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.
Background: Otitis media with effusion is a common and important pediatric clinical problem; it is the leading cause of hearing impairment in children. Medical treatment remains controversial. Aim: To evaluate the usefulness of using topical nasal steroids in the treatment of otitis media with effusion. Patients and Methods: Between November 2019 and October 2022, a prospective controlled clinical study was carried out in the department of otolaryngology at Al-Jerrahat Teaching Hospital in Medical City, Baghdad, Iraq. This study comprised 40 patients with bilateral otitis media with effusion (23 males, 17 females). Two groups were created for the patients. Patients in group A (20 patients) were treated with mometasone furoate nasal spra
... Show MoreBackground: The repair of bone defects remains a major clinical orthopaedic challenge. Bone is a highly vascularised tissue reliant on the close spatial and temporal connection between blood vessels and bone cells to maintain skeletal integrity. This study aimed to study the efficacy of Panax ginseng as a osteoinducer in tibia of rat and as a stimulator for bone healing and to study the immunohistochemical expression of osteonectin as bone formation markers in experimental and control groups during bone healing. Material and method: : In this study thirty albino male rats , weighting (200-300) gram ,aged (2-3) months ,will be used under control conditions of temperature ,drinking and food consumption. The animals will subject for an
... Show MoreMetasurface polarizers are essential optical components in modern integrated optics and play a vital role in many optical applications including Quantum Key Distribution systems in quantum cryptography. However, inverse design of metasurface polarizers with high efficiency depends on the proper prediction of structural dimensions based on required optical response. Deep learning neural networks can efficiently help in the inverse design process, minimizing both time and simulation resources requirements, while better results can be achieved compared to traditional optimization methods. Hereby, utilizing the COMSOL Multiphysics Surrogate model and deep neural networks to design a metasurface grating structure with high extinction rat
... Show MoreThe main goal of this paper is to introduce the higher derivatives multivalent harmonic function class, which is defined by the general linear operator. As a result, geometric properties such as coefficient estimation, convex combination, extreme point, distortion theorem and convolution property are obtained. Finally, we show that this class is invariant under the Bernandi-Libera-Livingston integral for harmonic functions.
Shell model and Hartree-Fock calculations have been adopted to study the elastic and inelastic electron scattering form factors for 25Mg nucleus. The wave functions for this nucleus have been utilized from the shell model using USDA two-body effective interaction for this nucleus with the sd shell model space. On the other hand, the SkXcsb Skyrme parameterization has been used within the Hartree-Fock method to get the single-particle potential which is used to calculate the single-particle matrix elements. The calculated form factors have been compared with available experimental data.
The research was aimed to identify fruits morphological characteristics of 33 taxa belonging to the Lepidieae tribe from Brassicaceae. The characteristics of the fruit's general shape, apex shape, dimensions, colors, surface ornamentation, and beak were determined, the results indicated the importance of each of those characters in isolated species, In general, all the tribe's fruits were open capsule and short silicula. According to the dimensions of fruit, three species can be distinguished as a group with dimensions greater than 20mm, as in Brossardia, Coluteocarpus, and Didymophysa, and depending on the shape, it was possible to differentiate the species within this group, while the other species were less than 20 mm. in dimensi
... Show MoreThe major goal of this research was to use the Euler method to determine the best starting value for eccentricity. Various heights were chosen for satellites that were affected by atmospheric drag. It was explained how to turn the position and velocity components into orbital elements. Also, Euler integration method was explained. The results indicated that the drag is deviated the satellite trajectory from a keplerian orbit. As a result, the Keplerian orbital elements alter throughout time. Additionally, the current analysis showed that Euler method could only be used for low Earth orbits between (100 and 500) km and very small eccentricity (e = 0.001).