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.

Water flow into unsaturated porous media is governed by the Richards’ partial differential equation expressing the mass conservation and Darcy’s laws. The Richards’ equation may be written in three forms,where the dependent variable is pressure head or moisture content, and the constitutive relationships between water content and pressure head allow for conversion of one form into the other. In the present paper, the “moisture-based" form of Richards’ equation is linearized by applying Kirchhoff’s transformation, which
combines the soil water diffusivity and soil water content. Then the similarity method is used to obtain the analytical solution of wetting front position. This exact solution is obtained by means of Lie’s

The research aims to identify the risks faced by projects and work on the administration, such as those risks by using professional Project Management System (Project Management Professional) by identifying those risks and their impact on the objectives of the project, if they occur and to provide appropriate responses to Ha.autam search application on the draft Law Faculty port by the General Mansour Construction Contracting company has been using a method personal interview with the heads of departments and project managers in the Al-Mansour and tools descriptive and quantitative analysis as was used (likelihood and impact of risk analysis, Ai_kaoa scheme Sbb- effect, analysis of probability and impact, risk matrix (probability

This research shows the experimental results of the bending moment in a flexible and rigid raft foundation rested on dense sandy soil with different embedded depth throughout 24 tests. A physical model of dimensions (200mm*200mm) and (320) mm in height was constructed with raft foundation of (10) mm thickness for flexible raft and (23) mm for rigid raft made of reinforced concrete. To imitate the seismic excitation shaking table skill was applied, the shaker was adjusted to three frequencies equal to (1Hz,2Hz, and 3Hz) and displacement magnitude of (13) mm, the foundation was located at four different embedment depths (0,0.25B = 50mm,0.5B = 100mm, and B = 200mm), where B is the raft width. Generally, the maximum bending

Mobile-based human emotion recognition is very challenging subject, most of the approaches suggested and built in this field utilized various contexts that can be derived from the external sensors and the smartphone, but these approaches suffer from different obstacles and challenges. The proposed system integrated human speech signal and heart rate, in one system, to leverage the accuracy of the human emotion recognition. The proposed system is designed to recognize four human emotions; angry, happy, sad and normal. In this system, the smartphone is used to   record user speech and send it to a server. The smartwatch, fixed on user wrist, is used to measure user heart rate while the user is speaking and send it, via Bluetooth,

Several recent approaches focused on the developing of traditional systems to measure the costs to meet the new environmental requirements, including Attributes Based Costing (ABCII). It is method of accounting is based on measuring the costs according to the Attributes that the product is designed on this basis and according to achievement levels of all the Attribute of the product attributes. This research provides the knowledge foundations of this approach and its role in the market-oriented compared to the Activity based costing as shown in steps to be followed to apply for this Approach. The research problem in the attempt to reach the most accurate Approach in the measurement of the cost of products from th

The first flow injection spectrophotometric method is characterized by its speed and sensitivity which have been developed for the determination of promethazine-HCl in pure and pharmaceutical preparation. It is based on the in situ detection of colored cationic radicals formed via oxidation of the drug with sodium persulphate to pinkish-red species and the same species was determined by using homemade Ayah 3SX3-3D solar flow injection photometer. Optimum conditions were obtained by using the high intensive green light emitted diode as a source. Linear dynamic range for the absorbance versus promethazine-HCl concentration was 0-7 mmol.L-1, with the correlation coefficient (r) was 0.9904 while the percentage linearity (r2%) was 98.09%. the L.

A mathematical eco-epidemiological model consisting of harvested prey–predator system involving fear and disease in the prey population is formulated and studied. The prey population is supposed to be separated into two groups: susceptible and infected. The susceptible prey grows logistically, whereas the infected prey cannot reproduce and instead competes for the environment’s carrying capacity. Furthermore, the disease is transferred through contact from infected to susceptible individuals, and there is no inherited transmission. The existence, positivity, and boundedness of the model’s solution are discussed. The local stability analysis is carried out. The persistence requirements are established. The global behavior of th

An experiment was carried out to study the effects of Time Factor, potassium and Molybdenum on Rhizobium growth. The objective of the experiment, which conducted under laboratory conditions, was to investigate the interaction effects of using three levels of Molybdenum (0, 0.25, 2.50 mg Mo . Kg-1 sterile soil) and four levels of potassium (0, 25, 50, 100 mg K . Kg-1 sterile soil) on the viable counts of Rhizobium growth in the sterile soil after 3, 9, 15 and 21 days of incubation at 28°C. The results indicated that Molybdenum level 2.50 mg Mo . Kg-1 sterile soil and potassium level 50 mg K . Kg-1 sterile soil recorded the biggest significant increase in the viable counts of Rhizobium growth in the sterile soil especially after 15 da