In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

     Steganography involves concealing information by embedding data within cover media and it can be categorized into two main domains: spatial and frequency. This paper presents two distinct methods. The first is operating in the spatial domain which utilizes the least significant bits (LSBs) to conceal a secret message. The second method is the functioning in the frequency domain which hides the secret message within the LSBs of the middle-frequency band of the discrete cosine transform (DCT) coefficients. These methods enhance obfuscation by utilizing two layers of randomness: random pixel embedding and random bit embedding within each pixel. Unlike other available methods that embed data in sequential order with a fixed amount.

The fuzzy sets theory has been applied in many fields, such as operations research, control theory and management sciences, etc. In particular, an application of this theory in decision making problem is linear programming problems with fuzzy technological coefficients numbers, as well as studying the parametric linear programming problems in the case of changes in the objective function. In this paper presenting a new procedure which connects and makes link between fuzzy linear programming problem with fuzzy technological coefficients numbers and parametric linear programming problem with change in coefficients of the objective function, then develop a numerical example illustrates the steps of solution to this kind of problems.

In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods i

Thin films of Mn2O3 doped with Cu have been fabricated using the simplest and cheapest chemical spray pyrolysis technique onto a glass substrate heated up to 250 oC. Transmittance and absorptance spectra were studied in the wavelength range (300 -1100) nm. The average transmittance at low energy was about 60% and decrease with Cu doping, Optical constants like refractive index, extinction coefficient and dielectric constants (εr), (εi) are calculated and correlated with doping process.

 In this research the Cobalt Oxide (Co3O4) films are prepared by the method of chemical spray pyrolysis deposition at different thicknesses such that (250, 350, 450, and 550) ± 20 nm.      The optical measurement shows that the Co3O4 films have a direct energy gap, and they in general increase with the increase of the thickness. The optical constants are investigated and calculated such as absorption coefficient, refractive index, extinction coefficient and the dielectric constants for the wavelengths in the range (300-900) nm.     The electrical conductivity (σ) and the activation energies (Ea1, Ea2) have been investigated on (Co3O4) thin films as a function of thickness. The films

The current study was achieved on the effects of laser energy and annealing temperature on x-ray structural and optical properties, such as the UV-Visible spectra of cadmium sulfide (CdS). The films were prepared using pules laser deposition technique (PLD) under vacuum at a pressure of 2.5×10^-2 mbar with different laser energies (500-800 mJ) and annealing at a temperature of 473K. X-ray diffraction patterns and intensity curves for the CdS showed that the formation of CdS multi-crystallization films at all laser energies. The optical properties of the films were studied and the variables affecting them were investigated in relation to laser energy and changes in temperature.