eigenfunctions
در نشریات گروه علوم پایه-
In this work, we have solved the radial Schrö-dinger equation for the Woods–Saxon potential together with coulomb (r>Rc), centrifugal terms and spin orbit in-teraction by using a new type of Nikiforov-Uvarov (NU) method. This approach is based on the solution of the Second-Order Linear Differential Equations (SOLDE). The mandatory specific choices of the required parameters in this technique restricts the application of this method to the Schrödinger equation with complicated potential pro-files, which means that the NU method cannot efficiently be employed to solve more realistic physical systems. Due to the mentioned difficulties in evaluating the equivalent second order algebraic equation in the NU method, the analytical NU method has to be extended to more effi-cient version that is combined with numerical methods (that leads to a semi-analytical method). We have solved it by combination of the NU method with the numerical fitting schema. The numerical fitting schema helps us to find the mentioned second order algebraic equation. Oth-erwise, complicated changes of variables or overwhelming algebraic treatments to deriving the energy eigenvalues and the wavefunctions are required. The current approach is simpler, more flexible and efficient. This technique can also be developed to be suitable for the equations other than the Schrodinger one. The Woods–Saxon potential is also a short-range interaction in the potential model for nuclear physics and has predictions for the nuclear shell model and distribution of nuclear densities. We have ob-tained a semi-analytical energy eigenvalues and eigen-functions for various values of n, l, and j quantum num-bers. Agreement of 5/2+ and 1/2+ wavefunctions with the published works is also obtained which also shows the ac-curacy of our method.
Keywords: Nikiforov-Uvarov method, curve fitting, Eigenvalues, Eigenfunctions, Woods–Saxon, Spin-Orbit Interaction -
The main objective of this article is to establish a new model and find some vortex axisymmetric solutions of finite core size for this model. We introduce the hydrodynamical equations governing the atmospheric circulation over the tropics, the Boussinesq equation with constant radial gravitational acceleration. Solutions are expanded into series of Hermite eigenfunctions. We find the coefficients of the series and show the convergence of them. These equations are critically important in mathematics. They are similar to the 3D Navier-Stokes and the Euler equations. The 2D Boussinesq equations preserve some important aspects of the 3D Euler and Navier-Stokes equations such as the vortex stretching mechanism. The inviscid 2D Boussinesq equations are known as the Euler equations for the 3D axisymmetric swirling flows.This model is the most frequently used for buoyancy-driven fluids, such as many largescale geophysical flows, atmospheric fronts, ocean circulation, clued dynamics. In addition, they play an important role in the Rayleigh-Benard convection.
Keywords: Boussinesq equation, Vortex theory, Single center vortex, Eigenfunctions, Hermite function -
A Sturm-Liouville problem with n-potential functions in the second order differential equation and which contains spectral parameter depending on linearly in one boundary condition is considered. The asymptotic formulas for the eigenvalues, nodal parameters (nodal points and nodal lengths) of this problem are calculated by the Prüfer's substitutions. Also, using these asymptotic formulas, an explicit formula for the potential functions are given. Finally, a numerical example is given.Keywords: Eigenvalues, Eigenfunctions, Prüfer's Substitutions, Sturm-Liouville problem, Inverse Nodal problem
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Theory of a Superluminous Vacuum Quanta as the Fabric of SpaceInternational Journal of Mathematical Modelling & Computations, Volume:11 Issue: 2, Spring 2021, P 5
Our observations of magneton with Ferrolens shows evidence pointing to such magneton entity, and more evidently in recent results with the synthetic vacuum unipole experiments. Physics formalism ansatz novel model analyses demonstrate how vacuum quanta may have sufficient energy for vacuum genesis, by constructing eigenspinors of zero_point microblackhole Hamiltonian quantum mechanics with Helmholtz decomposition matrix of gradient and rotational tensors, that are characteristic of translational vortex fields. With these mathematical physics processes, we obtain resulting energy fields spatial property partial differential equations characterizing eigenstate energetics of zero_point vacuum quagmire, as well as eigenstate vortex fields of microblackhole, both together making up plasmodial zones within quagmire. Specific eigenspinors Hamiltonian partial differential equations quantifying energy and fields eigenfunctions. Vacuum that is dipole vacuum may have superposition of complex input of quagmire vortex fields acting to create non-Hermitian quantum relativistic physics.
