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.

في هذا البحث نحاول تسليط الضوء على إحدى طرائق تقدير المعلمات الهيكلية لنماذج المعادلات الآنية الخطية والتي تزودنا بتقديرات متسقة تختلف أحيانا عن تلك التي نحصل عليها من أساليب الطرائق التقليدية الأخرى وفق الصيغة العامة لمقدرات K-CLASS. وهذه الطريقة تعرف بطريقة الإمكان الأعظم محدودة المعلومات "LIML" أو طريقة نسبة التباين الصغرى"LVR

Diarrhea is one of the most commonly encountered minor ailments in the community pharmacies. It is associated with significant morbidity and mortality. However, the majority of pharmacists in Iraq did not manage diarrheal cases in a proper way. Therefore, the current study aimed to evaluate the benefit of a new mobile application (diarrhea management step by step) to improve the pharmacist's role in the management of diarrhea. The study was conducted from 21th September to 21th October 2021 using a pre-post design via a simulated patient (SP) technique. A validated diarrhea scenario was presented to each pharmacist by the SP twice, once before and the other after giving the mobile application to the pharmacist. Furthermore, pharmaci

In parallel with the shell model using the harmonic oscillator's single-particle wave functions, the Hartree-Fock approximation was also used to calculate the neutron skin thickness, the mirror charge radii, and the differences in proton radii for ¹³O-¹³B and ¹³N-¹³C mirror nuclei. The calculations were done for both mirror nuclei in the psdpn model space. Depending on the type of potential used, the calculated values of skin thickness are affected. The symmetry energy and the symmetry energy's slope at nuclear saturation density were also determined, and the ratio of the density to the saturation density of nuclear matter and the symmetry energy has a nearly linear correlation. The mirror ener

     The goal of this paper is to show the kinematic characteristics of gaseous stellar dynamics using scaling coefficient relationships (such as Tully-Fisher) in different spiral galaxies. We selected a sample of types of spiral morphology  (116 early, 150 intermediate, and 146 late) from previous literature work, and used statistical software (statistic-win-program) to find out the associations of multiple factors under investigation, such as the main kinematic properties of the gaseous-stellar (mass, luminosity, rotational speed, and baryons) in different types of spiral galaxies. We concluded that there is a robust positive connection between Log Vrot.max.) and Log Mstar(B-V), as well as between Log Vrot.max. and Log Mbar (

Tin oxide films (SnO2) of thickness (1 ?m) are prepared on glass substrate by post oxidation of metal films technique. Films were irradiated with Nd:YAG double frequency laser of wavelength (532 nm) pulses of three energies (100, 500, 1000) mJ. The optical absorption, transmission, reflectance, refractive index and optical conductivity of these films are investigated in the UV-Vis region (200-900) nm. It was found that the average transmittance of the films is around (80%) at wavelength (550 nm) and showed high transmission (? 90 %) in the visible and near infrared region. The absorption edge shifts towards higher energies, which is due to the Moss-Burstien effect and it lies at (4 eV). The optical band gap increased with increasing of ene

Abstract: Stars whose initial masses are between (0.89 - 8.0) M☉ go through an Asymptotic Giant Branch (AGB) phase at the end of their life. Which have been evolved from the main sequence phase through Asymptotic Giant Branch (AGB). The calculations were done by adopted Synthetic Model showed the following results: 1- Mass loss on the AGB phase consists of two phases for period (P <500) days and for (P>500) days; 2- the mass loss rate exponentially increases with the pulsation periods; 3- The expansion velocity VAGB for our stars are calculated according to the three assumptions; 4- the terminal velocity depends on several factors likes metallicity and luminosity. The calculations indicated that a super wind phase (S.W) developed on the A

Radiotherapy is medical use of ionizing radiation, and commonly applied to the cancerous tumor because of its ability to control cell growth. The amount of radiation used in photon radiation therapy called dose (measured in grey unit), which depend on the type and stage of cancer being treated. In our work, we studied the dose distribution given to the tumor at different depths (zero-20 cm) treated with different field size (4×4- 23×23 cm). Results show that the deeper treated area has less dose rate at the same beam quality and quantity. Also it has been noted increasing in the field increasing in the depth dose at the same depth even if the radiation energy is constant. Increasing in radiation dose attributed to the scattere