Search results for "Third order"
showing 10 items of 26 documents
A Simple Approach for Determination of Numerical Values of Ferrite Nonlinear Susceptibilities
2020
This article presents a straightforward approach for determination of numerical values of nonlinear susceptibilities of soft magnetic ferrites. It is shown that numerical values of susceptibilities can be calculated from the measured amplitudes of harmonics in the output voltage of ferrite core transformer. For this purpose, useful expressions for the susceptibilities are derived and as example, numerical values of the largest nonlinear susceptibilities those of the third and fifth orders are calculated. Additionally, errors of the measured susceptibilities also are determined. Based on the expressions obtained, the analysis of phase shifts between components of flux density on different fr…
Numerical values of MnZn ferrite nonlinear susceptibilities in a lossless approximation
2017
On the basis of expressions for nonlinear magnetic susceptibilities of soft ferrites obtained earlier the analysis of phase shifts between components of flux density on different frequencies and the magnetic field strength is carried out. Only the largest nonlinear susceptibilities those of third and fifth order are considered. It is shown that in the frequency range where losses are small and can be neglected the susceptibility of third order is negative but that of fifth order is positive. These statements allow explaining the shape of output voltage of toroidal transformer with soft ferrite core induced by strong harmonic field strength in the input. Numerical values of nonlinear suscept…
A class of third order iterative Kurchatov–Steffensen (derivative free) methods for solving nonlinear equations
2019
Abstract In this paper we show a strategy to devise third order iterative methods based on classic second order ones such as Steffensen’s and Kurchatov’s. These methods do not require the evaluation of derivatives, as opposed to Newton or other well known third order methods such as Halley or Chebyshev. Some theoretical results on convergence will be stated, and illustrated through examples. These methods are useful when the functions are not regular or the evaluation of their derivatives is costly. Furthermore, special features as stability, laterality (asymmetry) and other properties can be addressed by choosing adequate nodes in the design of the methods.
A geometrical criterion for nonexistence of constant-sign solutions for some third-order two-point boundary value problems
2020
We give a simple geometrical criterion for the nonexistence of constant-sign solutions for a certain type of third-order two-point boundary value problem in terms of the behavior of nonlinearity in the equation. We also provide examples to illustrate the applicability of our results.
On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations
2020
Abstract By using comparison principles, we analyze the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations. Due to less restrictive assumptions on the coefficients of the equation and on the deviating argument τ , our criteria improve a number of related results reported in the literature.
Perimeter symmetrization of some dynamic and stationary equations involving the Monge-Ampère operator
2017
We apply the perimeter symmetrization to a two-dimensional pseudo-parabolic dynamic problem associated to the Monge-Ampere operator as well as to the second order elliptic problem which arises after an implicit time discretization of the dynamical equation. Curiously, the dynamical problem corresponds to a third order operator but becomes a singular second order parabolic equation (involving the 3-Laplacian operator) in the class of radially symmetric convex functions. Using symmetrization techniques some quantitative comparison estimates and several qualitative properties of solutions are given.
Third-order accurate monotone cubic Hermite interpolants
2019
Abstract Monotonicity-preserving interpolants are used in several applications as engineering or computer aided design. In last years some new techniques have been developed. In particular, in Arandiga (2013) some new methods to design monotone cubic Hermite interpolants for uniform and non-uniform grids are presented and analyzed. They consist on calculating the derivative values introducing the weighted harmonic mean and a non-linear variation. With these changes, the methods obtained are third-order accurate, except in extreme situations. In this paper, a new general mean is used and a third-order interpolant for all cases is gained. We perform several experiments comparing the known tec…
Study of the v3 = 1 State of 80SeF6 by Fourier Transform Spectroscopy
1997
The Fourier transform infrared spectrum of monoisotopic 80SeF6 has been recorded in the 760-792 cm-1 region with an effective resolution of ca. 2.3 x 10(-3) cm-1. The 80SeF6 sample was prepared by burning monoisotopic 80Se powder (99.2%) in an excess of fluorine. The analysis of infrared transitions of the nu3 band enabled the determination of parameters of the Hamiltonian developed up to the third order and the fourth order. The standard deviation obtained is equal to 4 x 10(-4) cm-1 for the third-order development and 3.2 x 10(-4) cm-1 for the fourth-order development. In the two analyses, 2900 lines were assigned and fitted. Copyright 1997 Academic Press. Copyright 1997Academic Press
Deformations of third-order Peregrine breather solutions of the nonlinear Schrödinger equation with four parameters
2013
We present a new representation of solutions of the one-dimensional nonlinear focusing Schr\"odinger equation (NLS) as a quotient of two determinants. This formulation gives in the case of the order 3, new solutions with four parameters. This gives a very efficient procedure to construct families of quasirational solutions of the NLS equation and to describe the apparition of multirogue waves. With this method, we construct analytical expressions of four-parameters solutions; when all these parameters are equal to 0, we recover the Peregrine breather of order 3. It makes possible with this four-parameters representation, to generate all the types of patterns for the solutions, like the tria…
Konishi form factor at three loops in N=4 supersymmetric Yang-Mills theory
2017
We present the first results on the third order corrections to on-shell form factor (FF) of the Konishi operator in $\mathcal{N}=4$ supersymmetric Yang-Mills theory using Feynman diagrammatic approach in modified dimensional reduction ($\overline{DR}$) scheme. We show that it satisfies the KG equation in $\overline{DR}$ scheme while the result obtained in four dimensional helicity (FDH) scheme needs to be suitably modified not only to satisfy the KG equation but also to get the correct ultraviolet (UV) anomalous dimensions. We find that the cusp, soft and collinear anomalous dimensions obtained to third order are same as those of the FF of the half-BPS operator confirming the universality o…