Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

In this work, we introduce a new kind of perfect mappings, namely j-perfect mappings and j-ω-perfect mappings. Furthermore we devoted to study the relationship between j-perfect mappings and j-ω-perfect mappings. Finally, certain theorems and characterization concerning these concepts are studied; j = , δ, α, pre, b, β

Propranolol is a nonselective-adrenergic blocker used in the treatment of hypertension, cardiac arrhythmias, and angina pectoris. A significant problem in propranolol therapy is that it undergoes extensive presystemic metabolism after oral administration leading to reduced bioavailability. In this study, two new propranolol derivatives have been designed, synthesized and characterized. These compounds were formed by acylation of propranolol followed by nucleophilic substitution reaction of acylated propranolol, these derivatives were analyzed for IR, CHN, melting points, and evaluated for their lipophilic properties compared with propranolol. The lower partition coefficient of these two derivatives revealed that the prodrug approach may be

Novel heterocyclic polyimide 5(a,b) have been synthesized based on polyacrylic backbone. The synthetic route start with nucleophilic substitution of 2-amino, or 4-amino, pyridine 1(a,b) to the polyacryloyl chloride afforded poly substituted amide 2(a,b). Another nucleophilic substitution were carried with adipoyl chloride to form polyimide chloride 3(a,b). Treatment of 3(a,b) with hydrazine hydrate afforded acid hydrazide polyimide 4(a,b), which upon cyclocondensation with carbon disulfide gave the target heterocyclic polyimide. The synthesized compounds were identified by spectroscopic methods: FT-IR, 1H-NMR and 13C-NMR.

    This study identified the genus Coelastrella Chodat, 1922 which was isolated from a sediment sample taken from the Tigris river in Baghdad Governorate, Iraq. The alga was isolated and cultured in modified Chu 10 media and the morphological features of the isolated algae were observed in light microscopy (LM); it showed some characteristic features of this genus, such as its ellipsoidal or lemon- shaped cells, a visible pyrenoid and the chloroplast parietal. To ensure correct identification of the isolated alga, a molecular analysis using 18S rRNA gene and DNA sequencing revealed a match with C. terrestris (Reisigl) Hedewald & N. Hanagata 2002. This species is a new record in Iraq

Copper oxide (CuO) nanoparticles were synthesized through the thermal decomposition of a copper(II) Schiff-base complex. The complex was formed by reacting cupric acetate with a Schiff base in a 2:1 metal-to-ligand ratio. The Schiff base itself was synthesized via the condensation of benzidine and 2-hydroxybenzaldehyde in the presence of glacial acetic acid. This newly synthesized symmetric Schiff base served as the ligand for the Cu(II) metal ion complex. The ligand and its complex were characterized using several spectroscopic methods, including FTIR, UV-vis, 1H-NMR, 13C-NMR, CHNS, and AAS, along with TGA, molar conductivity and magnetic susceptibility measurements. The CuO nanoparticles were produced by thermally decomposing the