### فهرست مطالب

• Volume:2 Issue: 1, Winter 2021
• تاریخ انتشار: 1399/10/12
• تعداد عناوین: 6
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• Ahmad Zavvartorbati * Pages 1-16
In this paper, Galerkin and collocation methods based on shifted Legendre polynomials and spectral methods have been applied on nonlinear Volterra-Fredholm-Hammerstein (VFH) integral equations, these methods transfer the finding solution of a nonlinear integral equation to finding the solution of nonlinear algebraic equations, in order to solve these nonlinear algebraic equations we use Newton method composed by generalized minimal residual (NGMRes) method, the iteration number and running time for implementation of NGMRes method are important parameters that have been considered to solve this type of integral equations. These methods are applied on several various nonlinear VFH integral equations that confirm accuracy and efficiency of the methods.
Keywords: Volterra-Fredholm-Hammerstein integral equations, Collocation method, Galerkin method, Spectral methods, Newton-Krylove GMRes
• Morteza Jiryaei Sharahi *, Ali Ramazan Boroujerdi Pages 17-41
Determining of the seismic bearing capacity has a great importance for foundations located near sloping ground in geotechnical earthquake engineering. In this paper a new formulation based on the pseudo-dynamic method is presented to calculate the seismic bearing capacity of strip foundations resting on C-φ soil which are adjacent to slope using limit equilibrium method. The seismic bearing capacity coefficient Nγe for the simultaneous resistance of surcharge, unit weight and cohesion is calculated considering two-sided composite rupture surface which is the combination of a logarithmic spiral and planar surfaces. This failure mechanism comprises of two slip surfaces which are assumed that a realistic failure surface occurs on the side of slope and the resistance mobilization is taken into account on the side without slope. Using the presented approach a parametric study is conducted to study the effect of various parameters such as soil cohesion, soil friction angle, slope angle, horizontal, and vertical seismic coefficients. Results show the bearing capacity coefficient increases by approximately 176 and 264% when β increases from 10 to 20° and from 20 to 30°, respectively. The results of this study are compared with the few pseudo-static results available in the literature. Present procedure give lower amount of bearing capacity of strip footings in comparison with the results of pseudo-static analysis.
Keywords: Seismic Bearing capacity, slopes, Pseudo-dynamic, limit equilibrium
• Robabeh Sahandi *, Behnaz Farnam Pages 42-47
‎In ‎this ‎paper ‎w‎e study the existence of positive solutions for a class of boundary ‎problems.
Keywords: Boundary value problem, positive solution, Fixed point index, Jensen's inequality‎
• Fatemeh Sheshpari *, Masoud Amelsakhi Pages 48-60
Geothermal energy is one of the most environmental-friendly and cost effective energy sources with potential to replace fossil fuels and help mitigate global warming. Recent technological progress, energy price variability, difficulty of oil and gas supply from foreign countries and the need to reduce fossil fuel deployment have made the exploitation of geothermal energy, especially for heating and cooling purposes, an attractive and viable energy alternative. Energy pile provides a mean to reduce energy consumption for space heating and cooling, while functioning as a support for superstructure. Despite of the environmental benefits of energy pile, some countries are still reluctant in implementing energy pile. This is because of knowledge gap on the influence of temperature cycles on energy pile ultimate and serviceability limit states. This paper reviews the geo exchanger and energy pile systems and highlights their applicability and efficiency as well as advantages and limits. To investigate the effects of soils on energy pile, in present study a two dimensional (2D), axisymmetric numerical model for the energy piles has been created using finite element method based on the field test. The main purpose of this study is investigating energy pile response in various soils. This was performed by considering some different hypothetical layers with underlain bedrock and their results which included displacement, strain and stresses induced by thermal load compared with four layered soil experimental data. The results showed that soil properties have important effect on the response of energy pile. Also temperature affects pile reactions.
Keywords: Geothermal Energy, heat exchanger, fossil fuels, Finite element, COMSOL
• Enayatolah Yazdankish * Pages 61-70

The Morse potential has important and significance rule to describe the diatomic molecule energy and structure. However there is no any analytical solution for Schrodinger equation with this potential without approximation, therefore other ways such as numerical, perturbation, variation and so on are taken to deal with this potential. In this work the the Nikiforov-Uvarov method is taken to obtain its energy eigenvalues and eigenfunctions. In the ground state the Schrodinger equation with this potential have exact solution but with arbitrary l-state the Morse potential with centrifugal term have no exact solution therefore it is solved analytically with use the Pekeris approximation. Here in this work we solved the Schrodinger in the space of D dimension and use the Nikiforove-Uvarov method which is based on solving the hyper geometric type second-order differential equations by means of the special orthogonal functions.

Keywords: solving of Schrodinger equation, Morse potential, Nikiforov-Uvarov method
• Elaheh Khamseh * Pages 71-77
Pairings are particular bilinear maps, and they have been defined based on elliptic curves whichare abelian groups. In cryptography and security problems use these pairings. Mrabet et al. proposedpairings from a tensor product of groups in 2013. Also Mahalanobis et al. proposed bilinear cryptographyusing groups of nilpotency class two in 2017. In this paper, I develop a novel idea of a bilinear cryptosystemusing Lie algebras from p-groups. First the researcher proposes pairing on Lie algebras from elliptic curves,and then pairings that can be constructed on Lie algebras from some of the non-abelian p-groups.
Keywords: Lie algebra, Bilinear map, p-group