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.

This research had been conducted to investigate response of two Antirrhinum majus L. varieties, tall and dwarf variety to foliar application of Indole 3-acetic acid and Benzyladenin at (0, 60, 120, 180, 240 ppm), through plant height, fresh weight, dry weight of shoot, length of inflorescence (raceme), number of flowering buds per raceme and chlorophyll content in leaves at complete flowering stage.

Results of treatment of the tall variety with IAA and BA showed that IAA had the highest significant increase in plant height, while BA had the highest significant increase in chlorophyll content .Increasing concentrations of both IAA and BA resulted a significant increase in all growth parameters, this was obvious in floweri

     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

In this research various of 2,5-disubstituted 1,3,4-oxadiazole (Schiff base, oxo-thiazolidine , and other compounds) were synthesized from 2,5-di(4,4?- amino-1,3,4-oxadiazole ) which use quently synthesized from mixture of 4-amino benzoic acid and hydrazine in the presence of polyphosphorus acid. The synthesized compounds were characterized by using some Spectral data (UV, FT-IR, and 1H-NMR).

Background: Temporomandibular joint disorder (TMD) is a general term that describe a wide variety of conditions that include myogenic pain, internalderangement, arthritic problem, ankylosis of the joint and growth disorders. The aims of study was to evaluate the value of 3 Tesla magnetic resonance imaging in assessment of articular disc position and configuration in patients with temporomandibular joint disorders and to evaluate the correlations of these MRI findings with the clinical signs and symptoms. Materials and methods: A total forty six (30 study and 16 control) participants aged between18 and 49 years, were examined according to Helkimo anamnestic index (questionnaire for anamnesis) and clinical dysfunction index scoring criteria

This research is concerned with the study of the projective plane over a finite field . The main purpose is finding partitions of the projective line PG( ) and the projective plane PG( ) , in addition to embedding PG(1, ) into PG( ) and PG( ) into PG( ). Clearly, the orbits of PG( ) are found, along with the cross-ratio for each orbit. As for PG( ), 13 partitions were found on PG( ) each partition being classified in terms of the degree of its arc, length, its own code, as well as its error correcting. The last main aim is to classify the group actions on PG( ).

A series of new copolyimides containing pendant 1,3,4-oxadiazole moiety were synthesized via multisteps. In the first step five N-(5-substituted-1,3,4-oxadiazole-2-yl)maleamic acids were prepared via reaction of maleic anhydride with 2-amino-5-substituted-1,3,4-oxadiazoles. The obtained amic acids were dehydrated in the second step affording the corresponding N-(5-substituted-1,3,4-oxadiazole-2-yl) maleimides. In the third step the newly synthesized maleimides were introduced successfully in free radical copolymerization reaction with four vinylic monomers including acrylo nitrile, methacrylonitrile, methyl acrylate and methyl meth acrylate respectively producing twelve new copolymers having different physical properties which may serve

     This paper aims to find out if FOXP-3 was expressed in samples from Iraqi cervical cancer patients. Expression of FOXP-3 was detected in 55 cervical tissue samples by immunohistochemistry. Since thirty-five cases of aggressive cervical cancer were included, along with 20 normal samples used as controls. The nucleus and cytoplasm levels of FOXP-3 were counted, considering the ratio of positive cells and intensity. FOXP3 cytoplasmic staining was found in 27 out of 35 cases. Only 11 out of 35 samples displayed nuclear lymphocyte staining. Furthermore, four samples expressed this marker in both the nuclear and cytoplasm of the cervical cells. There is a highly significant difference in FOXP3 expression in the cytoplasm of

     Understanding Caspase-3 (CASP-3) and interleukin-32 (IL32) roles in SARS-CoV-2 infection is critical to linearize the pathogenesis of the virus as well as the resultant disease which may uncover novel therapeutic targets in treating COVID-19 patients. This study aimed to evaluate caspase‐3 (CASP3) and interleukin 32 (IL32) roles and their correlation with the disease severity among patients.  The case-control study (140 patients and 60 healthy controls) was performed with molecular and ELISA assays. CASP3 and IL32 serum levels were determined along with other clinical data of patients. CASP3 levels were classified as significantly higher (p < 0.001), while IL-32 levels were significantly lower in production (p

      Coronavirus 2 is the cause of coronavirus disease 2019 (COVID-19), which leads to severe acute respiratory illness. Matrix metalloproteinases (MMPs) have been linked to leukocyte infiltration and chemokine activation during inflammatory responses. Tissue inhibitors of metalloproteinase (TIMP) family are thought to dampen the proinflammatory effects of these MMPs. The molecular pathways of lung fibrosis are mediated by MMPs and TIMPs. In this study, we sought to investigate the probable link between MMPs, specifically MMP-3, TIMP-2, and COVID-19. The study included 58 COVID-19 patients and 30 apparently healthy individuals matched in terms of age and sex. Multiplex real- time PCR was used to detect the ORF1ab, E, and N genes of