Mathematics / Matematik
http://hdl.handle.net/11147/8
Collection of Mathematics / Matematik Bölümü koleksiyonu2018-07-21T11:16:41ZExactly solvable Hermite, Laguerre, and Jacobi type quantum parametric oscillators
http://hdl.handle.net/11147/6839
Exactly solvable Hermite, Laguerre, and Jacobi type quantum parametric oscillators
Atılgan Büyükaşık, Şirin; Çayiç, Zehra
We introduce exactly solvable quantum parametric oscillators, which are generalizations of the quantum problems related with the classical orthogonal polynomials of Hermite, Laguerre, and Jacobi type, introduced in the work of Büyükaşık et al. [J. Math. Phys. 50, 072102 (2009)]. Quantization of these models with specific damping, frequency, and external forces is obtained using the Wei-Norman Lie algebraic approach. This determines the evolution operator exactly in terms of two linearly independent homogeneous solutions and a particular solution of the corresponding classical equation of motion. Then, time-evolution of wave functions and coherent states are found explicitly. Probability densities, expectation values, and uncertainty relations are evaluated and their properties are investigated under the influence of the external terms.
2016-12-01T00:00:00ZAnalytic investigation of a reaction-Diffusion brusselator model with the time-space fractional derivative
http://hdl.handle.net/11147/6808
Analytic investigation of a reaction-Diffusion brusselator model with the time-space fractional derivative
Aslan, İsmail
It is well known that many models in nonlinear science are described by fractional differential equations in which an unknown function appears under the operation of a derivative of fractional order. In this study, we propose a reaction-diffusion Brusselator model from the viewpoint of the Jumarie's modified Riemann-Liouville fractional derivative. Based on the (G'/G)-expansion method, various kinds of exact solutions are obtained. Our results could be used as a starting point for numerical procedures as well.
2014-04-01T00:00:00ZOn pseudo semisimple rings
http://hdl.handle.net/11147/6803
On pseudo semisimple rings
Büyükaşık, Engin; Mohamed, Saad H.; Mutlu, Hatice
A necessary and sufficient condition is obtained for a right pseudo semisimple ring to be left pseudo semisimple. It is proved that a right pseudo semisimple ring is an internal exchange ring. It is also proved that a right and left pseudo semisimple ring is an SSP ring
2013-03-01T00:00:00ZRings over which flat covers of simple modules are projective
http://hdl.handle.net/11147/6793
Rings over which flat covers of simple modules are projective
Büyükaşık, Engin
Let R be a ring with identity. We prove that, the flat cover of any simple right R-module is projective if and only if R is semilocal and J(R) is cotorsion if and only if R is semilocal and any indecomposable flat right R-module with unique maximal submodule is projective.
2012-06-01T00:00:00Z