This paper aims to find new analytical closed-forms to the  solutions of the nonhomogeneous functional differential equations of the n^th order with finite and constants delays and various initial delay conditions in terms of elementary functions using Laplace transform method. As well as, the definition of dynamical systems for ordinary differential equations is used to introduce the definition of dynamical systems for delay differential equations which contain multiple delays with a discussion of their dynamical properties: The exponential stability and strong stability

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In this research, the X-ray diffraction pattern was used, which was obtained experimentally after preparation of barium oxide powder. A program was used to analyze the X-ray diffraction lines of barium oxide nanoparticles, and then the particle size was calculated by using the Williamson-Hall method, where it was found that the value of the particle size is 25.356 nm. Also, the dislocation density was calculated, which is equal to1.555 x1015 (lines/nm2), and the value of the unit cell number was also calculated, as it is equal to 23831.

Cr2O3 thin films have been prepared by spray pyrolysis on a glass substrate. Absorbance and transmittance spectra were recorded in the wavelength range (300-900) nm before and after annealing. The effects of annealing temperature on absorption coefficient, refractive index, extinction coefficient, real and imaginary parts of dielectric constant and optical conductivity were expected. It was found that all these parameters increase as the annealing temperature increased to 550°C.

The effect of heat treatment on the optical properties of the bulk heterojunction blend nickel (II) phthalocyanine tetrasulfonic acid tetrasodium salt and Tris (8-hydroxyquinolinato) Aluminum (NiPcTs/Alq3) thin films which prepared by spin coating was described in this study. The films coated on a glass substrate with speed of 1500 rpm for 1.5 min and treated with different annealing temperature (373, 423 and 473) K. The samples characterized using UV-Vis, X ray diffraction and Fourier transform Infrared (FTIR) spectra, XRD patterns indicated the presence of amorphous and polycrystalline blend (NiPcTs/Alq3). The results of UV visible shows that the band gap increase with increasing the annealing temperature up to 373 K and decreases with

This article studied some linear and nonlinear optical characteristics of different pH solutions from anthocyanin dye extract at 180 oC from red cabbage. First, the linear spectral characteristics, including absorption and transmittance in the range 400-800 nm for anthocyanin solution 5% v/v with different pHs, were achieved utilizing a UV/VIS spectrophotometer. The experimental results reveal a shift in the absorption toward the longer wavelength direction as pH values increment. Then, the nonlinear features were measured using the Z-scan technique with a CW 532 nm laser to measure the nonlinear absorption coefficient through an open aperture. A close aperture (diameter 2 mm) calculates the nonlinear refractive index. The open Z-scan sh

The effect of 0.662MeV gamma radiation on the optical properties of the CdTe thin films was studied. 300nm thickness of CdTe samples were irradiated with doses (10, 20, 30,60krad) in room temperature. The absorption spectra for all the samples were recorded using UV- Visible spectrometer in order to calculate the energy gap, width of localized states and optical constants(refractive index, extinction coefficient, real and imaginary parts of dielectric constant). The optical energy gap was found to decrease from (1.53 to 1.48 eV), while the width of localized states increased from (1.34 to 1.49 eV) with the increasing of radiation dose. The behavior of energy gap with the irradiation dose makes the material a good candidate for dosimetry

Polyaniline Multi walled Carbon nanotubes (PANI/MWCNTs) nanocomposite thin films have been prepared by non-equilibrium atmospheric pressure plasma jet on glass substrate with different weight percentage of MWCNTs 1, 2, 3, 4%. The diameter of the MWCNTs was in the range of 8-55 nm and length - - 55 55 μm. the nanocomposite thin films were characterized by UV-VIS, XRD, FTIR, and SEM. The optical studies show that the energy band gap of PANI/MWCNTs nanocomposites thin films will be different according to the MWCNTs polyaniline concentration. The XRD pattern indicates that the synthesized PANI/MWCNTs nanocomposite is amorphous. FTIR reveals the presence of MWCNTs nanoparticle embedded into polyaniline. SEM surface images show that the MWCNT

In this work, pure and Ag-doped nickel oxide (NiO) thin films were deposited on glass substrates with different dopant concentrations (0.1, 0.2, 0.3 and 0.4 wt.%) by pulsed-laser deposition (PLD) technique at room temperature. These films were annealed at temperature of 450 °C. The structural and optical properties of the prepared thin films were studied. It was found that annealing process has lead to increase the transmittance of the deposited films. Also, the transmittance was found to increase with doping concentration of silver in the deposited NiO films. The optical energy gap was decreased from 3.5 to 3.2 eV as the doping concentration was increased to 0.4 %.