Nonexistense of global solutions of a quasilinear bi-hyperbolic equation with dynamical boundary conditions

In this work, the nonexistence of the global solutions to a class of initial boundary value problems with dissipative terms in the boundary conditions is considered for a quasilinear system of equations. The nonexistence proof is achieved by the use of a lemma due to O. Ladyzhenskaya and V.K. Kalantarov and by the usage of the so called generalized convexity method. In this method one writes down a functional which reflects the properties of dissipative boundary conditions and represents the norm of the solution in some sense, then proves that this functional satisfies the hypotheses of Ladyzhenskaya-Kalantarov lemma. Hence from the conclusion of the lemma one deduces that in a finite time $t_2$, this functional and hence the norm of the solution blows up

Any ll-state solutions of the Hulth\'en potential by the asymptotic iteration method

In this article, we present the analytical solution of the radial Schr\"{o}dinger equation for the Hulth\'{e}n potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any $l$ states. We obtain the energy eigenvalues and the corresponding eigenfunctions for different screening parameters. The wave functions are physical and energy eigenvalues are in good agreement with the results obtained by other methods for different $\delta$ values. In order to demonstrate this, the results of the asymptotic iteration method are compared with the results of the supersymmetry, the numerical integration, the variational and the shifted 1/N expansion methods.Comment: 14 pages and 1 figur

Arbitrary l-state solutions of the rotating Morse potential by the asymptotic iteration method

For non-zero $\ell$ values, we present an analytical solution of the radial Schr\"{o}dinger equation for the rotating Morse potential using the Pekeris approximation within the framework of the Asymptotic Iteration Method. The bound state energy eigenvalues and corresponding wave functions are obtained for a number of diatomic molecules and the results are compared with the findings of the super-symmetry, the hypervirial perturbation, the Nikiforov-Uvarov, the variational, the shifted 1/N and the modified shifted 1/N expansion methods.Comment: 15 pages with 1 eps figure. accepted for publication in Journal of Physics A: Mathematical and Genera

The Energy Eigenvalues of the Two Dimensional Hydrogen Atom in a Magnetic Field

In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the no magnetic field case analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for $n=2-10$ and $m=0-1$ states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.Comment: 13 pages and 5 table

Comparison of oxidation stability of virgin olive oils from different locations of Turkey

Ten kinds of virgin olive oil of two major cultivars (Ayvalık and Memecik) produced in several areas of Turkey (Bayındır, Edremit, Ortaklar, Burhaniye, Ezine, Tire, Havran, Ayvalık, Altınoluk, and Küçükkuyu) were analysed. The quality characteristics, fatty acid composition, total phenol, ando-diphenol content of the samples were determined. Oxidative stability and free radical scavenging activity were determined using Rancimat test, Schaal oven test, and DPPH method. It was found that while Memecik oil from Ortaklar demonstrated the strongest oxidative stability, Ayvalık oil from Ezine had the lowest oxidative stability among the samples. Fatty acid composition and especially oleic acid/linoleic acid ratio was previously defined as a parameter that can help distinguish cultivars from one another; however, this study proved that total phenol, especially o-diphenol content of the oil, has the strongest effect on oxidative stability compared to other factors including fatty acid composition