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.

When a vehicle is left parked in the sun for an extended period, the gathered heat causes damage to several interiors within the cabin and causes discomfort for people and animals left inside the car. In the present work, the effect of the orientation of a parked white minibus on temperature distribution and cooling load calculation is studied experimentally in an open environment. Two different cases were studied facing south and facing east. For several hours, the temperature inside the car cabin had been monitored and measured at five separate locations. The cooling load calculations are carried out based on the experimental measurements. The results show that the overheating of parked cars always happens as a result

Coronary artery disease (CAD) is a major health concern and leading of death in individuals with type 2 diabetes mellitus (T2DM). Glutathione S – Transferase(GST) are known for their broad range of detoxification and in the metabolism of xenobiotics . The role of functional variants of these genes in the development of various disorder is proven. We investigated the possible role of these variants in the development of CAD in T2DM patients. In this case – control study a total of 60 patients (T2DM = 30 ; T2DM – CAD = 30) and 30 controls were included. Serum lipid profiles were measured and DNA was extracted from the blood samples. Multiplex PCR for GSTT1/M1 (present / null) polymorphism, were performed for genotyping of study pa

Electronic properties such as density of state, energy gap, HOMO (the highest occupied molecular orbital) level, LUMO (the lowest unoccupied molecular orbital) level and density of bonds, as well as spectroscopic properties like infrared (IR), Raman scattering, force constant, and reduced masses for coronene C₂₄, reduced graphene oxide (rGO) C₂₄O₅and interaction between C₂₄O₅and NO₂gas molecules were investigated. Density functional theory (DFT) with the exchange hybrid function B3LYP with 6-311G** basis sets through the Gaussian 09 W software program was used to do these calculations. Gaussian view 05 was em

Praise be to God, Lord of the worlds, and prayers and peace be upon our master Muhammad and his family and companions until the Day of Judgment.
      The words of God Almighty are for the sake of the greatest and greatest speech, and the scholars, may God have mercy on them, raced.
To dive into knowing the word of God and what he intended, so they wrote in it the literature and collected works in it, and explained it to those after them.
      And when the noble companions, were extremely eloquent and eloquent, because the Holy Qur’an was revealed in the language of the Quraysh, and all the Arabs knew their language, they understood the Holy Qur’an and applied it p

Massive multiple-input multiple-output (massive-MIMO) is a promising technology for next generation wireless communications systems due to its capability to increase the data rate and meet the enormous ongoing data traffic explosion. However, in non-reciprocal channels, such as those encountered in frequency division duplex (FDD) systems, channel state information (CSI) estimation using downlink (DL) training sequence is to date very challenging issue, especially when the channel exhibits a shorter coherence time. In particular, the availability of sufficiently accurate CSI at the base transceiver station (BTS) allows an efficient precoding design in the DL transmission to be achieved, and thus, reliable communication systems can be obtaine

The corrosion inhibition of low carbon steel in1N HCl solution in the presence of peach juice at temperature (30,40,50,and 60)°C at concentration ( 5, 10, 20, 30, 40and 50 cm3/L)were studied using weight loss and polarization techniques. Results show that the inhibition efficiency was increased with the increase of inhibitor concentration and increased with the increase of temperature up to 50ºC ,above 50ºC (i.e. at 60 ºC) the values of efficiency decreases. Activation parameters of the corrosion process such as activation energies, Ea, activation enthalpies, ΔH, and activation entropies, ΔS, were calculated. The adsorption of inhibitor follows Langmuir isotherm. Maximum inhibition efficiency obtained was a bout 91% at 50ºC in the

Background: Frovatriptan succinate (FVT) is an effective medication used to treat migraines; however, available oral formulations suffer from low permeability; accordingly, several formulations of FVT were prepared. Objective: Prepare, optimize, and evaluate FVT-BE formulation to develop enhanced intranasal binary nano-ethosome gel. Methods: Binary ethosomes were prepared using different concentrations of phospholipid PLH90, ethanol, propylene glycol, and cholesterol by thin film hydration and characterized by particle size, zeta potential, and entrapment efficiency. Furthermore, in-vitro, in-vivo, ex-vivo, pharmacokinetics, and histopathological studies were done. Results: Regarding FVT-loaded BE, formula (F9) demonstrated the best paramet