When diffusing object is illuminated by a laser, it gives the impression of being covered with a very fine grain structure. This structure commonly is nothing but the result of the interference of random waves from the object.In the early years of the invention of the laser sources, the CND control was considered a birth which severely affects the image resolution. Various studies have been developed to remove.The development of new systems for capturing images CCD coupled with tools image processing techniques has made the CND control most interesting for industrial control real-time and non-destructive.Metrology of photography and optic interferometry are two methods that provide the ability to analyze and determine deformations of structures.The CND technique is the most answered and more particularly the technical of interferometry. This method is simple to implement, follow the evolution of the interference of a speckle fields diffracted by an object and a reference fields. Images are recorded by a CCD camera and digitally processed by computer to generate correlograms from which is extracted the gauging.CND techniques have provided only qualitative measures as correlation fringes.The application process and digital image processing techniques to measure phase yielded quantitative measures.Among the techniques for calculating phase, the phase shift method is the most used because it is the most accurate. This technique is based on a combination of shifted interferograms to extract the phase. It requires a phase modulator for generating phase-shifted interferograms speckle and an algorithm for calculating the phase.

The paper does not meet the standards of \"Advances in Linear Algebra & Matrix Theory\".

This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's Retraction Guidelines. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused.

Editor guiding this retraction: Prof. Mubariz Garayev and Prof. Qingwen Wang
(EiC of ALAMT)

We examined the adaptation of the
postural response to repeated predictable platform oscillations. Our main goals
were to determine whether the short-term changes that occurred during a minute
long continuous postural perturbation trial were maintained in subsequent
trials and to determine how many trials were required before participants fully
adapted to the postural task. Ten participants performed ten minute-long
postural trials on a platform that oscillated at 0.25 Hz before increasing to
0.50 Hz half way through each trial. Postural muscle onset latencies, burst
amplitudes, and anterior posterior displacements of the center of pressure
(COP) and center of mass (COM) were calculated for the last five cycles
performed in each trial at 0.50 Hz. The postural strategy evolved in two
phases: 1) immediate decrease in COP displacement; 2) earlier activation of the postural
muscles with smaller muscle burst amplitudes. After seven trials the postural
response remained consistent.

A double system of exponents with piecewise continuous complex-valued coefficients are considered. Under definite conditions on the coefficients the frame property of this system in Lebesgue spaces of functions is investigated. Such systems arise in the spectral problems for discontinuous differential operators.

Abstract:
This paper presents a method to solve the American option pricing problem in the Black Scholes framework that generalizes the Barone-Adesi, Whaley method [1]. An auxiliary parameter is introduced in the American option pricing problem. Power series expansions in this parameter of the option price and of the corresponding free boundary are derived. These series expansions have the Baroni-Adesi, Whaley solution of the American option pricing problem as zero-th order term. The coefficients of the option price series are explicit formulae. The partial sums of the free boundary series are determined solving numerically nonlinear equations that depend from the time variable as a parameter. Numerical experiments suggest that the series expansions derived are convergent. The evaluation of the truncated series expansions on a grid of values of the independent variables is easily parallelizable. The cost of computing the n-th order truncated series expansions is approximately proportional to n as n goes to infinity. The results obtained on a set of test problems with the first and second order approximations deduced from the previous series expansions outperform in accuracy and/or in computational cost the results obtained with several alternative methods to solve the American option pricing problem [1]-[3]. For example when we consider options with maturity time between three and ten years and positive cost of carrying parameter (i.e. when the continuous dividend yield is smaller than the risk free interest rate) the second order approximation of the free boundary obtained truncating the series expansions improves substantially the Barone-Adesi, Whaley free boundary [1]. The website:
http://www.econ.univpm.it/recchioni/finance/w20 contains material including animations, an interactive application and an app that helps the understanding of the paper. A general reference to the work of the authors and of their coauthors in mathematical finance is the website:
http://www.econ.univpm.it/recchioni/finance.

Abstract:
We use perturbation techniques to solve the polynomial equation in Banach space. Our techniques provide more accurate information on the location of solutions and yield existence and uniqueness in cases not covered before. An example is given to justify our method.

Abstract:
The dynamic response of mechanical and civil structures subjected to high-amplitude vibration is often dangerous and undesirable. Sometimes controlled vibration is desirable as in the machinery used in the formation of rigid hard material as Ceramics and diamond. This process is done via the passive control methods. The main purpose of this paper is to how reduction of vibration of nonlinear system subjected to multi-excitation forces via a nonlinear absorber. The nonlinear differential equations describing the model, which describe ultrasonic cutting machine are solved by using perturbation method. The effects of different parameter on the response of the system are studied. The stability of the numerical solution is investigated by using frequency response equations and phase-plane method. The simulation results are achieved using Matlab and Maple programs. A comparison is made with the available published work.

Abstract:
The analytical and numerical solutions of the response of an inclined cable subjected to external and parametric excitation forces is studied. The method of perturbation technique are applied to obtained the periodic response equation near the simultaneous principal parametric resonance in the presence of 2:1 internal resonance of the system. All different resonance cases are extracted. The effects of different parameters and worst resonance case on the vibrating system are investigated. The stability of the system are studied by using frequency response equations and phase-plane method. Variation of the parameters α2, α3, β2, γ2, η2, γ3, η3, f2 leads to multi-valued amplitudes and hence to jump phenomena. The simulation results are achieved using MATLAB 7.6 programs.

Abstract:
Analytical solutions for the effect of chemical reaction on the unsteady free convection flow past an infinite vertical permeable moving plate with variable temperature has been studied. The plate is assumed to move with a constant velocity in the direction of fluid flow. The highly nonlinear coupled differential equations governing the boundary layer flow, heat and mass transfer are solved using two-term harmonic and non-harmonic functions. The parameters that arise in the perturbation analysis are Prandtl number (thermal diffusivity), Schmidt number (mass diffusivity), Grashof number (free convection), modified Grashof number, Chemical reaction parameter (rate constant), Skin friction coefficient and Sherwood number (wall mass transfer coefficient). The study has been compared with available exact solution in the literature and they are found to be in good agreement. It is observed that: The concentration increases during generative reaction and decreases in destructive reaction. The concentration increases with decreasing Schmidt number. The effect of increasing values of K leads to a fall in velocity profiles. The velocity decreases with increasing values of the Schmidt number. An increase in modified Grashof number leads to an increase in velocity profiles. The skin friction increases with decreasing Schmidt number. In generative reaction the skin friction decreases and in destructive reaction the skin friction increases.

Abstract:
In this paper, homotopy perturbation method is applied to solve moving boundary and isoperimetric problems. This method does not depend upon a small parameter in the equation. homotopy is constructed with an imbedding parameter p, which is considered as a “small parameter”. Finally, we use combined homotopy perturbation method and Green’s function method for solving second order problems. Some examples are given to illustrate the effectiveness of methods. The results show that these methods provides a powerful mathematical tools for solving problems.