Keywords: quantum cosmology, Hamiltonian operator, eigenfunctions, magneton, observables, general formalism, Hamiltonian analysis, vortex eigenspinors, Gradient zero point source rotational microblackhole sink tensors -
International Journal Of Nonlinear Analysis And Applications, Volume:13 Issue: 1, Winter-Spring 2022, PP 3427 -3440
In this article, we discuss two boundary value problems for fractional-order differential equations. We show unique solutions exist and some data continuous dependence, with aim of proving some characteristics for these solutions of a coupled system of conjugate orders. These coupled systems are equivalent to coupled systems of second-order differential equations. Therefore, the analysis of the spectra of these problems is a consequence of that of second-order differential equations.
Keywords: Boundary value problem, Liouville-Caputo fractional derivative, Data continuous dependence, Eigenvalues, Eigenfunctions -
گاهی در عمل داده ها به صورت تابعی از یک متغیر دیگر هستند که به این نوع داده ها، داده های تابعی گفته می شود. اگر متغیر پاسخ اسکالر و به صورت رسته ای یا گسسته باشد و متغیرهای کمکی به صورت تابعی، آنگاه برای تحلیل این نوع داده ها از مدل خطی تابعی تعمیم یافته استفاده می شود.در این مقاله یک مدل بریده شده خطی تابعی تعمیم یافته بررسی و برای به دست آوردن برآورد پارامترهای مدل از یک رهیافت ماکسیمم درستنمایی استفاده می شود. درنهایت در یک مطالعه شبیه سازی و دو مثال کاربردی مدل و روش های ارایه شده پیاده سازی می شوند.
کلید واژگان: عملگر کوواریانس، توابع ویژه، رگرسیون تابعی، مدل خطی تابعی تعمیم یافته، بسط کارهونن لوئه وSometimes, in practice, data are a function of another variable, which is called functional data. If the scalar response variable is categorical or discrete, and the covariates are functional, then a generalized functional linear model is used to analyze this type of data. In this paper, a truncated generalized functional linear model is studied and a maximum likelihood approach is used to estimate the model parameters. Finally, in a simulation study and two practical examples, the model and methods presented are implemented.
Keywords: Covariance operator, Eigenfunctions, Functional regression, Generalized functional linear model, Karhunen–Loève expansion -
در این مقاله، نظریه طیفی را برای مقادیر ویژه و توابع ویژه یک مساله مقدار مرزی شامل عملگر خطی بسل کسری ارائه می کنیم. بعلاوه ما نشان می دهیم که این عملگر، خودالحاقی است ، مقادیر ویژه مساله مقدار مرزی حقیقی هستند و توابع ویژه متناظرشان متعامدند.کلید واژگان: مساله مقدار مرزی، مقادیر ویژه، توابع ویژه، نظریه طیفیIn this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal.Keywords: Boundary value problem, Eigenvalues, Eigenfunctions, Spectral theory
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An inverse nodal problem has first been studied for the Sturm-Liouville equation with one turning point. The asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated and an asymptotic of the nodal points is obtained. For this problem, we give a reconstruction formula for the potential function. Furthermore, numerical examples have been established and results have been illustrated in tables and graphics.
Keywords: Turning point, Inverse nodal problem, Nodal Points, eigenvalues, Eigenfunctions -
Einstein, M"{o}bius, and Proper Velocity gyrogroups are relativistic gyrogroups that appear as three different realizations of the proper Lorentz group in the real Minkowski space-time $bkR^{n,1}.$ Using the gyrolanguage we study their gyroharmonic analysis. Although there is an algebraic gyroisomorphism between the three models we show that there are some differences between them. Our study focus on the translation and convolution operators, eigenfunctions of the Laplace-Beltrami operator, Poisson transform, Fourier-Helgason transform, its inverse, and Plancherel's Theorem. We show that in the limit of large $t,$ $t rightarrow +infty,$ the resulting gyroharmonic analysis tends to the standard Euclidean harmonic analysis on ${mathbb R}^n,$ thus unifying hyperbolic and Euclidean harmonic analysis.
Keywords: Gyrogroups, gyroharmonic analysis, Laplace Beltrami operator, eigenfunctions, generalized Helgason-Fourier transform, Plancherel’s theorem -
In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. Furthermore, we obtain the zeros of eigenfunctions.Keywords: Turning point, Inverse nodal problem, Nodal Points, Eigenvalues, Eigenfunctions
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In this paper, uniqueness theorem is studied for boundary value problem with «aftereffect» on a finite interval with discontinuity conditions in an interior point. The oscillation of the eigenfunctions corresponding to large modulus eigenvalues is established and an asymptotic of the nodal points is obtained. By using these new spectral parameters, uniqueness theorem is proved.Keywords: Uniqueness Theorem, nodal Points, discontinuous conditions, eigenvalues, eigenfunctions
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