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.

<p>In combinatorial testing development, the fabrication of covering arrays is the key challenge by the multiple aspects that influence it. A wide range of combinatorial problems can be solved using metaheuristic and greedy techniques. Combining the greedy technique utilizing a metaheuristic search technique like hill climbing (HC), can produce feasible results for combinatorial tests. Methods based on metaheuristics are used to deal with tuples that may be left after redundancy using greedy strategies; then the result utilization is assured to be near-optimal using a metaheuristic algorithm. As a result, the use of both greedy and HC algorithms in a single test generation system is a good candidate if constructed correctly. T

Asthma is a chronic respiratory disorder in which immunological and structural cells play a role. The limits of conventional medicines necessitate the development of innovative therapeutic techniques for asthma. In the present study, we investigated the possible protective effect of cinnamic acid (CA) on ovalbumin-induced asthma in a mouse model. Sixty albino male mice BALB/c type weighing (20-30) grams were chosen at random and divided into five groups each one contains 12 animal: Group I: PBS/liquid paraffin control. Group II: asthma model group. Group III: cinnamic acid control group; mice received cinnamic acid (50 mg/kg) in liquid paraffin orally by gavage. Group IV: asthma model / group of (25 mg / kg) cinnamic acid; mice received

The present study aimed to identify the therapeutic evaluation of chitosan extracted from the fungus cushroom and pure chitosan on glucose and lipid profile in the blood of 35 male rabbits with hyperlipidemia induced experimentally by cholesterol. The tests included estimation of glucose levels, total cholesterol, triglycerides, high-density lipoproteins, low-density lipoproteins, and very low-density lipoproteins. hyperlipidemia was induced in the male rabbits used in the study which was administered orally with cholesterol 150mg/kg body weight for a week. rabbits were divided into seven groups: control, cholesterol, pure chitosan, mushroom chitosan, cholesterol and pure chitosan, cholesterol and mushroom chitosan and cholestero

Ciprofloxacin is widely used in treating adults infected with Gram-negative bacteria. It is contraindicated in children, growing adolescents and during pregnancy due to joint toxicity. Its toxicity concerning other organs needs to be clarified. Thus, this study was designed to study the possible cardiac damage induced by two selected doses of ciprofloxacin in juvenile rats.Eighteenth healthy juvenile rats (4 weeks old and their weight 30 ± 2 gm) were utilized in this study and divided into three groups. Group-I control; group II and group III, respectively injected IP with 25 mg/kg and 50 mg/kg ciprofloxacin every 12 hours for one week. Serum enzymes activities alanine aminotransferase (ALT), aspartate aminotransferase  (AST), cr

       In the present paper, by making use of the new generalized operator, some results of third order differential subordination and differential superordination consequence for analytic functions are obtained. Also, some sandwich-type theorems are presented.

In the present work, a z-scan technique was used to study the nonlinear optical properties, represented by the nonlinear refractive index and nonlinear absorption coefficients of nanoparticles cadmium sulfide thin film. The sample was prepared by the chemical bath deposition method. Several testing were done including, x-ray, transmission and thickness of thin film. z-Scan experiment was performed at two wavelengths (1064 nm and 532 nm) and different energies. The results showed the effect of self-focusing in the material at higher intensities, which evaluated n2 to be (0.11-0.16) cm2/GW. The effect of two-photon absorption was studied, which evaluated β to be (24-106) cm/GW. In addition, the optical limiting behavior has been studied.