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.

Indexes of topological play a crucial role in mathematical chemistry and network theory, providing valuable insights into the structural properties of graphs. In this study, we investigate the Resize graph of G2(3), a significant algebraic structure arising from the exceptional Lie group (G2) over the finite field F3. We compute several well-known topological indices, including the Zagreb indices, Wiener index, and Randić index, to analyze the graph's connectivity and complexity. Our results reveal intricate relationships between the algebraic structure of G2(3) and its graphical properties, offering a deeper understanding of its combinatorial and spectral characteristics. These findings contribute to the broader study of algebraic graph t

Background: Pain and the usage of local anesthetic agents are still real problem in pediatric dentistry, for these reasons, the use of minimal invasive dentistry (MID) in regard to the patient comfort is important especially for children, anxious and uncooperative patients. Chemomechanical caries removal (CMCR) methods involve the selective removal of the carious dentine hence it avoided the painful removal of the sound dentine and the anxiety resulted due to the vibration of the hand piece which is also decreased thus it appears to be more acceptable and comfortable to the patient. Aims of this study: This study was conducted among group of children to assess and compare the anxiety rating scale (during and after treatment) between the

Newly prepared derivatives of Heterocyclic of dicarboxylic acid include 1, 2, 4-Triazoledicarboxylic acid. Thiocarbohydrazine (TCH) reacts with aliphatic and aromatic dicarboxylic acids, and when these resulting compounds interact with compounds containing a group of carbonyl they result in Schiff base, which are very important in the industrial and medical fields and the acids used (oxalic acid, succinic, terephthalic) to prepare the triazole, then the reaction with Para-chlorobenzendihaide. and some physical properties were measured for these products. The biological activity of the prepared compounds has been studied, and it has been shown that they have different effects on the bacteria, compounds prepared with Fourier Transform Infrare

The aim of this paper is to derive a posteriori error estimates for semilinear parabolic interface problems. More specifically, optimal order a posteriori error analysis in the - norm for semidiscrete semilinear parabolic interface problems is derived by using elliptic reconstruction technique introduced by Makridakis and Nochetto in (2003). A key idea for this technique is the use of error estimators derived for elliptic interface problems to obtain parabolic estimators that are of optimal order in space and time.

The human gastrointestinal system is a complex ecosystem crucial for well-being. During sepsis-induced gut injury, the integrity of the intestinal barrier can be compromised. Lipopolysaccharide (LPS), an endotoxin from Gram-negative bacteria, disrupts the intestinal barrier, contributing to inflammation and various dysfunctions. The current study explores the protective effects of limonene, a natural compound with diverse biological properties, against LPS-induced jejunal injury in mice. Oral administration of limonene at dosages of 100 and 200 mg/kg was used in the LPS mouse model. The Murine Sepsis Score (MSS) was utilized to evaluate the severity of sepsis, while serum levels of urea and creatinine served as indicators of renal f

Hepatocellular carcinoma (HCC) is the third most common cause of cancer-related death. Therefore, it is critical for researchers to understand molecular biology in greater depth.  In several diseases including cancer, abnormal miRNA expression has been linked to apoptosis, proliferation, differentiation, and metastasis. Many miRNAs have been studied in relation to cancer, including miR-122, miR-223, and others. Hepatitis B and C viruses are the most important global risk factors for HCC. This study is intended to test whether serum miRNAs serve as a potential biomarker for both HCC and viral infections HBV and C. The expression of miRNA in 64 serum samples was analyzed by RT-qPCR. Compared to healthy volunteers, HCC patients' sera expre

Electrocoagulation process was employed for the treatment of river water flows in Iraq. In this study, a batch Electrocoagulation process was used to treat river water taken from Al - Qadisiyah water treatment plant. electrolysis time, voltage and inter-electrode spacing were the most important parameters to study . A statistical model was developed using the RSM model. The optimum condition after studying the parameter effect the process was 1 cm separating, 30 volts . The RSM model shows the ideal condition of removal for both the TSS and turbidity at 1 cm, 20 volts and 55 min.