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.
An optimization study was conducted to determine the optimal operating pressure for the oil and gas separation vessels in the West Qurna 1 oil field. The ASPEN HYSYS software was employed as an effective tool to analyze the optimal pressure for the second and third-stage separators while maintaining a constant operating pressure for the first stage. The analysis involved 10 cases for each separation stage, revealing that the operating pressure of 3.0 Kg/cm2 and 0.7 Kg/cm2 for the second and third stages, respectively, yielded the optimum oil recovery to the flow tank. These pressure set points were selected based on serval factors including API gravity, oil formation volume factor, and gas-oil ratio from the flow tank. To impro
... Show MoreThe aim of this work is to learn the relationship of the stability of (β) emitter isobars with their shape for some isobaric elements with even mass number (A=152 - 162). To reach this goal firstly the most stable isobar have been determined by plotting mass parabola (plotting the binding energy (B.E) as a function of the atomic number (Z)) for each isobaric family. Then three-dimensional representation graphics for each nucleus in these isobaric families have been plotted to illustrate the deformation in the shape of a nucleus. These three-dimensional representation graphics prepared by calculating the values of semi-axis minor (a), major (b) and (c) ellipsoid axis’s. Our results show that the shape of nuclides which is represented the
... Show MoreThe two-frequency shell model approach is used to calculate the
ground state matter density distribution and the corresponding root
mean square radii of the two-proton17Ne halo nucleus with the
assumption that the model space of 15O core nucleus differ from the
model space of extra two loosely bound valence protons. Two
different size parameters bcore and bhalo of the single particle wave
functions of the harmonic oscillator potential are used. The
calculations are carried out for different configurations of the outer
halo protons in 17Ne nucleus and the structure of this halo nucleus
shows that the dominant configuration when the two halo protons in
the 1d5/2 orbi
The present work aimed to study the efficiency of nanofiltration (NF) and reverse osmosis (RO) process for water recovery from electroplating wastewater and study the factors affecting the performance of two membrane processes. Nanofiltration and reverse osmosis membranes are made from polyamide as spiral wound module. The inorganic materials ZnCl2, CuCl2.2H2O, NiCl2.6H2O and CrCl3.6H2O were used as feed solutions. The operating parameters studied were: operating time, feed concentrations for heavy metal ions, operating pressure, feed flow rate, feed temperature and feed pH. The experimental results showed, the permeate concentration increased and water flux decreased with increase in time from 0 to 70 min. The permeate concentrations incre
... Show MoreThis paper is concerned with pre-test single and double stage shrunken estimators for the mean (?) of normal distribution when a prior estimate (?0) of the actule value (?) is available, using specifying shrinkage weight factors ?(?) as well as pre-test region (R). Expressions for the Bias [B(?)], mean squared error [MSE(?)], Efficiency [EFF(?)] and Expected sample size [E(n/?)] of proposed estimators are derived. Numerical results and conclusions are drawn about selection different constants included in these expressions. Comparisons between suggested estimators, with respect to classical estimators in the sense of Bias and Relative Efficiency, are given. Furthermore, comparisons with the earlier existing works are drawn.
The reason for applying the project is for the development of some physiological variables and skill performance using a device for the first time applied in Iraq to a sample of badminton players, and this device has a patent on 7/2/2019. An experimental method is used for a sample of (12) players from (Al-Orthodoxy club). The experimental group is applied the proposal technique, while, the control group is instructed by the coach.The results of the research attribute to the role of the proposal exercises of fit light technology, thus, this technology has increased the attention and focusing of the sample and some physiological variables and smash shot skill. It has been concluded that the exercises using fit light technology is helped to i
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