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#### A numerical solution of an inverse parabolic problem

(Işık University Press, 2012-05-07)

In this paper, we will first study the existence and uniqueness of the solution of an inverse problem for a linear equation with non-linear boundary conditions (radiation terms), via an auxiliary problem. Furthermore, a ...

#### Asymptotic expansions for the ergodic moments of a semi-markovian random walk with a generalized delaying barrier

(Işık University Press, 2012)

In this study, a semi-Markovian random walk process (X(t)) with a generalized delaying barrier is considered and the ergodic theorem for this process is proved under some weak conditions. Then, the exact expressions and ...

#### On tracking of solutions of parabolic variational inequalities

(Işık University Press, 2012-04-19)

The problem of constructing a feedback control algorithm for a parabolic variational inequality is considered. This algorithm should provide tracking a prescribed trajectory by a solution of the given inequality. Two solving ...

#### Energy preserving integratıon of KDV-KDV systems

(Işık University Press, 2012-07-01)

Coupled Korteweg de Vries (KdV) equations in Hamiltonian form are integrated by the energy preserving average vector field (AVF) method. Numerical results confirm long term preservation of the energy and the quadratic ...

#### Haar basis method to solve some inverse problems for two-dimensional parabolic and hyperbolic equations

(Işık University Press, 2013)

A numerical method consists of combining Haar basis method and Tikhonov regularization method. We apply the method to solve some inverse problems for twodimensional parabolic and hyperbolic equations using noisy data. In ...

#### Application of the generalized clifford-dirac algebra to the proof of the dirac equation fermi-bose duality

(Işık University Press, 2013)

The consideration of the bosonic properties of the Dirac equation with arbitrary mass has been continued. As the necessary mathematical tool the structure and different representations of the 29-dimensional extended real ...

#### Interaction between selection and segregation ratios with redefined concept of fitness differentials

(Işık University Press, 2013-01-11)

Taking into account the redefined concept of fitness differentials among the genotypes, natures of equilibria of models of differential selection in the two sexes under random mating with Mendelian segregation as well as ...

#### The dirac equation as the consequence of the quantum-mechanical spin 1/2 doublet model

(Işık University Press, 2013)

The detailed consideration of the relativistic canonical quantum-mechanical model of an arbitrary →s -multiplet is given. The group-theoretical analysis of the algebra of experimentally observable physical quantities for ...

#### Energy preserving integration of bi-Ham

(Işık University Press, 2013-01-04)

The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg ...

#### On the existence of solution for an inverse problem

(Işık University Press, 2013)

We consider a boundary detection problem. We present physical motivations. We formulate the problem as a shape optimization problem by introducing the Neumann condition of the accessible part in a cost functional to be ...