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.

Aim: To evaluate the effect of ultrasonic agitation for retrograde biodceramic root repair, MTA and biodentine filling materials on push-out bond strength to dentine walls. Materials and Methods: Ninety extracted human teeth with single straight roots were selected randomly. After disinfection and cleaning, the coronal portions were sectioned to standardize the root canal length at 15mm. following root canal shaping, obturation and apical roots resection, retrograde cavities were prepared. Teeth were categorized depending on the filling material used into three groups, 30 teeth each. Group A filled with bioceramic root repair material, B with MTA and C with Biodentine material. These groups were divided in to three subgroup (n= 10). Subgrou

Instruments for the measurements of radon, thoron and its decay
products in air are based mostly on the detection of alpha particles.
The health hazards of radon on general public are well known. In
order to understand the level and distribution of ²²²Rn concentrations
indoor in Al-Fallujah City; new technique was used, this technique
was three radon–thoron mixed field dosimeters is made up of a twin
chamber cylindrical system and three LR-115 type II detectors were
employed. The aim of this work was to measurement radon gas using
SSNTD technique door in in Al-Fallujah City, and estimation of
excess in cancer due to increment in radon gas. Results for samples
which are collected from January to

It is well known that the rate of penetration is a key function for drilling engineers since it is directly related to the final well cost, thus reducing the non-productive time is a target of interest for all oil companies by optimizing the drilling processes or drilling parameters. These drilling parameters include mechanical (RPM, WOB, flow rate, SPP, torque and hook load) and travel transit time. The big challenge prediction is the complex interconnection between the drilling parameters so artificial intelligence techniques have been conducted in this study to predict ROP using operational drilling parameters and formation characteristics. In the current study, three AI techniques have been used which are neural network, fuzzy i

Background: The repair of bone defects remains a major clinical challenge in dentistry. Bone is a highly vascularized tissue reliant on the close spatial and temporal connection between blood vessels and bone cells to maintain skeletal integrity. The health promotive , preventive, and curative properties of herbs were recognized by the ancient and the present pharmacist and physicians to form the theoretical foundations in Medicine. Objective: Immunohistochemistry of osteocalcin and histological study to prove that symphytum officinale oil when applied locally on generated bone defect healing in rat tibia, it was very effectiveness. Patients and Methods: 0ur study fourty male rats , weighting (250-350) grams ,aged (5 7)months ,was

This competition between competing forces, organized into axes with conflicting objectives, is reflected in all regional affairs and the goals and interests of countries within them, including Iraq. Among the most important aspects impacted by the repercussions of international and regional competition in the region is Iraqi national security, based on its vital importance in preserving the sovereignty and entity of the Iraqi state, protecting the interests and cohesion of the state and people, ensuring and defending their present and future, and interacting with various regional and international activities. The Kurdistan Region, as an important part of Iraq with its own unique characteristics, may be one of the most important regi

In this study, a brand-new double transform known as the double INEM transform is introduced. Combined with the definition and essential features of the proposed double transform, new findings on partial derivatives, Heaviside function, are also presented. Additionally, we solve several symmetric applications to show how effective the provided transform is at resolving partial differential equation.