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.

English allows for consonant sequences at the beginning of words, which poses a challenge for speakers of other languages, especially those whose native languages do not contain such sequences, such as Arabic. Therefore, this study aims to investigate students’ recognition and production of initial consecutive consonants in relation to gender, and the significance of the statistical differences between students in recognition and pronunciation of consecutive consonants. Consequently, a cohort of fifty-two Iraqi college students (18 males and 34 females) were selected as a sample. A multiple-choice test of two phases was used as a research instrument. The results showed that females outperformed males in recognizing and producing c

We use of multi-choice Goal Programming (MCGP), which is a developed model of Goal Programming where it is used in circumstances of the multiplicity and difference of goals when choosing between decision alternatives in cases of allocating resources, as it is a model that seeks to find the closest and best solutions to the specific values ​​of the goals within the aspiration levels, as the first goal in the multi-choice goal programming model that is used to reduce the total cost of storage and shortage, while the other goal was to reduce the difference between the real demand that the hospitals need from the blood transfusion center and the units that already achieved. The case Iraqi Center

Abstract: Microfluidic devices present unique advantages for the development of efficient drug assay and screening. The microfluidic platforms might offer a more rapid and cost-effective alternative. Fluids are confined in devices that have a significant dimension on the micrometer scale. Due to this extreme confinement, the volumes used for drug assays are tiny (milliliters to femtoliters).

 In this research, a microfluidic chip consists of micro-channels carved on substrate materials built by using Acrylic (Polymethyl Methacrylate, PMMA) chip was designed using a Carbon Dioxide (CO₂) laser machine. The CO2 parameters have influence on the width, depth, roughness of the chip. In order to have regular

Embedding an identifying data into digital media such as video, audio or image is known as digital watermarking. In this paper, a non-blind watermarking algorithm based on Berkeley Wavelet Transform is proposed. Firstly, the embedded image is scrambled by using Arnold transform for higher security, and then the embedding process is applied in transform domain of the host image. The experimental results show that this algorithm is invisible and has good robustness for some common image processing operations.

Abstract

     This research deals with Building A probabilistic Linear programming model  representing, the operation of production in the Middle Refinery Company (Dura, Semawa, Najaif) Considering the demand of each product (Gasoline, Kerosene,Gas Oil, Fuel Oil ).are random variables ,follows certain probability distribution, which are testing by using Statistical programme (Easy fit), thes distribution are found to be Cauchy distribution ,Erlang distribution ,Pareto distribution ,Normal distribution ,and General Extreme value distribution .              &

In this article, the solvability of some proposal types of the multi-fractional integro-partial differential system has been discussed in details by using the concept of abstract Cauchy problem and certain semigroup operators and some necessary and sufficient conditions. 

            In this paper, the Normality set  will be investigated. Then, the study highlights some concepts properties and important results. In addition, it will prove that every operator with normality set has non trivial invariant subspace of  .

methodology six sigma Help  to reduce defects by solving problems effectively, and works Lean to reduce losses through the flow of the manufacturing process and when integrating these two methodologies (Lean and six sigma), the methodology of Lean six sigma will form the entrance to the organizers of the optimization process and increase the quality and reduce lead times and costs . by focusing on the needs of the customer. this process uses statistical tools and techniques to analyze and improve processes.

 We have conducted this research in the General Company for Electrical Industries and adopted its product (machine cooling water three taps) as a sample for research. In order to determine t

The study aimed to determine of some Optimum conditions for bioremediation and removing of seven mineral elements included hexavalent chromium, nickel, cobalt, cadmium, lead, iron and copper as either alone or in group by living and heat treated cells of baker’s yeast Saccharomyces cerevisiae. The dried baker's yeast from Aldnaamaya China Company was used in this study. Biochemical tests was used to ensure yeast belonging to S. cerevisiae and then used to remove the mentioned mineral elementes under different conditions which included incubation period, pH, and temperature. It was found that the best of these conditions was 60 minutes for duration of incubation, 6 for pH, 25 ᵒC for temperature. During the study the behavior of living