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

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

Analytical Treatment of the Oscillating Yukawa Potential

Using a suitable Laguerre basis set that ensures a tridiagonal matrix representation of the reference Hamiltonian, we were able to evaluate in closed form the matrix elements of the generalized Yukawa potential with complex screening parameter. This enabled us to treat analytically both the cosine and sine-like Yukawa potentials on equal footing and compute their bound states spectrum as the eigenvalues of the associated analytical matrix representing their Hamiltonians. Finally we used a carefully designed complex scaling method to evaluate the resonance energies and compared our results satisfactorily with those obtained in the literature.Comment: 8 pages 2 table

Efficient design and evaluation of countermeasures against fault attacks using formal verification

This paper presents a formal verification framework and tool that evaluates the robustness of software countermeasures against fault-injection attacks. By modeling reference assembly code and its protected variant as automata, the framework can generate a set of equations for an SMT solver, the solutions of which represent possible attack paths. Using the tool we developed, we evaluated the robustness of state-of-the-art countermeasures against fault injection attacks. Based on insights gathered from this evaluation, we analyze any remaining weaknesses and propose applications of these countermeasures that are more robust

Güvenilirlik Analiz Metodunun Köprülere Uygulanmasi

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2008Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2008Günümüzde köprülerin yapısal değerlendirmesi konusunda ilerleme kaydetmiş olan ülkelerde köprülerin yapısal analizinde güvenilirlik metodlarının kullanımı gün geçtikçe artmaktadır. Ülkemizdeki köprüler ağır yüklere maruz bırakılmakta ve buna ilaveten bu köprülerin yetersiz onarım ve bakım uygulamaları ile uzun süre hizmet vermesi beklenmektedir. Bu çalışmada Ankara il sınırları içinde 1969 yılında T.C. Karayolları tarafından yapılmış olan Peçenek Köprüsü’nün dizayn yükü ve yıkılmasına sebep olan taşıt yükü arasındaki ilişki güvenilirlik analiz metoduna göre incelenmiştir.Nowadays, the use of reliability methods for structural analysis of bridges is rapidly increasing in countries that have shown progress in the subject of structural evaluation of bridges. In Turkey, bridges are being subjected to heavy loads. Furthermore, the bridges are being expected to be of service for long times without adequate repair and maintenance. In this work, the relation between the design load and the vehicular load that led to the collapse of Peçenek bridge, built by the Turkish Highways Department in 1969 within the Ankara province, has been investigated using the reliability analysis method

Heritability and cross-species comparisons of human cortical functional organization asymmetry

The human cerebral cortex is symmetrically organized along large-scale axes but also presents inter-hemispheric differences in structure and function. The quantified contralateral homologous difference, that is asymmetry, is a key feature of the human brain left-right axis supporting functional processes, such as language. Here, we assessed whether the asymmetry of cortical functional organization is heritable and phylogenetically conserved between humans and macaques. Our findings indicate asymmetric organization along an axis describing a functional trajectory from perceptual/action to abstract cognition. Whereas language network showed leftward asymmetric organization, frontoparietal network showed rightward asymmetric organization in humans. These asymmetries were heritable in humans and showed a similar spatial distribution with macaques, in the case of intra-hemispheric asymmetry of functional hierarchy. This suggests (phylo)genetic conservation. However, both language and frontoparietal networks showed a qualitatively larger asymmetry in humans relative to macaques. Overall, our findings suggest a genetic basis for asymmetry in intrinsic functional organization, linked to higher order cognitive functions uniquely developed in humans

Criterion for polynomial solutions to a class of linear differential equation of second order

We consider the differential equations y''=\lambda_0(x)y'+s_0(x)y, where \lambda_0(x), s_0(x) are C^{\infty}-functions. We prove (i) if the differential equation, has a polynomial solution of degree n >0, then \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1}\hbox{and}\quad s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1},\quad n=1,2,.... Conversely (ii) if \lambda_n\lambda_{n-1}\ne 0 and \delta_n=0, then the differential equation has a polynomial solution of degree at most n. We show that the classical differential equations of Laguerre, Hermite, Legendre, Jacobi, Chebyshev (first and second kind), Gegenbauer, and the Hypergeometric type, etc, obey this criterion. Further, we find the polynomial solutions for the generalized Hermite, Laguerre, Legendre and Chebyshev differential equations.Comment: 12 page

The rotating Morse potential model for diatomic molecules in the tridiagonal J-matrix representation: I. Bound states

This is the first in a series of articles in which we study the rotating Morse potential model for diatomic molecules in the tridiagonal J-matrix representation. Here, we compute the bound states energy spectrum by diagonalizing the finite dimensional Hamiltonian matrix of H2, LiH, HCl and CO molecules for arbitrary angular momentum. The calculation was performed using the J-matrix basis that supports a tridiagonal matrix representation for the reference Hamiltonian. Our results for these diatomic molecules have been compared with available numerical data satisfactorily. The proposed method is handy, very efficient, and it enhances accuracy by combining analytic power with a convergent and stable numerical technique.Comment: 18 Pages, 6 Tables, 4 Figure

The Klein-Gordon equation with the Kratzer potential in d dimensions

We apply the Asymptotic Iteration Method to obtain the bound-state energy spectrum for the d-dimensional Klein-Gordon equation with scalar S(r) and vector potentials V(r). When S(r) and V(r) are both Coulombic, we obtain all the exact solutions; when the potentials are both of Kratzer type, we obtain all the exact solutions for S(r)=V(r); if S(r) > V(r) we obtain exact solutions under certain constraints on the potential parameters: in this case, a possible general solution is found in terms of a monic polynomial, whose coefficients form a set of elementary symmetric polynomials.Comment: 13 page

Electrical conduction and dielectric relaxation properties of AlN thin films grown by hollow-cathode plasma-assisted atomic layer deposition

In this study, aluminum nitride (AlN) thin films were deposited at 200 �C, on p-type silicon substrates utilizing a capacitively coupled hollow-cathode plasma source integrated atomic layer deposition (ALD) reactor. The structural properties of AlN were characterized by grazing incidence x-ray diffraction, by which we confirmed the hexagonal wurtzite single-phase crystalline structure. The films exhibited an optical band edge around ∼5.7 eV. The refractive index and extinction coefficient of the AlN films were measured via a spectroscopic ellipsometer. In addition, to investigate the electrical conduction mechanisms and dielectric properties, Al/AlN/p-Si metal-insulator-semiconductor capacitor structures were fabricated, and current density-voltage and frequency dependent (7 kHz-5 MHz) dielectric constant measurements (within the strong accumulation region) were performed. A peak of dielectric loss was observed at a frequency of 3 MHz and the Cole-Davidson empirical formula was used to determine the relaxation time. It was concluded that the native point defects such as nitrogen vacancies and DX centers formed with the involvement of Si atoms into the AlN layers might have influenced the electrical conduction and dielectric relaxation properties of the plasma-assisted ALD grown AlN films. � 2016 IOP Publishing Ltd