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.

In this research, we dealt with the study of the Non-Homogeneous Poisson process, which is one of the most important statistical issues that have a role in scientific development as it is related to accidents that occur in reality, which are modeled according to Poisson’s operations, because the occurrence of this accident is related to time, whether with the change of time or its stability. In our research, this clarifies the Non-Homogeneous hemispheric process and the use of one of these models of processes, which is an exponentiated - Weibull model that contains three parameters (α, β, σ) as a function to estimate the time rate of occurrence of earthquakes in Erbil Governorate, as the governorate is adjacent to two countr

The present study aimed at identifying the effectiveness of Macaton method in improving some sensory and cognitive skills in autistic children. In order to achieve the aims of the study, the researcher used the experimental method. The present study sample was (10) children whose ages ranged between (7-10) years and were diagnosed medically with autism disorder. The researcher randomly selected the sample and divided it into two groups: the first group consisted of (5) children representing the experimental group, and (5) children representing the control group after extracting the equivalence between the two groups in terms of age, intelligence, economic and social level and the degree of communication. The program was implemented for t

The influence of fiber orientation and water absorption on fatigue crack growth resistance for cold cure acrylic (PMMA) reinforced by chopped and woven -glass-fibers were investigated. A weight of 2 g for chopped fibers and the same weight for woven -glass-fibers (one layer) were used to prepare samples. Some of these samples would storage in dry condition; the others were immersed in water for 15 days. Fatigue test was carried out. The results shows that, for PMMA, the initial bending stress for dry specimen was 3.392 N/cm2 and the number of cycles were 1364, the initial bending stress for wet samples was 4.20 N/cm2, and the number of cycles was 2411. The samples would cut in two pieces because of the cracks would propagated fast during

In present work an investigation for precise hole drilling via continuous wave (CW) CO2 laser at 150 W maximum output power and wavelength 10.6 μm was achieved with the assistance of computerized numerical controlled (CNC) machine and assist gases. The drilling process was done for thin sheets (0.1 – 0.3 mm) of two types of metals; stainless steel (sst) 321H, steel 33 (st). Changing light and process parameters such as laser power, exposure time and gas pressure was important for getting the optimum results. The obtained results were supported with computational results using the COMSOL 3.5a software code.

Soil improvement has developed as a realistic solution for enhancing soil properties so that structures can be constructed to meet project engineering requirements due to the limited availability of construction land in urban centers. The jet grouting method for soil improvement is a novel geotechnical alternative for problematic soils for which conventional foundation designs cannot provide acceptable and lasting solutions. The paper's methodology was based on constructing pile models using a low-pressure injection laboratory setup built and made locally to simulate the operation of field equipment. The setup design was based on previous research that systematically conducted unconfined compression testing (U.C.Ts.). Th

In this work the interaction of plasma jet with water and hydrogen peroxide liquids used for assisted teeth bleaching by plasma jet had been study. A homemade plasma jet system was used. The plasma jet supply by 15 W electrical power generated by high voltage power supply of 9.6 kV peak to peak and frequency of 33 kHz .this power supply generate high electric field on electrodes that would be enough to ionize the argon gas. Some important agents were study such as the effect of the Ar gas flow rates on the length of the plasma jet, the influence of plasma jet on some properties of water and two hydrogen peroxide concentrations 25 % and 30 % like pH, conductivity and liquid temperature for different exposure time. The liquids temperature

The performance analyses of 15 kWp (kW peak) Grid -Tied solar PV system (that considered first of its type) implemented at the Training and Energy Research Center Subsidiary of Iraqi Ministry of Electricity in Baghdad city has been achieved. The system consists of 72 modules arranged in 6 strings were each string contains 12 modules connected in series to increase the voltage output while these strings connected in parallel to increase the current output. According to the observed duration, the reference daily yields, array daily yields and final daily yields of this system were (5.9, 4.56, 4.4) kWh/kWp/day respectively. The energy yield was 1585 kWh/kWp/year while the annual total solar irradiation received by solar array system was 198

Background/Objectives: Nonsurgical periodontal treatment (NSPT) is the gold-standard technique for treating periodontitis. However, an individual’s susceptibility or the inadequate removal of subgingival biofilms could lead to unfavorable responses to NSPT. This study aimed to assess the potential of salivary and microbiological biomarkers in predicting the site-specific and whole-mouth outcomes of NSPT. Methods: A total of 68 periodontitis patients exhibiting 1111 periodontal pockets 4 to 6 mm in depth completed the active phase of periodontal treatment. Clinical periodontal parameters, saliva, and subgingival biofilm samples were collected from each patient at baseline and three months after NSPT. A quantitative PCR assay was us

Structural and optical properties of CdO and CdO0.99Cu0.01 thin
films were prepared in this work. Cadmium Oxide (CdO) and
CdO0.99Cu0.01semiconducting films are deposited on glass substrates
by using pulsed laser deposition method (PLD) using SHG with Qswitched
Nd:YAG pulsed laser operation at 1064nm in 6x10-2 mbar
vacuum condition and frequency 6 Hz. CdO and CdO0.99Cu0.01 thin
films annealed at 550 C̊ for 12 min. The crystalline structure was
studied by X-ray diffraction (XRD) method and atomic force
microscope (AFM). It shows that the films are polycrystalline.
Optical properties of thin films were analyzed. The direct band gap
energy of CdO and CdO0.99Cu0.01 thin films were determined from
(αhυ)1/2 v