In this work, we are obviously interested in a general solution for the calculation of the image of a single bar in partially coherent illumination. The solution is based on the theory of Hopkins for the formation of images in optical instruments in which it was shown that for all practical cases, the illumination of the object may be considered as due to a self – luminous source placed at the exit pupil of the condenser , and the diffraction integral describing the intensity distribution in the image of a single bar – as an object with half – width (U0 = 8 ) and circular aperture geometry is viewed , which by suitable choice of the coherence parameters (S=0.25,1.0.4.0) can be fitted to the observed distribution in various types of mi

A new panel method had been developed to account for unsteady nonlinear subsonic flow. Two boundary conditions were used to solve the potential flow about complex configurations of airplanes. Dirichlet boundary condition and Neumann formulation are frequently applied to the configurations that have thick and thin surfaces respectively. Mixed boundary conditions were used in the present work to simulate the connection between thick fuselage and thin wing surfaces. The matrix of linear equations was solved every time step in a marching technique with Kelvin's theorem for the unsteady wake modeling. To make the method closer to the experimental data, a Nonlinear stripe theory which is based on a two-dimensional viscous-inviscid interac

The nonlinear optical properties for polymeric (PMMA) doping with dye Rhodmine (R3Go) has been studied .The samples are prepared by normal polymerization method with concentrations of 5x10^-5mol/l and a thickness of 272.5µm.

                         Plasma effect was studied on samples prepared before and after exposure to the Nd: YAG laser for three times 5, 10 and 15 minutes. Z-Scan technique is used to determine the nonlinear optical properties such as; refractive index (n₂) and the coefficient of nonlinear absorption (β). It was found that the nonlinear properties is change by increasi

Quantum calculations on the most stable structure were carried
out for calculating the electronic properties, energies and the charge
density at the Carbon and Hydrogen atoms by Semi-empirical
method (PM3) of zigzag carbon nano tube CNT (9,0) (SWCNTs), at
the equilibrium geometry depending on the pictures of Zigzag
CNT(9,0) which was found to has D3d symmetry point group by
applying for (Gaussian 2003) program. In this work the results
include calculation the relation for axial bonds length, which are the
vertical C-C bonds (annular bonds) in the rings and bonds length
which are in the outer ring that called the circumferential bonds. Also
include a different kind of vibration modes like breathing, puckering

    This paper  concerns with the state and proof the existence and uniqueness theorem of triple state vector solution (TSVS) for the triple nonlinear parabolic partial differential equations (TNPPDEs) ,and triple state vector equations (TSVEs), under suitable assumptions. when the continuous classical triple control vector (CCTCV) is given by using the method of Galerkin (MGA). The existence theorem of a continuous classical optimal triple control vector (CCTOCV) for the continuous classical optimal control governing by the TNPPDEs under suitable conditions is proved.  

The distribution of chilled water flow rate in terminal unit is an important factor used to evaluate the performance of central air conditioning unit. A prototype of A/C unit has been made, which contains three terminal units with a complete set of accessories (3-way valve, 2-way valve, and sensors) to study the effect of the main parameters, such as total water flow rate and chilled water supply temperature with variable valve opening. In this work, 40 tests were carried out. These tests were in two groups, 20 test for 3-way valve case and 20 test for 2-way valve case. These tests were performed at three levels of valve opening, total water flow rate and water supply temperature according to the design matrices establis

The aim of this paper is to investigate the theoretical approach for solvability of impulsive abstract Cauchy problem for impulsive nonlinear fractional order partial differential equations with nonlocal conditions, where the nonlinear extensible beam equation is a particular application case of this problem.

Iraqi oil crudes have some of the physical and chemical characteristics that distinguish it from other types of oil crudes in the world. Some of these features such us molecular composition, rheological, viscosity and emulsions are studied carefully by researchers. In this work, a comparative study of the linear and the non-linear optical properties for typical heavy and light crude oils of Iraqi origin was studied utilizing Z-scan technique. The He -Ne laser of wavelength 632.8 nm had been used for this purpose. These samples were collected from Basra and Kut oil fields. The values of the non-linear refractive index (n₂), non-linear absorption coefficient (β), and third-order electrical susceptibility (χ³) were e

The numerical resolve nonlinear system of Volterra integral equation of the second kind (NLSVIEK2) has been considered. The exponential function is used as the base function of the collocation method to approximate the resolve of the problem. Arithmetic epitome are performed which have already been solved by weighted residual manner,  Taylor manner and block- by- block(2, 3, 5).