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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 Mar 18 2020
Journal Name
Baghdad Science Journal
Synthesis of Six and Seven-membered Heterocyclic Molecules Containing an Adamantyl Fragment and an X-ray Crystal Structure of (E)-N-(adamantan-1-yl)-1-(3-nitrophenyl)methanimine

       Our work included a synthesis of three new imine derivatives—1,3-thiazinan-4-one, 1,3-oxazinan-6-one and 1,3-oxazepin-4,7-dione—which contained an adamantyl fragment. These were produced via the condensation of the Schiff`s base (E)-N-(adamantan-1-yl)-1-(3-aryl)methanimine with 3-mercaptopropanoic acid; 3-chloropropanoic acid; and maleic, citraconic anhydride, respectively. These new imines were prepared via the condensation of adamantan-1-ylamine and 3-nitro-, 3-bromobenzaldehyde in n-BuOH. We obtained a good yield of products. FTIR, 1H NMR spectroscopy and C.H.N.S analysis were used to diagnostic the products. The molecular structure of (E)-N-(adamantan-1-yl

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Publication Date
Tue Sep 01 2020
Journal Name
Baghdad Science Journal
Numerical Solution of Mixed Volterra – Fredholm Integral Equation Using the Collocation Method

Volterra Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained

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Publication Date
Sat Oct 01 2011
Journal Name
Iraqi Journal Of Physics
Fabrication of PbxS1-x Detector and Studying the Effect of x Content on its some Physical Properties

A polycrystalline PbxS1-x alloys with various Pb content ( 0.54 and 0.55) has been prepared successfully. The structure and composition of alloys are determined by X-ray diffraction (XRD), atomic absorption spectroscopy (AAS) and X-ray fluorescence (XRF) respectively. The X-ray diffraction results shows that the structure is polycrystalline with cubic structure, and there are strong peaks at the direction (200) and (111), the grain size varies between 20 and 82 nm. From AAS and XRF result, the concentrations of Pb content for these alloys were determined. The results show high accuracy and very close to the theoretical values. A photoconductive detector as a bulk has been fabricated by taking pieces of prepared alloys and polished chemic

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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
the photoconductive properties of pbxs1-x films

Optical detector was manufactured Bashaddam thermal evaporation technique at room temperature under pressure rays studied characteristics of reactive Scout efficiency quantitative ratio of the signal and the ability equivalent to noise

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Publication Date
Tue Jun 01 2021
Journal Name
Minar International Journal Of Applied Sciences And Technology
STRUCTURAL AND ELECTRICAL PROPERTIES OF (CDO)1-X (V2O5)X PREPARED BY PULSE LASER DEPOSITION TECHNIQUE FOR SOLAR CELL APPLICATIONS

In this work ,pure and doped(CdO)thin films with different concentration of V2O5x (0.0, 0.05, 0.1 ) wt.% have been prepared on glass substrate at room temperature using Pulse Laser Deposition technique(PLD).The focused Nd:YAG laser beam at 800 mJ with a frequency second radiation at 1064 nm (pulse width 9 ns) repetition frequency (6 Hz), for 500 laser pulses incident on the target surface At first ,The pellets of (CdO)1-x(V2O5)x at different V2O5 contents were sintered to a temperature of 773K for one hours.Then films of (CdO)1-x(V2O5)x have been prepared.The structure of the thin films was examined by using (XRD) analysis..Hall effect has been measured in orded to know the type of conductivity, Finally the solar cell and the effici

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Publication Date
Wed Oct 28 2020
Journal Name
Iraqi Journal Of Science
On y-closed Rickart Modules

     In a previous work, Ali and Ghawi studied closed Rickart modules. The main purpose of this paper is to define and study the properties of y-closed Rickart modules .We prove that, Let  and   be two -modules such that  is singular. Then  is -y-closed Rickart module if and only if   Also, we study the direct sum  of  y-closed Rickart modules.

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Publication Date
Fri Jan 26 2024
Journal Name
Iraqi Journal Of Science
Projectivity on y-closed Submodules

In this notion we consider a generalization of the notion of a projective modules , defined using y-closed submodules . We show that for a module M = M1M2 . If M2 is M1 – y-closed projective , then for every y-closed submodule N of M with M = M1 + N , there exists a submodule M`of N such that M = M1M`.

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Publication Date
Tue Apr 30 2024
Journal Name
Iraqi Journal Of Science
Synthesis, Characterization and Antimicrobial Evaluation for New Esters Derivatives Containing Two 1, 3, 4-Oxadiazole Units

     This work includes the synthesis of new ester compounds containing two 1,3,4-oxadiazole rings, 15a-c and 16a-c. This was done over seven steps, starting with p-acetamido-phenol 1 and 2-mercaptobenzoimidazole 2. The structure of the products was determined using FT-IR, 1H NMR, and mass spectroscopy. The evaluation of the antimicrobial activities of some prepared compounds was achieved against four types of bacteria (two types of gram-positive bacteria; Staphylococcus aureus and Bacillus subtilis, and two types of gram-negative bacteria, Pseudomonas aeruginosa and E. Coli), as well as against one types of fungus (C. albino). The results show moderate activit against the study bacteria, and the theoretical analysis of the toxi

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Publication Date
Mon Oct 01 2012
Journal Name
Iraqi Journal Of Physics
Structural and optical properties for nano GaxSb1-x films

Alloys of GaxSb1-x system with different Ga concentration (x=0.4, 0.5, 0.6) have been prepared in evacuated quartz tubes. The structure of the alloys were examined by X-ray diffraction analysis (XRD) and found to be polycrystalline of zincblend structure with strong crystalline orientation (220). Thin films of GaxSb1-x system of about 1.0 μm thickness have been deposited by flash evaporation method on glass substrate at 473K substrate temperature (Ts) and under pressure 10-6 mbar. This study concentrated on the effect of Ga concentration (x) on some physical properties of GaxSb1-x thin films such as structural and optical properties. The structure of prepared films for various values of x was polycrystalline. The X-ray diffraction analy

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Publication Date
Wed Apr 01 2009
Journal Name
Journal Of The Faculty Of Medicine Baghdad
The Value of the chest X-Ray for diagnosing left ventricular Dysfunction

Background: The use of the chest x-ray measurements which includes the cardiothoracic ratio(C-T) and frontal area (FA) of the heart by the CXR are useful measures for primary assessment of the cardiac dysfunction.
Patients and Methods: A Prospective study was done from the 1st of January 2005 to the 1st of October in the same year on a 120 consecutive patients who have been admitted for coronary and L.V angiogram at IBN-AL-BITAR hospital. The C-T ratio and the frontal area were measured.
Results: The study comprised 120 subjects who were admitted for coronary and L.V angiogram for diagnostic reasons. 89subjects (74.2%) are male and 31subjects (25.8%) are female .17(14%) subjects have left ventricular d

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