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On the Evaluation Overlap Integrals with the Same and Different Screening Parameters Over Slater Type Orbitals via the Fourier-Transform Method

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Communications in Theoretical Physics 2005年第1期43卷 151-158页

作者： M.Yavuz N.Yükcü E.OEztekin H.Yilmaz S.Doendür DepartmentofPhysics OndokuzMayisUniversityFacultyofArtsandSciencesKurupelit55139Samsun-Turkey

In this paper, derivation of analytical expressions for overlap integrals with the same and different screening parameters of Slater type orbitals (STOs) via the Fourier-transform method is presented. Consequently, it is relatively easy to express the Fourier integral representations of the overlap integrals with same and different screening parameters mentioned as finite sums of gegenbauer, Gaunt, binomial coefficients, and STOs.

关键词： overlap integrals gegenbauer polynomials slater type orbitals

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Exploration of uniform heat flux on the flow and heat transportation of ferrofluids along a smooth plate： Comparative investigation

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International Journal of Biomathematics 2018年第4期11卷 57-75页

作者： Muhammad Usman Muhammad Hamid Syed Tauseef Mohyud Din Asif Waheed Wei Wang School of Mathematical Sciences Peking University Beijing 100871 P. R. China Department of Mathematics Faculty of Sciences HITEC University Taxila Cantt Pakistan Department of Mathematics COMSATS Institute of Information Technology Attock Pakistan

The paper is devoted to a new extension in gegenbauer wavelet method （GWM） to investigate the transfer of heat and MHD boundary-layer flow of ferrofluids beside a flat plate with velocity slip. A homogenous model study is conducted in which we assumed the heat transfer and forced convective flow of ferrofluids along a flat plate with a uniform wall heat flux. In the direction of transverse to plate, a magnetic field is imposed. Three various magnetic nanoparticle types including Mn-ZnFe204, CoFe204, Fe3O4 are incorporated inside the base fluid. Two types of base fluids （water and kerosene） with bad thermal conductivity as compared to nanoparticles of solid magnetic have been assumed. The mathematical model is tackled via modified gegenbauer wavelet method （MGWM）. A simulation is accomplished for individual ferrofluid mixture by assuming the prevailing impacts of uniform and slip heat fluxes. The variation of heat transfers and skin friction were also observed at the surface of the plate and we analyzed the better heat transfer for every mixture. Kerosene-based magnetite （Fe304） delivers the better rate of heat transfer at wall due to its association with the kerosene-based Mn-Zn and cobalt ferrites. The slip velocity and magnetic field effects on the temperature, dimensionless velocity, rate of heat transfer and skin friction are examined for various magnetic nanoparticles inside the kerosene oil and water. We observed that the primary influence of magnetic field reduces the dimensionless surface temperature and accelerates the dimensionless velocity as compared to the hydrodynamic case, thus enhancing the rate of heat transfer and skin friction ferrofluids. Moreover, a detailed evaluation of outcomes obtained by MGWM, already published work and numerical RK-4 were found to be in excellent agreement. The error and convergence analysis are presented. Comparison of results,graphical plots, error and convergence analysis reveal the appropriateness of proposed method. T

关键词： gegenbauer polynomials collocation method ferrofluids heat flux numericalsolution.

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Operator Methods and SU(1,1) Symmetry in the Theory of Jacobi and of Ultraspherical polynomials

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Advances in Pure Mathematics 2017年第2期7卷 213-261页

作者： Alfred Wünsche Formerly: Institut für Physik Humboldt-Universit&auml t Nichtklassische Strahlung (Max-Planck-Group) Berlin Germany

Starting from general Jacobi polynomials we derive for the Ul-traspherical polynomials as their special case a set of related polynomials which can be extended to an orthogonal set of functions with interesting properties. It leads to an alternative definition of the Ultraspherical polynomials by a fixed integral operator in application to powers of the variable u in an analogous way as it is possible for Hermite polynomials. From this follows a generating function which is apparently known only for the Legendre and Chebyshev polynomials as their special case. Furthermore, we show that the Ultraspherical polynomials form a realization of the SU(1,1) Lie algebra with lowering and raising operators which we explicitly determine. By reordering of multiplication and differentiation operators we derive new operator identities for the whole set of Jacobi polynomials which may be applied to arbitrary functions and provide then function identities. In this way we derive a new “convolution identity” for Jacobi polynomials and compare it with a known convolution identity of different structure for gegenbauer polynomials. In short form we establish the connection of Jacobi polynomials and their related orthonormalized functions to the eigensolution of the Schrödinger equation to Pöschl-Teller potentials.

关键词： Orthogonal polynomials Lie Algebra SU(1 1) and Lie Group SU(1 1) Lowering and Raising Operators Jacobi polynomials Ultraspherical polynomials gegenbauer polynomials Chebyshev polynomials Legendre polynomials Stirling Numbers Hypergeometric Function Operator Identities Vandermond’s Convolution Identity Poschl-Teller Potentials

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