The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

Refractive indices (nD), viscosities (η) and densities (r) were deliberated for the binary mixtures created by dipropyl amine with 1-octanol, 1-heptanol, 1-hexanol, 1-pentanol and tert-pentyl alcohol at temperature 298.15 K over the perfect installation extent. The function of Redlich-Kister were used to calculate and renovated of the refractive index deviations (∆nD), viscosity deviations (ηE), excess molar Gibbs free energy (∆G*E) and excess molar volumes(Vm E). The standard errors and coefficients were respected by this function. The values of ∆nD, ηE, Vm E and ∆G*E were plotted against mole fraction of dipropyl amine. In all cases the obtained ηE, ∆G*E, Vm E and ∆nD values were negative at 298.15K. Effect of carbon atoms

In this work, the effects of size, and temperature on the linear and nonlinear optical properties in InGaN/GaN inverse parabolic and triangular quantum wells (IPQW and ITQW) for different concentrations at the well center were theoretically investigated. The indium concentrations at the barriers were fixed to be always x_max = 0.2. The energy levels and their associated wave functions are computed within the effective mass approximation. The expressions of optical properties are obtained analytically by using the compact density-matrix approach. The linear, nonlinear, and total absorption coefficients depending on the In concentrations at the well center are investigated as a function of the incident photon energy for different

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 work is divided into two parts first part study electronic structure and vibration properties of the Iobenguane material that is used in CT scan imaging. Iobenguane, or MIBG, is an aralkylguanidine analog of the adrenergic neurotransmitter norepinephrine and a radiopharmaceutical. It acts as a blocking agent for adrenergic neurons. When radiolabeled, it can be used in nuclear medicinal diagnostic techniques as well as in neuroendocrine antineoplastic treatments. The aim of this work is to provide general information about Iobenguane that can be used to obtain results to diagnose the diseases. The second part study image processing techniques, the CT scan image is transformed to frequency domain using the LWT. Two methods of contrast

Aging of asphalt pavements typically occurs through oxidation of the asphalt and evaporation of the lighter maltenes from the binder. The main objective of this study is to evaluate influence of aging on performance of asphalt paving materials.nAsphalt concrete mixtures, were prepared, and subjected to short term aging (STA) procedure which involved heating the loose mixtures in an oven for two aging period of (4 and 8) hours at a temperature of 135 o C. Then it was subject to Long term aging (LTA) procedure using (2 and 5) days aging periods at 85 o C for Marshall compacted specimens. The effect of aging periods on properties of asphalt concrete at optimum asphalt content such as Marshall Properties, indirect tensile strength at 25 o C,

Transparent nano- coating was prepared by Sol-Gel method from titanium dioxide TiO₂ which has the ability to self-cleaning coating used for hospitals, laboratories, and places requiring permanent sterilization. Three primary colors are selected (red, blue, and yellow) as preliminary study to the effect of these colors on the nano-coating. Three traditional oil paints color were used as base, then coated by a layer of TiO₂-Sol and deposited on the paints. The optical properties of TiO₂-Sol were measured; the maximum absorption wavelength at (λ_max=387 nm), the refractive index (n=1.4423) and the energy band gap (E_g=3.2 eV). The structure properties found by X-ray diffraction of TiO

Nanoparticles of copper sulfide have been prepared by simple reaction between using copper nitrate with different concentrations ratio 0.1, 0.3, and 0.5 mM, thiourea by a simple chemical route. The prepared Nano powders have been deposited onto glass substrates by casting method at 60°C. The structure of the product Nano- films has been studied by x-ray diffraction, where the patterns showed that all the samples have a hexagonal structure of covellite copper sulfide with the average crystalline sizes 14.07- 16.51 nm. The morphology has been examined by atomic force microscopy, and field emission scan electron microscopy. The AFM images showed particles with almost spherical and rod shapes with average diameter sizes of 49.11- 90.64 nm.

Aromaticity, antiaromaticity and chemical bonding in the ground (S0), first singlet excited (S1) and lowest triplet (T1) electronic states of disulfur dinitride, S2N2, were investigated by analysing the isotropic magnetic shielding, σiso(r), in the space surrounding the molecule for each electronic state. The σiso(r) values were calculated by state-optimized CASSCF/cc-pVTZ wave functions with 22 electrons in 16 orbitals constructed from gauge-including atomic orbitals (GIAOs). The S1 and T1 electronic states were confirmed as 11Au and 13B3u, respectively, through linear response CC3/aug-cc-pVTZ calculations of the vertical excitation energies for eight singlet (S1–S8) and eight triplet (T1–T8) electronic states. The aromaticities of S