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

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

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

DEEP LEARNING BASED AERIAL IMAGERY CLASSIFICATION FOR TREE SPECIES IDENTIFICATION

Forest monitoring and tree species categorization has a vital importance in terms of biodiversity conservation, ecosystem health assessment, climate change mitigation, and sustainable resource management. Due to large-scale coverage of forest areas, remote sensing technology plays a crucial role in the monitoring of forest areas by timely and regular data acquisition, multi-spectral and multi-temporal analysis, non-invasive data collection, accessibility and cost-effectiveness. High-resolution satellite and airborne remote sensing technologies have supplied image data with rich spatial, color, and texture information. Nowadays, deep learning models are commonly utilized in image classification, object recognition, and semantic segmentation applications in remote sensing and forest monitoring as well. We, in this study, selected a popular CNN and object detection algorithm YOLOv8 variants for tree species classification from aerial images of TreeSatAI benchmark. Our results showed that YOLOv8-l outperformed benchmark’s initial release results, and other YOLOv8 variants with 71,55% and 72,70% for weighted and micro averaging scores, respectively