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.

We study the physics of flow due to the interaction between a viscous dipole and boundaries that permit slip. This includes partial and free slip, and interactions near corners. The problem is investigated by using a two relaxation time lattice Boltzmann equation with moment-based boundary conditions. Navier-slip conditions, which involve gradients of the velocity, are formulated and applied locally. The implementation of free-slip conditions with the moment-based approach is discussed. Collision angles of 0°, 30°, and 45° are investigated. Stable simulations are shown for Reynolds numbers between 625 and 10 000 and various slip lengths. Vorticity generation on the wall is shown to be affected by slip length, angle of incidence,

This study examines the relationship between the increase in the number of tourists coming to Tunisia and GDP during the period 1995-2017, using the methodology of joint integration, causal testing and error correction model. The research found the time series instability of the logarithm of the number of tourists coming to Tunisia and the output logarithm but after applying the first differences, these chains become stable, THUS these time series are integrated in the first differences. Using the Johansson method, we found the possibility of a simultaneous integration relationship between the logarithm of the number of tourists coming to Tunisia and the logarithm of GDP in Tunisia, and there is a causal relationship in one direc

The experiment was carried out in the green house of botanical garden belong to Department of Biology/College of Education for Pure Science Ibn AL-Haitham, University of Baghdad for growing season 2017-2018 to evaluate effect of lead stress with concentrations (0, 50, 100, 150) mg.L -1 and Selenium concentrations (0, 15, 30) mg.L-1 on growth of dill plant using pots. The experiment was designed according to completely randomized design (CRD) with three replications. Result indicated that dill plants subjected to lead stress with height concentrations caused decrease in plant parameters (plant height, no. of branches. plant-1, root length, shoot dry weight, the content of nitrogen, phosphorus and potassium, protein concentration, no. of umbe

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This research paper presents a standard economic study. This study aims to build an economic standard form of the investment effect in Human Capital on Economic Growth in Algeria. The study showed that there is an inverse relationship between the investment and human capital. This is expressed by expending on education and economic growth. This contradicts with the economic theory. Such matter could be explained by that expending on education does not contribute in the economic growth. This refers to that the education sector result does not employee or save jobs. Thus, it does not contribute in growth; in addition, the Algerian economy depends on petrol in the first class. This means the ab

Background: Bisphosphonates are potent inhibitors of osteoclastic bone resorption and widely used for the treatment of osteoporosis, and osteogenesis imperfecta in children. Clinical and experimental studies have demonstrated that Bisphosphonates delay or inhibit tooth eruption. This study tries to focus on the effect of bisphosphonate on teeth development and jaw bones growth. Materials and methods: The present study includes 65 neonatal rats during lactation period from 15 Albino Wister rats mother. Alendronate (one type of Bisphosphonates) was administrated orally (15 mg/kg) into 10 pregnant rats two times a week, while other 5 rats regard as control. Then the neonatal rats sacrificed in I, 6, 11, 16 and 21 days. The lower first molar we

An efficient modification and a novel technique combining the homotopy concept with  Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced  in this paper  . Both methods are very efficient and effective. The whole integral part of ADM is used instead of the integral part of homotopy technique. The major feature in current technique gives us a large convergence region of iterative approximate solutions .The results acquired by this technique give better approximations for a larger region as well as previously. Finally, the results conducted via suggesting an efficient and easy technique, and may be addressed to other non-linear problems.

Successfully, theoretical equations were established to study the effect of solvent polarities on the electron current density, fill factor and efficiencies of Tris (8-hydroxy) quinoline aluminum (Alq3)/ ZnO solar cells. Three different solvents studied in this theoretical works, namely 1-propanol, ethanol and acetonitrile. The quantum model of transition energy in donor–acceptor system was used to derive a current formula. After that, it has been used to calculate the fill factor and the efficiency of the solar cell. The calculations indicated that the efficiency of the solar cell is influenced by the polarity of solvents. The best performance was for the solar cell based on acetonitrile as a solvent with electron current density of (5.0

The present study aimed to investigate the possible production of Thioflavin T and the effect of NaCl concentrations and growth phases on the growth rate, doubling time and proline of C. saipanensis N. Hanagata (Scenedesmaceae, Shaerophleales). The alga was cultured in BG 11 medium and six NaCl concentrations were used in the experiments during different growth phases. The results have unveiled the presence of Triflavin T in the alga. The study results showed a growth rate decrease at all NaCl concentrations except in control treatment, while the doubling time, was recorded highest value (14 days) at the NaCl concentration of 0.08 M. The highest value of Proline (0.509 mg. Lˉ¹) was recorded at the treatment of 0.08 M of NaCl and recorded