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.
Abstract
The research aims to identify the level of effectiveness of the teaching practices of science and mathematics teachers in light of the national framework for future skills in Omani schools. To achieve the objectives of the study, the researchers used the descriptive approach, as he designed a note card consisting of (30) phrases distributed on three axes: basic skills, practical skills, and technical skills. After verifying the validity and reliability of the tools, they were applied to a sample of (116) teachers. The results of the research revealed that the level of effectiveness of the teaching practices of mathematics teachers has recorded a medium degree with a mean (3.05). The results a
... Show MoreThe current research aims to identify the effect of the Bransford and Stein model on the achievement of fifth-grade literary students for geography and their reflective thinking. To achieve the objective of the research, the following two null hypotheses were formulated:
- There is no statistically significant difference at the significance level (0.05) between the average scores of the experimental group students who studied geography using the Bransford and Stein model and the average scores of the control group students who studied the same subject in the usual way in the achievement test. 2- There is no statistically significant difference at the significance level (0.05) between the average scores of the experimental gr
Since cancer is becoming a leading cause of death worldwide, efforts should be concentrated on understanding its underlying biological alterations that would be utilized in disease management, especially prevention strategies. Within this context, multiple bodies of evidence have highlighted leptin’s practical and promising role, a peptide hormone extracted from adipose and fatty tissues with other adipokines, in promoting the proliferation, migration, and metastatic invasion of breast carcinoma cells. Excessive blood leptin levels and hyperleptinemia increase body fat content and stimulate appetite. Also, high leptin level is believed to be associated with several conditions, including overeating, emotional stress, inflammation, obesity,
... Show MoreIn this study light elements 10B , 10Be for 10B(n,p)10Be reaction as well as proton energy from 0.987 MeV to 2.028 MeV with threshold energy (1.04MeV) are used according to the available data of reaction cross sections. The more recent cross sections data of 10Be(p,n)10B reaction is reproduced in fin steps in the specified energy range , as well as cross section (p,n) values were derived from the published data of (n,p) as a function of energy in the same fine energy steps by using the reciprocity theory of principle inverse reaction . This calculation involves only the first excited state of 10B , 10Be in the reactions 10Be(p,n)10B and 10B(n,p)10Be.
RESRAD is a computer model designed to estimate risks and radiation doses from residual radioactive materials in soil. Thirty seven soil samples were collected from the area around the berms of Al-Tuwaitha site and two samples as background taken from an area about 3 km north of the site. The samples were measured by gamma-ray spectrometry system using high purity germanium (HPGe) detector. The results of samples measurements showed that three contaminated area with 238U and 235U found in the study area. Two scenarios were applied for each contaminated area to estimate the dose using RESRAD (onsite) version 7.0 code. The total dose of resident farmer scenario for area A, B and C are 0.854, 0.033 and 2.15×10-3 mSv.yr-1, respectively. Whi
... Show MoreThat internal control is particularly important in improvingperformance and tax reform، they play an important role in the regularity ofwork and development and the anti corruption and activating the decisionsand tax legislation، as contained in the organizational plan and the means،procedures and components designed from which to ensure a policy andimplementation plans The research aims to review the reality of the internalcontrol in the General Commission for Taxes and stand on the deficiencies init, with the strengthening of the role of internal control in the GeneralAuthority for taxes based on the laws and regulations and by using modernmeans to work as well as developing the performance of employees in thebody، including helpin
... Show MoreThe study aimed at ideutifying the impact of scieutific skills in strategy and liabits of mind amony stueuts in tenth grade . The study demanded to choose a sampie that coutaiun (42) student of the fourth grade of the secondary school who were dirided into tow groups , the first is experimental studied according to scieutific skill strategy , and the other controlling , studied according to the usualway . An achievement test has been taken that adopted staudard for mind skills as research tools that are applid after ascertaining sincerity proved at the end of the experiment .The study has reached to the conclusion that there are statistically significant differnces in farour of the experiment group in both
... Show More