In this work, a new formula of intensity distribution in image plane of elliptical object was founded (Elliptical spread function), by using optical system including circular aperture. The Gauss quadrature method of numerical integral was used for calculating equation's integrals. Curves are shown for system having focal error and intensity distribution in focal axis.  

the behavior of the first-order black and gray solitons propagtedin optical fiber in the presence of frequency chirp is studied analytically and numerically results show that phase profile of black solitons changes abruptly

    In this project we analyze data of a large sample of gas rich dwarfs galaxies including; Low Surface Brightness Galaxies (LSBGs), Blue Compact Galaxies (BCGs), and dwarfs Irregulars (dIr). We then study the difference between properties of these galaxies in the range of radio frequencies (B-band).       The data are available in HIPASS catalogue and McGaugh’s Data Page.  We depended also NASA/IPACExtragalactic Databes web site http://ned.ipac.caltech.edu in the data reduction.       We measured the gas evolution (HI mass), gas mass-to-luminosity ratio, and abundance of the elements such as the oxygen abundance for these galaxies. Our results show a

Thermonuclear reaction rates are calculated for three oxygen isotopes ^14,15,16O in CNO cycles reactions occurring in red giant stars. These reactions are:, , , , and . Reaction rates have been calculated using Matlab codes, and related comparisons were made with NACRE II and Reaclib libraries, and the ratios of production to the destruction of ^15,16O isotopes were found. Present reaction rate results were close to most of the selected reactions, and in some cases larger with a factor of 1-3. ^15,16O production to destruction ratios indicated a special tendency to saturate at temperatures higher than ~ 2 GK, and these ratios were in general larger than 1 indicating an excess of producing such isotopes in re

In this research, the frequency-frequency interactions in chaotic systems has been experimentally and numerically studied. We have injected two frequencies on chaotic system where one of these frequencies is modulated with chaotic waveform and the other is untiled as a scanning frequency to find modulating frequency. It is observed that the Fast Fourier Transformation (FFT) peaks amplitude increased when the value of the two frequencies are matched. Thus, the modulating frequency could be observed, this leads to discover a new method to detect the modulating frequency without synchronization.