Singular integral equation for an electric dipole taking into account the finite metal conductivity from which it is made

A singular integral equation for an electric dipole has been obtained, which makes it possible to take into account the finite conductivity of the metal from which it is made. The derivation of the singular integral equation is based on the application of the Greens function for free space, written in a cylindrical coordinate system, taking into account the absence of the dependence of the field on the azimuthal coordinate, on a point source located on the surface of an electric dipole. Methods for its solution are proposed. In contrast to the well-known mathematical models of an electric dipole, built in the approximation of an ideal conductor, the use of the singular integral equation obtained in this work makes it possible to take into account heat losses and calculate the efficiency.

On solving initial value problems for partial differential equations in maple

Objectives In this paper, we present and employ symbolic Maple software algorithm for solving initial value problems (IVPs) of partial differential equations (PDEs). From the literature, the proposed algorithm exhibited a great significant in solving partial differential equation arises in applied sciences and engineering. Results The implementation include computing partial differential operator (), Greens function () and exact solution () of the given IVP. We also present syntax, , to apply the partial differential operator to verify the solution of the given IVP obtained from . Sample computations are presented to illustrate the maple implementation.

On establishing qualitative theory to nonlinear boundary value problem of fractional differential equations

In this article, we study a class of nonlinear fractional differential equation for the existence and uniqueness of a positive solution and the Hyers–Ulam-type stability. To proceed this work, we utilize the tools of fixed point theory and nonlinear analysis to investigate the concern theory. We convert fractional differential equation into an integral alternative form with the help of the Greens function. Using the desired function, we studied the existence of a positive solution and uniqueness for proposed class of fractional differential equation. In next section of this work, the author presents stability analysis for considered problem and developed the conditions for Ulam’s type stabilities. Furthermore, we also provided two examples to illustrate our main work.

Transport of Topological Edge States in 2D Zigzag Edge Tungsten Ditelluride Nanoribbon

In this paper, we have investigated the transport of topological edge states in 2D Zigzag edge Tungsten Ditelluride Nanoribbon (ZTDNR).We have found that zigzag edge nanoribbon (NR) of Tungsten Ditelluride develops topological edge states in the presence of intrinsic spin orbit interaction (SOC). We have used three band tight binding model for the electrons of dz2 , dxy, and dx2 - y2 orbitals with SOC for calculating band structure of NR and Non Equilibrium Greens Function (NEGF) formalism for transport in the NR. We have investigated transport in a pristine device, transport in the presence of a finite potential barrier, transport with constriction within the device and transport with edge imperfections.

Spectral analysis of Hahn-Dirac system

In this paper, we study some spectral properties of the one-dimensional Hahn-Dirac boundary-value problem, such as formally self-adjointness, the case that the eigenvalues are real, orthogonality of eigenfunctions, Greens function, the existence of a countable sequence of eigenvalues, eigenfunctions forming an orthonormal basis of L2w,q ((w0. a): E).

THE DIRICHLET PROBLEM FOR AN ORDINARY DIFFERENTIAL EQUATION OF THE SECOND ORDER WITH THE OPERATOR OF DISTRIBUTED DIFFERENTIATION

В работе исследуется линейное обыкновенное дифференциальное уравнение второго порядка с оператором непрерывно распределенного дифференцирования, и для него изучается двухточечная краевая задача методом функции Грина. Вводится в рассмотрение специальная функция, в терминах которой строится функция Грина задачи Дирехле и доказываются основные свойства. Определены достаточные условия на ядро оператора непрерывно распределенного дифференцирования, гарантирующие выполнения условия разрешимости задачи Дирихле. В случае, когда однородная задача Дирихле для рассматриваемого однородного уравнения имеет нетривиальное решение получено неравенство типа Ляпунова для ядра оператора непрерывно распределенного дифференцирования. In this paper, we study a linear ordinary differential equation of the second order with operator of continuously distributed differentiation, and for him we study the two-point boundary value problem by the Greens function method. A special function is introduced, in terms of which the Green function of the Direchle problem is constructed and the main properties are proved. Sufficient conditions on the kernel of the operator of continuously distributed differentiation are determined that guarantee the fulfillment of the solvability condition for the Dirichlet problem. In the case when the homogeneous Dirichlet problem for the homogeneous equation under consideration has a nontrivial solution, an analog of the Lyapunov inequality is obtained for the kernel of a continuously distributed ifferentiation operator.

Interacting Green’s Function and Lehmann Representation in Photoemission Experiments and Interaction Effects

The Phenomenon of photoelectric effect was discovered by W. Hertz in 1887 experimentally long ago, and as time passed theoretical explanation was given, the important work of Albert Einstein in 1905 that earned him Nobel Prize in 1921. Then experiments were done to measure Plank’s constant h and the measurement of electron charge, and the award of Nobel Prize to R.A. Millikan in 1923. As Quantum mechanics and quantum field theory was developed, more refined and complex theories to explain photoelectric effect were developed. Especially the theory of Green’s functions, and Greens function Lehmann representation were developed to explain the phenomena of photoemission. Some significant details of the phenomena of photoemission and its theoretical understanding are presented in this article.