Matematik Bölümü

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2D gravity and the Hamilton-Jacobi formalism
(Soc Italiana Fisica, 2002) Baleanu, Dumitru; Güler, Yılmaz; 56389
Hamilton-Jacobi formalism is used to study 2D gravity and its SL(2, R) hidden symmetry. If the contribution of the surface term is considered, the obtained results coincide with those given by the Dirac and Faddeev-Jackiw approaches.
A zero-crossing technique for the multidetermination of thiamine HCl and pyridoxine HCl in their mixture by using one-dimensional wavelet transform
(Pergamon-Elsevier Science LTD, 2003) Baleanu, Dumitru; Baleanu, Dumitru; 56389
A new zero-crossing technique based on one-dimensional wavelet transform (WT) was developed and applied on a commercial vitamin product and binary mixtures containing thiamine HCl and pyridoxine HCl in the presence of the interference of the analysed signals. We selected from the data of the UV-Vis absorption spectra a signal consisting of 1150 points corresponding to the concentration range 8-32 mg/ml for both vitamins and we subjected it to one-dimensional continuous WT Mexican (MEXICAN) and Meyer (MEYER). Since the peaks of the transformed signals were bigger than original ones a zero crossing technique was applied to obtain the regression equations. The validity of Beer-Lambert law was assumed for the transformed signals. An appropriate scale setting was choosing to obtain an alternative calibration for each method. The basic concepts about wavelet method were briefly explained and MATLAB 6.5 software was used for one-dimensional wavelet analysis, The obtained results were successfully compared among each other and with those obtained by other literature methods. The developed method is rapid, easy to apply. not expensive and suitable for analysing of the overlapping signals of compounds in their mixtures without any chemical pre-treatment.
About fractional calculus of singular Lagrangians
(IEEE, 2004) Baleanu, Dumitru; 56389
In this paper the solutions of the fractional Euler-Lagrange equations corresponding to singular fractional Lagrangians were examined. Despite of the complexity of solutions in the fractional case the gauge classical symmetry was preserved. Four examples of fractional singular Lagrangians were analyzed in details.
An approach to quantitative two-component analysis of a mixture containing hydrochlorothiazide and spironolactone in tablets by one-dimensional continuous daubechies and biorthogonal wavelet analysis of UV-spectra
(Taylor&Francis INC, 2003) Baleanu, Dumitru; Baleanu, Dumitru; Üstündağ, Özgür; 56389
In this study a new method of quantitative two-component analysis of a mixture of hydrochlorothiazide (HCT) and spironolactone (SP) in the presence of strongly overlapping signals was achieved by using one-dimensional continuous wavelet analysis. This new method was built on the simultaneous use of both continuous wavelet transform and the zero crossing technique for the quantitative resolution of this binary mixture. A series of solutions, in the concentration range of 2-22 mg/ml for both compounds, in methanol and 0.2 M sodium acetate buffer, pH = 5 (20:80), were considered. The absorption spectra of the standard solutions were recorded in the wavelength range of 215-330 nm. To apply our methods we selected 400 points from the absorption spectra and we subjected the corresponding signal to Daubechies2 (DAUB2) and Biorthogonal1.5 (BIOR1.5) one-dimensional wavelet transform. In the transformed signals, the amplitude of HCT was measured at the position of a zero crossing point of SP and vice versa. Thus simple linear regression analysis can be applied to establish calibrations for both components. These calibrations were validated with synthetic mixtures of HCT and SP. MATLAB 6.5 software was used for one-dimensional wavelet analysis, and the basic concepts about wavelet method are briefly explained. The method developed in this paper is rapid, easy to apply, inexpensive and it is suitable for analysis of the overlapping signals of compounds in their mixtures without any chemical pre-treatment.
Application of the wavelet method for the simultaneous quantitative determination of benazepril and hydrochlorothiazide in their mixtures
(AOAC International, 2004) Baleanu, Dumitru; Baleanu, Dumitru; 56389
The discrete and continuous wavelet transforms were applied to the overlapping signal analysis of the ratio data signal for simultaneous quantitative determination of the title subject compounds in samples. The ratio spectra data of the binary mixtures containing benazepril (BE) and hydrochlorothiazide (HCT) were transferred as data vectors into the wavelet domain. Signal compression, followed by a 1-dimension continuous wavelet transform (CWT), was used to obtain coincident transformed signals for pure BE and HCT and their mixtures. The coincident transformed amplitudes corresponding to both maximum and minimum points allowed construction of calibration graphs for each compound in the binary mixture. The validity of CWT calibrations was tested by analyzing synthetic mixtures of the investigated compounds, and successful results were obtained. All calculations were performed within EXCEL, C++, and MATLAB6.5 softwares. The obtained results indicated that our approach was flexible and applicable for the binary mixture analysis.
Chain and Hamilton-Jacobi approaches for systems with purely second-class constraints
(Soc Italiana Fisica, 2003) Baleanu, Dumitru; Güler, Yurdahan; 56389
The equivalence of the chain method and Hamilton-Jacobi formalism is demonstrated. The stabilization algorithm of Hamilton-Jacobi formalism is clarified and two examples are presented in details.
