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Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ y

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.

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Publication Date
Wed Jun 26 2019
Journal Name
Iraqi Journal Of Science
On the Grobner Basis of the Toric Ideal for 3 X n- Contingency Tables

In this paper, The Grobner basis of the Toric Ideal for - contingency tables related with the Markov basis B introduced by Hussein S. MH, Abdulrahman H. M in 2018 is found. Also, the Grobner basis is a reduced and universal Grobner basis are shown.

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Publication Date
Sun Oct 01 2017
Journal Name
Journal Of The Faculty Of Medicine Baghdad
Correlations between Serum Interleukins-2,-4 Levels and Some Biochemical Parameters in Iraqi Patients with Osteoporosis

Background: Osteoporosis is a frequent disease that is manifested by reduced in mineral density and raised in fracture risk. Recent studies have indicated that osteoporosis is caused by composite connections among local and systemic regulators of bone cell function.
Objective: The purpose of this study was to investigate the relationship between interleukin-2, interleukin-4, and some biochemical markers in Iraqi patients with osteoporosis.
Patients and Methods: Forty five osteoporotic patients were incorporated in this study (30 women and 15 men). Serum fasting glucose, lipid profile, alkaline phosphatase activity, calcium, magnesium, interleukin-2, and interleukin-4 were measured in osteoporotic patients and compared them with the

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Publication Date
Tue Apr 01 2014
Journal Name
Journal Of The Faculty Of Medicine Baghdad
Comparative Study of Allopurinol and Uralyt-4 in patients with Hyperuricemia in Diyala Governorate.

Background: Hyperuricemia represents a major public health problem; approximately most population has hyperuricemia, serum uric acid ≥6.5 mg/dL in women and ≥7.0 mg/dL in men.
Allopurinol has been approved for the treatment of hyperuricemia patients. Epidemiological and experimental studies suggest a linkage between hyperuricemia and type of treatment.
Objective: To assess the effect of allopurinol and uralyt- 4 and mixture of two drugs (allopurinol and uralyt-4) in hyperuricemia patients
Methods: A total of 60 serum patients with history of hyperuricemia, obtained from Baladrus Hospital in Diyala governorate, were included in this study. In addition, ten normal uric acid level persons used as contro

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Publication Date
Sat May 01 2021
Journal Name
Journal Of Physics: Conference Series
The substitutions of Strontium by yttrium and their effects on Bi<sub>2</sub>Sr<sub>2</sub>-<sub>x</sub>Y<sub>x</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10</sub>+<sub>δ</sub> superconducting compound
Abstract<p>Superconducting compound Bi<sub>2</sub>Sr2-<sub>x</sub>Y<sub>x</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10+δ</sub> were Synthesized by method of solid state reaction, at 1033 K for 160 hours temperature of the sintering at normal atmospheric pressure where substitutions Yttrium oxide with Strontium. When Y2O3 concentration (0.0, 0.1, 0.2, 0.3, 0.4 and 0.5). All specimens of Bi<sub>2</sub>Sr<sub>2</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10+δ</sub> superconducting compounds were examined. The resistivity of electrical was checked by the four point probe technique, It was found th</p> ... Show More
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Publication Date
Tue Mar 30 2021
Journal Name
Baghdad Science Journal
Approximate Analytical Solutions of Bright Optical Soliton for Nonlinear Schrödinger Equation of Power Law Nonlinearity

This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fast converging series by applying the proposed approach. On top of that, the number of computed terms is also significantly reduced. Compared to the RDTM, the nonlinear term in this method is replaced by related Adomian polynomials prior to the implementation of a multistep approach. As a consequence, only a smaller number of NLSE computed terms are required in the attained approximation. Moreover, the approximation also converges rapidly over a

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Publication Date
Wed Aug 09 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis and Antimicrobial Evaluation of Some Bis-1, 3, 4-Butane-1-3, 4-Oxadiazole Derivatives

A series of new Bis-1,4-Butane -1,3,4 – Oxadizole derivatives [III a-j] were synthesized from adipic acid dihydrazide and different aromatic acids in the presence of phosphours oxychloide. There compounds were characterized by their IR, microanalysis, and mass spectral data.    In vitro antimicrobial were synthesized. In vitro antimicrobial activity of these compounds against (Gram negative) and (Gram positive) were reported, some of these compounds prepared derivatives exhibited antimicrobial activity

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Publication Date
Thu Feb 27 2020
Journal Name
Iraqi Journal Of Science
Synthesis and Antimicrobial Studies of New [Tetrakis (1, 2, 4-Triazole / 1, 3, 4-Oxadiazole / 1, 3, 4-Thiadiazole] [Bis-(Benzene-1, 3, 5-Triyl)] Dioxymethylene Compounds

     Synthesis of new heterocyclic compounds containing four five-membered rings together was the main goal of this work. The new derivatives of [tetrakis (1,2,4-triazole /1,3,4-thiadiazole /1,3,4-oxadiazole][bis-(benzene-1,3,5-triyl)] dioxymethylene A7-A18 were synthesized by the reaction of [bis-(dimethyl 5-yl-isophthalate)] dioxymethylene compound A1 which was previously prepared from the reaction of 1,2-dibromomethan and dimethyl 5-hydroxyisophthalate, then treated with hydrazine hydrate to yield the corresponding acid hydrazide A2. In the next step, compound A2 was refluxed with 4-substituted isothiocyanate to give substituted thiosemicarbazides A3-A6. The treatment of the latter compounds in basic medium of 2M o

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Publication Date
Sun Apr 01 2018
Journal Name
Al–bahith Al–a'alami
‏Framing war against ISIS in New York Times/ from 10/17/2016 to 4/16/2017

The research is aimed at investigating how the New York Times framed the war against ISIS in its news coverage and which news sources it adopted while reporting on this war.
‏ The research could be classified under descriptive researches. The survey methodology has been adopted and the content analysis has been used. The research sample consists of all the news stories the New York Times have published about the war against ISIS from 10/17/2016 to 4/16/2017 according to the comprehensive sampling method. The number of news stories that were analyzed was (155) news story. The research tool was (coding scheme).
The research has reached the following conclusions:
‏ 1. In its news coverage of the war against ISIS, the New York T

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Publication Date
Tue Feb 28 2023
Journal Name
Iraqi Journal Of Science
Applications of the Finite Operator〖 〗_3 E_2 (■(q^(-N),a,b@c,d);q,-fθ) for the Polynomials B_n (a,b,c,d,f,x,y|q)

     In this work,   polynomials  and the finite q-exponential operator  are constructed. The operator  is used to combine an operator proof of the generating function with its extension, Mehler's formula with its extension and Roger's formula for the polynomials . The generating function with its extension,  Mehler's formula with its extension and Rogers formula for Al-Salam-Carlitz polynomials  are deduced by giving special values to polynomials .

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Publication Date
Fri Apr 01 2022
Journal Name
Baghdad Science Journal
Numerical Solutions of Two-Dimensional Vorticity Transport Equation Using Crank-Nicolson Method

This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

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