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.

The present study aimed to examine the effect of endosulfan insecticide on some molecular and biochemical parameters in white mice. Thirty mice were separated randomly into three groups for treatment with endosulfan. One group (G1) served as the control, while the other two groups received intraperitoneal injections of endosulfan G2 (3 mg/kg) and G3 (17 mg/kg) twice a week for 21 and 45 days, respectively. A biochemical study by measuring liver  function parameters, including (alanine aminotransferase (ALT) and aspartate aminotransferase (AST)) and kidney function parameters, including (Blood Urea and Creatinine) and malondialdehyde (MDA), catalase activity (CAT). This study also tested DNA damage by comet assay (normal%, low%, med

Cancer is in general not a result of an abnormality of a single gene but a consequence of changes in many genes, it is therefore of great importance to understand the roles of different oncogenic and tumor suppressor pathways in tumorigenesis. In recent years, there have been many computational models developed to study the genetic alterations of different pathways in the evolutionary process of cancer. However, most of the methods are knowledge-based enrichment analyses and inflexible to analyze user-defined pathways or gene sets. In this paper, we develop a nonparametric and data-driven approach to testing for the dynamic changes of pathways over the cancer progression. Our method is based on an expansion and refinement of the pathway bei

Let  be a non-trivial simple graph. A dominating set in a graph is a set of vertices such that every vertex not in the set is adjacent to at least one vertex in the set. A subset  is a minimum neighborhood dominating set if  is a dominating set and if for every  holds. The minimum cardinality of the minimum neighborhood dominating set of a graph  is called as minimum neighborhood dominating number and it is denoted by  . A minimum neighborhood dominating set is a dominating set where the intersection of the neighborhoods of all vertices in the set is as small as possible, (i.e., ). The minimum neighborhood dominating number, denoted by , is the minimum cardinality of a minimum neighborhood dominating set. In other words, it is the

Seeds, beans, leaves, fruit peel and seeds of five plants (Ferula assa-foetida, Coffea robusta, Olea europaea, Punica granatum and Vitis vinifera, respectively) were extracted with four solvents (distilled water, 80% methanol, 80% acetone and a mixed solvent that included methanol, ethanol, acetone and n-butanol at proportions 7:1:1:1). Such manipulation yielded 20 extracts, which were phytochemically analyzed for total polyphenols (TP) and flavonoids (TF). The DPPH (2,2-diphenyl-1-picrylhydrazyl) radical scavenging activity (RSA) and DPP-4 (dipeptidyl peptidase-4) relative inhibition activity (RIA) were also assessed for each extract. The results revealed that mixed solvent extract of V.

For the graph ⁠, the behavior associated with to the majority of the graphical properties of this graph is covered in this article. The reflection of the capabilities of on the Ly constructions is one of the key ideas addressed throughout this paper. For instance, by this technique we can comprehend the mechanism via which groups of relatively tiny structure are exist within Ly.

This study included effect of polyherbs mixture treatment of diabetic patients type II for two months. The polyherbs mixture contains Nigella sativa seeds, Boswellia carterri gum, Citrus aurantifolia fruits, Elettaria cardamomum fruits. Also this study included estimation of some biochemical parameters in the serum Diabetes Mellitus (D.M.) patients-type II and knowing the relationship of these parameters with this disease. The parameters are glucose, cholesterol ,High density , Low density lipoproteins( HDL-C, LDL-C) respectively , Triglycerides TG, urea, total protein , albumin , Alkaline phosphatase ALP,Transaminase GOT, GPT enzymes . Take (77) samples of diabetic patients serum type II which included (47) samples for group one: herbs

A series of new 4-(((4-(5-(Aryl)-1,3,4-oxadiazol-2-yl)benzyl)oxy)methyl)-2,6-dimethoxy phenol (6a-i) were synthesized from cyclization of 4-(((4-hydroxy-3,5-dimethoxy benzyl)oxy)methyl)benzohydrazide with substituted carboxylic acid in the presences of phosphorusoxy chloride.The resulting compounds were characterized by IR, 1H-NMR, 13C-NMR, and HRMS data. 2,2-Diphenyl-1-picrylhydrazide (DPPH) and ferric reducing antioxidant power (FRAP) assays were used to screen their antioxidant properties. Compounds 6i and 6h exhibited significant antioxidant ability in both assay. Furthermore, type of substituent and their position of the aryl attached 1,3,4-oxadiazole ring at position five are play an important roles in enhancing or declining the antio