The great majority of applications involve induction heating of metals; the impact of induced conduction current density J into total heat generation is much greater than the impact of displacement current density ∂D∂t. It is for this reason that, in the modeling of induction hardening, the...
Derive the equations for the equivalent resistance of resistors in parallel and in series. What happens to the current as more resistors are added to a series circuit? To a parallel circuit? Three resistors with resistances 25 ohm...
In the Gauss–Seidel method, the ith equation is solved for xi(k+1) in terms of the already calculated values of x(k+1) from the current iteration and the rest of the variables from the previous iteration. An analogous situation exists for the successive over-relaxation method. The ...
Further, the CME validity is not affected by the slow-gain limiting condition TG≫TR of Haus ME for active modelocking. In that way we aim at bringing the phenomena associated with fast gain dynamics into the standard framework of the Haus ME, both allowing to obtain analytical insights ...
In this paper, we extend our research by further modifying the underlying space and time structure as explained below. Our current work was inspired by the well-known leapfrog method [11] used by the molecular dynamics community to solve Newton’s equations of motion. In their books, Hockney ...
The accounting equation is based on the premise that the sum of a company’s assets is equal to its total liabilities and shareholders’ equity. It's a core concept in modern accounting that provides the basis for keeping a company’s books balanced across a given accounting cycle....
(MFE) multivariate public key cryptosystem, is proposed by Wang, Yang, Hu and Lai. We use the second order linearization equation attack method by Patarin to break MFE. Given a ciphertext, we can derive the plaintext within 2-multiplications, after performing once for any given public key ...
This work deals with the initial value problem for an inhomogeneous nonlinear Schrödinger equation {iu˙−(−Δ)γu+ϵ|x|ρ|u|p−1u=0;u|t=0=u0. (1.1) The nonlinear equations of Schrödinger type have a deep influence in physical modeling. The fractional Schrödinger equation ...
So the finding of exact soliton solutions for extended NLSE is very important for mathematicians and physicists51,52,53,54,55. To the best of our knowledge, such an abundance of solutions has never been established in earlier literature. The goal of the current research is to determine how ...
For example, in the solution of the equation of state, the positive real root is the one of interest. In any case, the physical constraints of the problem may dictate the feasible region of search where only a subset of the total number of roots may be indicated. Also, the physical ...