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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 May 17 2023
Journal Name
Journal Of The Australian Ceramic Society
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Publication Date
Sat Feb 02 2019
Journal Name
Journal Of The College Of Education For Women
The effect of learning program in developing some social concepts for nursery kids about ( 4 – 5 ): The effect of learning program in developing some social concepts for nursery kids about ( 4 – 5 )

Abstact:
Nursery is one of educational institution in the process of developing the
social concepts that it includes a quirking the knowledge and experiences that
help the kid to adjust with environment through arrangement words ,
movements and concrete things which are transferred to the kids so as to
realize these concepts .
Social concepts are numbers of words and statements with social nature
which the kids learn through the family or nursery in order to effect their
educational style of independent and helping the others .
The re searcher adopted this theory because of the little studies in the
filed of social concepts in the nursery.
The aims of the study are as following :
1- building tools for

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Publication Date
Tue Aug 16 2016
Journal Name
International Journal Of Computer Applications
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Publication Date
Wed Jun 20 2018
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Synthesis, Characterization and Antimicrobial Evaluation with DFT Study of New Two-Amino-4-(4-Chlorophenyl) Thiazole Derivatives

2-amino-4-(4-chloro phenyl)-1,3-thiazole (1) was synthesized by refluxing thiourea with para-chloro phenacyl bromide in absolute methanol. The condensation of amine compound (1)  with phenylisothiocyanate in the presence of pyridine will  produce 1-(4-(4-chlorophenyl)thiazol-2-yl)-3-phenylthiourea(2), which is  upon treatment with 2,4 dinitrophenyl hydrazine by conventional method, afforded 1- ( 4 - ( 4 – chlorophenyl ) thiazol – 2 – yl ) – 3 - phenylhydrazonamide,N' - ( 2 , 4 -dinitrophenyl) ,(3).The characterization of the titled compounds were performed utilizing FTIR spectroscopy, 1HNMR and CHNS elemental analysis, and by me

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Publication Date
Mon Jul 20 2020
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Determined the Concentration Elements to Human Nail Using X- Ray Fluorescence Technique

Cancer constitutes a serious disease and a major health problem in worldwide, a lot of people were infected with this dangerous disease, Therefore, there must be attention to this disease through diagnosis and prevention there. In this study, we determined the relationship between the Cancer and the concentration of trace elements by comparing the concentration trace elements for infected and non-infected people. The trace elements concentrations to nails are one of the diagnostic criteria that easily to detect and dated this disease without any harm to the patient. Eight nails samples were collected from cancer-infected and eight samples from non-infected of the relatives of first-degree. All samples were measured by the concentrations

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Publication Date
Wed Feb 02 2022
Journal Name
Iraqi Journal Of Science
Effect of Solvent type and Annealing Temperature on Efficiency for Eosin -y Dye Sensitized Solar Cells

Dye-sensitized solar cell (DSSC) is one of the photochemical electric cells, which consists of the photoelectrode, the dye, the electrolyte, and the counter electrode. The advantage of DSSC is the low cost of the solar energy conversion into electricity because of inexpensive materials and the relative ease of the fabrication processes. In this study was selected solvent dye resolve to know most efficient in terms of conversion efficiency. A dye solution of water or ethanol and maxing in which eosin – y dissolves behaves like a colloid and explores the effect of sintering temperature of TiO2 films on the efficiency of dye sensitized solar cells. A study conducted on several samples at different temperatures. Exemplary efficiency of the

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Publication Date
Fri Mar 28 2014
Journal Name
Advances In Life Science And Technology
Synthesis and Characterization of Novel Schiff Bases, N-Acyl and Diazetines Derived from 3-((5-hydrazinyl-4-phenyl-4H-1,2,4- triazol-3-yl)methyl)-1H-indole

This work involves synthesis of some new heterocyclic compounds including 1, 3-diazetine. The new Schiff bases [VI] ad derived from 3-((5-hydrazinyl-4-phenyl-4H-1, 2, 4-triazol-3-yl) methyl)-1H-indole [V] which was synthesized by refluxing 5-((1H-indol-3-yl) methyl)-4-phenyl-4H-1, 2, 4-triazole-3-thiol [IV] with hydrazine hydrate in absolute ethanol and this amino compound [V] condensation with different aromatic aldehydes in absolute ethanol to yielded a new Schiff bases [VI] ad. N-acyl compounds [VII] ad were synthesized by addition reaction of acetyl chloride to imine group of Schiff bases in dry benzene. The new diazetine derivatives [VIII] ad synthesized by the reaction of N-acyl compounds [VII] ad with sodium azide in dimethylformamid

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Publication Date
Sun Jun 05 2016
Journal Name
Baghdad Science Journal
Preparation and Spectroscopic Studies of Some Metal Ion Complexes of 2-((4-Formyl-3-Hydroxynaphthalen-2-yl) Diazenyl) Benzoic Acid

New azo ligand 2-((4-formyl-3-hydroxynaphthalen-2-yl) diazenyl) benzoic acid (H2L) was synthesized from the reaction of 2-aminobenzoic acid and2-hydroxy-1-naphthaldehyde. Monomeric complexes of this ligand, of general formulae [MII(L)(H2O)] with (MII = Mn, Co, Ni, Cu, Zn, Pd, Cd and Hg ) were reported. The compounds were isolated and characterized in solid state by using 1H-NMR, FT-IR, UV–Vis and mass spectral studies, elemental microanalysis, metal content, magnetic moment measurements, molar conductance and chloride containing. These studies revealed tetrahedral geometries for all complexes except PdII complex is Square planar. The study of complexes formation via molar ratio of (M:L) as (1:1). Theoretical treatments of compounds in gas

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Publication Date
Sun Jun 12 2011
Journal Name
Baghdad Science Journal
Superconducting Properties of the (Bi0.8Pb0.2)2(Sr0.9Ba0.1)2 Ca2Cu3-x Nix O10+? System.

The effect of substitution of Ni on Cu in (Bi0.8Pb0.2)2(Sr0.9Ba0.1)2 Ca2Cu3-x Nix O10+? for (x=0,0.1….1,2,3) superconductor system and sintering time has been investigated .The samples were prepared by solid-state reaction methods. The results show that the optimum sintering temperature is equal to 850 ºC, and the sintering time is equal to 140 h. The highest transition temperature (Tc) obtained for (Bi0.8Pb0.2)2(Sr0.9Ba0.1)2 Ca2Cu3-x NixO10+? composition was 113 with x=0.8 Phase analyses of the samples by X-ray diffraction (XRD) analysis showed an orthorhombic structure with a high Tc phases (2223) as a dominant phase and low Tc phase (2212) in addition to some impurity phases.

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Publication Date
Sun Jan 03 2016
Journal Name
Journal Of The Faculty Of Medicine Baghdad
The prevalence of gallstone disease after sleeve gastrectomy and Roux en Y gastric bypass

Background: Obesity (body mass index >30) is increasing worldwide with an estimated 1.7 billion people currently affected by the disease, Gallstone represent the third most common disease observed among obese patients. Moreover about 30% of the patients who are candidates for bariatric surgery either have undergone a prior cholecystectomy or are found to present gallstones at time of surgery, On the other hand, newly formed gallstones may be diagnosed in 27% to 43% of patients who have undergone bariatric surgery within a very short period of time.
Objective: To determine the prevalence of gallstone disease requiring cholecystectomy after laparoscopic sleeve gastrectomy and roux en Y gastric bypass during a one year follow up and t

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