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.
Background: Oral SCC is a complex malignancy where environmental factors, viral infections and genetic alterations most likely interact, and thus give rise to the malignant condition. The HSP70 play a direct role in apoptosis inhibition by aligning the improved integrity of a cell’s proteins with the improved chances of that particular cell’s survival.P21 gene produces p21 protein which is a potent cyclin-dependent kinase inhibitor that plays a significant role in carcinogenesis. The aims of the study were to evaluate and compare the immun-histochemical expression of the HSP70 and cell cycle protein p21in NOM, OED, and OSCC. Correlate both marker expressions with each other. Materials and methods: Forty six formalin-fixed, par
... Show MoreWith the fast-growing of neural machine translation (NMT), there is still a lack of insight into the performance of these models on semantically and culturally rich texts, especially between linguistically distant languages like Arabic and English. In this paper, we investigate the performance of two state-of-the-art AI translation systems (ChatGPT, DeepSeek) when translating Arabic texts to English in three different genres: journalistic, literary, and technical. The study utilizes a mixed-method evaluation methodology based on a balanced corpus of 60 Arabic source texts from the three genres. Objective measures, including BLEU and TER, and subjective evaluations from human translators were employed to determine the semantic, contextual an
... Show MoreThe fluorescence emission of Rhodamine 6G (R6G) and Acriflavine dyes in PMMA polymer have been studied by changing the irradiation and exposure time of laser light to know the effect of this parameter. It was found that the fluorescence intensity decreases in the polymer samples doped dyes as the exposure time increases and then reaches stabilization at long times, this behavior called photobleaching, which have been shown in liquid phase less than solid phase. Using 2nd harmonic with wavelength 530 nm laser, the photobleaching effect in the two dye-doped polymers different solvent but same was studied. It was observed that photobleaching of by different solution and by using dip spin coating the photobleaching seem in liquid phase
... Show MoreNew binuclear Mn(II), Co(II), Ni(II), Cu(II), Zn(II), and Hg(II) Complexes of N2S2 tetradentate or N4S2 hexadentate symmetric Schiff base were prepared by the condensation of butane-1,4-diylbis(2-amino ethylcarbamodithioate) with 3-acetyl pyridine. The complexes having the general formula [M2LCl4] (where L=butane-1,4-diyl bis (2-(z)-1-(pyridine-3-ylethylidene amino))ethyl carbamodithioate, M= Mn(II), Co(II), Ni(II), Cu(II), Zn(II), and Hg(II)), were prepared by the reaction of the mentioned metal salts and the ligand. The resulting binuclear complexes were characterized by molar conductance, magnetic susceptibility ,infrared and electronic spectral measurements. This study indicated that Mn(II), Ni(II) and Cu(II) complexes have octahedral g
... Show MoreFocusing of Gaussian laser beam through nonlinear media can induce spatial self- phase modulation which forms a far field intensity pattern of concentric rings. The nonlinear refractive index change of material depends on the number of pattern rings. In this paper, a formation of tunable nonlinear refractive index change of hybrid functionalized carbon nanotubes/silver nanoparticles acetone suspensions (F-MWCNTs/Ag-NPs) at weight mixing ratio of 1:3 and volume fraction of 6x10-6 , 9x10-6 , and 18x10-6 using laser beam at wavelength of 473nm was investigated experimentally. The results showed that tunable nonlinear refractive indices were obtained and increasing of incident laser power density led to increase the nonlinear refractive inde
... Show MoreAnew Schiff base (NaHL) has been prepared from the reaction between the salt of amino acid glycine with 2-hydroxy naphthaldehyde. By tridentate Schiff base of (ONO), donors were characterized by using U.V and spectrophotometer techniques. Complexes of Co(II) Ni(II) Cu(II) and Zn(II) ion with the ligand have been prepared, these complexes were identified by infrared, electronic spectral data, elemental analysis, magnetic moments, and molar conductivity measurements. It is concluded from the elemental analysis that all the complexes have (1:2) [metal:ligand] molar ratios, octahedral, with the exception to Zn(II) complex which have (1:1)[metal:ligand] molar ratio.
... Show Moreحضرت معقدات كل من الفنادايل, الخارصين, النحاس والكادميوم بتكافؤهم الثنائي والذهب بتكافؤه الثلاثي بأستخدام صبغة ازوجديدة (6،4،2-ثلاثي هيدروكسي-3-((3-هيدروكسي فنيل) ثنائي زينيل ) فنيل ) ايثان-1-اون المحضرة من ملح الديازونيوم مع ٦,٤,٢- ثلاثي هيدروكسي اسيتوفينون بعد عزل (E)-1-(2,4,6-trihydroxy-3-((3-hydroxyphenyl)diazenyl)phenyl)ethan-1-one تم تشخيصها بواسطة الطرق الطيفية المتاحة والتقنيات التشخيصية لكل من التحليل الدقيق للعناصرواطياف كل من ال
... Show MoreThe reaction of [Benzoyl hydrazine] with [Diphenyl mono oxime] and Glacial acetic acid was carried out in methanol gave a new tridentate ligand [Benzoic acid (2-hydroxyimino- 1, 2-diphyneylethylidene) - hydrazide]. This ligand was reacted with some metal ions (Fe(II), Co(II), Ni(II), and Cu(II)) in methanol with (1:1) metal : ligand ratio to give a series of new complexes of the general formula [M(L)Cl2.H2O], where M= Fe(11), Co(11), Ni(11) and Cu(11). All compounds were characterized by spectroscopic methods (I.R, UV-Vis), elemental microanalysis (C.H.N), atomic absorption, magnetic susceptibility, and conductivity measurements. From the obtained data the proposed molecular structures were suggested for the complexes of Fe
... Show MoreDiabetic mellitus is one of the main risk factors of fungal infections because poor glycemic control is associated with a high level of glucose in blood and saliva which could be treated as nutrient to fungi. This study aimed to isolate and identification of pathogenic fungi from diabetic patient. 140 samples were taken from different places of human body from the national center of diabetic patients that related to Mustansiriyah University / college of medicine and Al-yarmuk Hospital in Baghdad. 84 sample (60%) tested positive to fungi and 56 sample (40%) tested negative to fungi. The most frequented fungi isolated have been chosen for molecular identification by PCR (Millerozyma farinosa and Candida orthopsilosis) using specific pri
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