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.

The experimental proton resonance data for the reaction P+48Ti have been used to calculate and evaluate the level density by employed the Gaussian Orthogonal Ensemble, GOE version of RMT, Constant Temperature, CT and Back Shifted Fermi Gas, BSFG models at certain spin-parity and at different proton energies. The results of GOE model are found in agreement with other, while the level density calculated using the BSFG Model showed less values with spin dependence more than parity, due the limitation in the parameters (level density parameter, a, Energy shift parameter, E1and spin cut off parameter, σc). Also, in the CT Model the level density results depend mainly on two parameters (T and ground state back shift energy, E0), which are app

This paper presents an enhancement technique for tracking and regulating the blood glucose level for diabetic patients using an intelligent auto-tuning Proportional-Integral-Derivative PID controller. The proposed controller aims to generate the best insulin control action responsible for regulating the blood glucose level precisely, accurately, and quickly. The tuning control algorithm used the Dolphin Echolocation Optimization (DEO) algorithm for obtaining the near-optimal PID controller parameters with a proposed time domain specification performance index. The MATLAB simulation results for three different patients showed that the effectiveness and the robustness of the proposed control algorithm in terms of fast gene

The aim of this research is to estimate the parameters of the linear regression model with errors following ARFIMA model by using wavelet method depending on maximum likelihood and approaching general least square as well as ordinary least square. We use the estimators in practical application on real data, which were the monthly data of Inflation and Dollar exchange rate obtained from the (CSO) Central Statistical organization for the period from 1/2005 to 12/2015. The results proved that (WML) was the most reliable and efficient from the other estimators, also the results provide that the changing of fractional difference parameter (d) doesn’t effect on the results.

A new  light-weight nanocarbon prepared by spray-drying method  to obtain  particle size is 21.7 nm based of polylactic acid biodegradable film in antistatic packaging .Bio carbon (biochar) is  obtained from  plants and soils to naturally absorb and store carbon dioxide from the atmosphere . Therefor it has been used to support biodegradable polylactic acid (PLA) with to obtain 100% recyclable material.

Using plasticizer thymol of polylactic acid and biochar (bio carbon) as composites were prepared by a solution casting method with (0.5-10)wt% biochar. The composites  characterized by  FTIR, electrical conductivity, mechanical properties , contact angle and Colar and Brightness . Results show th

The Voluntary Obedience has great importance for the modern taxes systems and its management and this is meant the taxpayer whom in charge to pay of his taxes obligations voluntarily , he is very known of himself whereas he prepared his finishing accountings and present them as samples prepared by taxes management and settle the tax sum directly according to specified income , which has an impact to find end to tax evasion as result lead to increase the tax income and achieve the justice for the taxpayer and the state treasury

16S ribosomal RNA (16S rRNA) gene sequences used to study bacterial phylogeny and taxonomy have been by far the most common housekeeping genetic marker utilized for identification and ancestor determination. This study aimed to investigate, for the first time, the relationship between Klebsiella spp. isolated from clinical and environmental samples in Iraq.

     Fifty Klebsiella spp. isolates were isolated from clinical and environmental sources. Twenty-five isolates were collected from a fresh vegetable (Apium graveolens) and 25 from clinical samples (sputum, wound swab, urine). Enteric bacteria were isolated on selective and differential media and identified by an automatic identif