Compatibility of non-generic supersymmetries and geometric duality for a subclass of generalized pp-wave metrics
(Amer Inst Physics, 2004) Baleanu, Dumitru; Baskal, S.; 56389
Spinning point particle theories accommodate non-generic supercharges in connection with the existence of Killing-Yano tensors. Killing-Yano tensors of order two and three and their corresponding Killing tensors are found for a subclass of generalized pp-wave metrics. These metrics include the pp-wave itself, its possible generalizations and the Siklos metric which is conformal to that. The compatibility between geometric duality and non-generic symmetries is discussed within the context of the metric solutions. It is found that some of the metric solutions admit anti-de Sitter spacetimes while some are found to be purely radiative.
Continuous wavelet transformation applied to the simultaneous quantitative analysis of two-component mixtures
(Govi-Verlag Pharmazeutischer Verlag Gmbh, 2004) Baleanu, Dumitru; Baleanu, Dumitru; Üstündağ, O.; Aboul-Eneyin, H. Y.; 56389
Dual metrics and nongeneric supersymmetries for a class of Siklos space-times
(World Scientific Publ CO PTE LTD, 2002) Baleanu, Dumitru; Baskal, S.; 56389
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.
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.
Fractional Euler-Lagrange equations for constrained systems
(Amer Inst Physics, 2004) Avkar, Tansel; Baleanu, Dumitru; 56389
The fractional calculus is the name for the theory of integrals and derivatives of arbitrary order, which generalize the notions of n-fold integration and integer-order differentiation. Differential equations of fractional order appear in certain applied problems and in theoretical researches. In this paper, the Euler-Lagrange equations of the Lagrangians linear in velocities were derived using the fractional calculus. Two examples of constrained systems possessing a gauge invariance are investigated in details, the explicit solutions of Euler-Lagrange equations are obtained, and the recovery of the classical results is discussed.
Hamilton-Jacobi and symplectic analysis of a particle constrained on a circle
(Inst Physics Acad Sci Czech Republic, 2003) Baleanu, Dumitru; Güler, Yurdahan; 56389
Hamilton-Jacobi and modified Faddeev-Jackiw methods were applied to investigate the motion of a particle moving on a circle. The results of both methods were found to be equivalent with those of Dirac's formalism. Besides, the importance of the Lagrange multipliers was analyzed and the action of the second-class constrained system was given.
Hamilton-Jacobi formalism of Abelian Proca's model revisited
(Editrice Copmpositori Bologna, 2002) Baleanu, Dumitru; Güler, Yılmaz; 56389
The Abelian Proca model is investigated using the Hamilton-Jacobi formalism treating it as a field and as a singular system, The results of these two methods are in agreement with each other and with Dirac's formulation.
Hamilton-Jacobi formalism of the massive Yang-Mills theory revisited
(Editrice Copmpositori Bologna, 2003) Baleanu, Dumitru; 56389
Using Hamilton-Jacobi formalism we investigated the massive Yang-Mills theory on both extended and reduced phase-space. The integrability conditions were discussed and the actions were calculated.
Hamilton-Jacobi formulation of the Harada gauged Floreanini-Jackiw action
(Inst Physics Acad Sci Czech Republic, 2002) Baleanu, Dumitru; Güler, Y.; 56389
We study the front-form Harada gauged Floreanini-Jackiw action and its BRST-anti-BRST symmetry within Hamilton-Jacobi formalism.
Hamilton-Jacobi quantization of constrained systems
(Inst Physics Acad Sci Czech Republic, 2001) Baleanu, Dumitru; Güler, Yılmaz; 56389
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.
Hamilton-Jacobi quantization of systems with time-dependent constraints
(Kluwer Academıc/Plenum Publ, 2002) Baleanu, Dumitru; Güler, Yurdahan; 56389
Hamilton-Jacobi formalism is used to investigate time-dependent constraint systems. It is proved that the generalization of Dirac's canonical quantization method in the nonstationary case can be obtained naturally in Hamilton-Jacobi formalism. The example of the relativistic particle in a plane wave is analyzed in detail.
Killing-Yano symmetry for a class of space-times admitting parallel null 1-planes
(Soc Italiana Fisica, 2002) Baleanu, Dumitru; Baskal, S.; 56389
A possible generalization of plane fronted waves with parallel rays (gpp-wave) falls into a more general class of metrics admitting parallel null 1-planes. For gpp-wave metric, the zero-curvature condition is given, the Killing-Yano tensors of order two and three are found and the corresponding Killing tensors are constructed. Henceforth, the compatibility between geometric duality and non-generic symmetries is presented.
Killing-Yano tensors and angular momentum
(Inst Physics Acad Sci Czech Republic, 2004) Baleanu, Dumitru; Defterli, Özlem; 56389; 31401
New geometries were obtained by adding a suitable term involving the components of the angular momentum to the corresponding free Lagrangians. Killing vectors, Killing-Yano and Killing tensors of the obtained manifolds were investigated.
Killing-Yano tensors, surface terms and superintegrable systems
(Amer Inst Physics, 2004) Baleanu, Dumitru; Defterli, Özlem; 56389; 31401
Killing-Yano and Killing tensors are investigated corresponding to a set of two dimensional superintegrable systems. A suitable surface term is added to the corresponding free Lagrangian describing the motion of a particle on a 2-sphere of unit radius and we analyze the symmetries of the obtained geometries.

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Browsing Matematik Bölümü by Department "Çankaya Üniversitesi, Fen-Edebiyat Fakültesi,Matematik Bölümü"