.
Citation - WoS: 21
Citation - Scopus: 22
Hamilton-Jacobi treatment of a non-relativistic particle on a curved space
(Iop Publishing Ltd, 2001) Baleanu, Dumitru; Baleanu, D; Güler, Y; Güler, Yurdahan; 56389; Matematik
In this paper a non-relativistic particle moving on a hypersurface in a curved space and the multidimensional rotator are investigated using the Hamilton-Jacobi formalism. The equivalence with the Dirac Hamiltonian formalism is demonstrated in both Cartesian and curvilinear coordinates. The energy spectrum of the multidimensional rotator is equal to that of a pure Laplace-Beltrami operator with no additional constant arising from the curvature of the sphere.
Citation - WoS: 34
Chemometric quantitative analysis of pyridoxine HCl and thiamine HCl in a vitamin combination by principal component analysis, classical least squares, and inverse least squares techniques
(Marcel dekker inc, 2001) Dinç, E; Baleanu, Dumitru; Baleanu, D; Onur, F; 56389; Matematik
Three chemometric techniques were described for the analysis of pyridoxine hydrochloride and thiamine hydrochloride within a vitamin combination in the presence of spectral interferences. For these techniques, the training set was prepared by using synthetic mixtures containing two vitamins in multiple possible combinations for the range of 8-40 mu /mL in 0.1 M HCl. The absorbance values for the training set were obtained by direct measurements at 18 wavelengths in the region 222-305 nm for the zero order spectra. The numerical values were calculated by using the 'Maple V' software. Mean recoveries and relative standard deviations for the principal component analysis, classical least squares and inverse least squares techniques were found as 100.7% and 0.95%; 100.5% and 1.38% and, 99.3% and 1.04 for pyridoxine hydrochloride; and 99.7% and 1.03%; 99.1% and 1.05% and, 99.6% and 1.58% for thiamine hydrochloride, respectively. These three chemometric techniques were successfully applied to vitamin tablets marketed in Turkey. The results were compared with each other and good coincidence was observed.
Citation - WoS: 10
Citation - Scopus: 9
Dual metrics for a class of radiative space-times
(World Scientific Publ Co Pte Ltd, 2001) Baleanu, D; Baleanu, Dumitru; Baskal, S; 56389; Matematik
Second-rank nondegenerate Killing tensors for some subclasses of space-times admitting parallel null one-planes ace investigated. Lichnerowicz radiation conditions are imposed to provide a physical meaning to space-times whose metrics are described through their associated second-rank Killing tensors. Conditions under which the dual space-times retain the same physical properties are presented.
Citation - WoS: 11
Citation - Scopus: 9
Dual metrics and nongeneric supersymmetries for a class of Siklos space-times
(World Scientific Publ Co Pte Ltd, 2002) Baleanu, D; Baleanu, Dumitru; Baskal, S; 56389; Matematik
The presence of Killing-Yano tensors implies the existence of nongeneric supercharges in spinning point particle theories on curved backgrounds. Dual metrics axe defined through their associated nondegenerate Killing tensors of valence two. Siklos space-times, which are the only nontrivial Einstein spares conformal to nonflat pp-waves are investigated with regard to the existence of their corresponding Killing and Killing-Yano, tensors. It is found that a class of Siklos space-times admit dual metrics and nongeneric supercharges.
Citation - WoS: 38
Citation - Scopus: 41
Painleve test and higher order differential equations
(Taylor & Francis Ltd, 2002) Mugan, U; Jarad, Fahd; Jarad, F; 234808; Matematik
Starting from the second Painleve equation, we obtain Painlev'e type equations of higher order by using the singular point analysis.

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