An effective approach to removing zero-order term overlap and controlling image distortion in digital off-axis holography

2015 ◽  
Vol 356 ◽  
pp. 589-594
Author(s):  
Weipeng Zhang ◽  
Mingqing Wang ◽  
Ming Zheng ◽  
Jian Wu
Keyword(s):  
Order Term ◽  
Image Distortion ◽  
Zero Order

Iterative approach for zero-order term elimination in off-axis multiplex digital holography

2017 ◽  
Vol 383 ◽  
pp. 513-517 ◽  
Author(s):  
Dongliang Zhao ◽  
Dongzhuo Xie ◽  
Yong Yang ◽  
Hongchen Zhai
Keyword(s):  
Digital Holography ◽  
Order Term ◽  
Zero Order ◽  
Iterative Approach

scholarly journals Ergodic pairs for singular or degenerate fully nonlinear operators

2019 ◽  
Vol 25 ◽  
pp. 75 ◽  
Author(s):  
Isabeau Birindelli ◽  
Françoise Demengel ◽  
Fabiana Leoni
Keyword(s):  
Comparison Principle ◽  
Order Term ◽  
A Priori ◽  
Zero Order ◽  
Dirichlet Problems ◽  
Zeroth Order ◽  
Nonlinear Operators ◽  
Fully Nonlinear ◽  
Lipschitz Estimates ◽  
Ergodic Problem

We study the ergodic problem for fully nonlinear operators which may be singular or degenerate when the gradient of solutions vanishes. We prove the convergence of both explosive solutions and solutions of Dirichlet problems for approximating equations. We further characterize the ergodic constant as the infimum of constants for which there exist bounded sub-solutions. As intermediate results of independent interest, we prove a priori Lipschitz estimates depending only on the norm of the zeroth order term, and a comparison principle for equations having no zero order terms.

scholarly journals Response of Duffing's Oscillator to Harmonic Base Excitation and Significance of First Order Term

2020 ◽  
Vol 25 (3) ◽  
pp. 408-424
Author(s):  
K. Divya ◽  
K. Renji
Keyword(s):  
Fundamental Frequency ◽  
Order Approximation ◽  
Order Term ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Zero Order ◽  
Low Frequencies ◽  
First Order ◽  
Response Characteristics ◽  
First Order Approximation

Responses of systems with nonlinear stiffness subjected to base harmonic excitation are determined. An expression to estimate the amplitude in the fundamental frequency of oscillation is derived from first principles using Lindstedt's method. It is observed that the amplitude determined using the zero order approximation is in error at low frequencies. Therefore, an expression for the first order approximation of the amplitude of response at the fundamental frequency is derived. Zero order and first order approximation terms together form the response. Characteristics showing the variation of the amplitude with the excitation frequency for various nonlinear spring parameters are presented. The issue at low frequencies is resolved by the incorporation of the first order term. An expression for the phase difference and the expression of the asymptote where the responses converge are also derived.

scholarly journals Estimates for fully anisotropic elliptic equations with a zero order term

2019 ◽  
Vol 181 ◽  
pp. 249-264 ◽  
Author(s):  
A. Alberico ◽  
G. di Blasio ◽  
F. Feo
Keyword(s):  
Elliptic Equations ◽  
Order Term ◽  
Zero Order ◽  
Anisotropic Elliptic Equations

Radius renormalization in limit cycles

1993 ◽  
Vol 440 (1908) ◽  
pp. 189-199 ◽  
Keyword(s):  
Limit Cycle ◽  
Limit Cycles ◽  
Normal Forms ◽  
Order Term ◽  
Higher Order ◽  
Zero Order ◽  
Perturbative Expansion ◽  
Higher Order Corrections

Oscillatory problems that exhibit limit cycles due to small nonlinearities are studied within the framework of the method of normal forms. It is shown that the zero-order term in the perturbative expansion of the solution can be chosen so that the radius of the asymptotic circle approximation to the limit cycle is unaffected by higher-order corrections.

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