Isatin (1H-indole-2, 3-dione) and its analogs are an important class of heterocyclic compounds. N-benzyl isatins and Schiff bases of isatin analogs have been reported to demonstrate a variety of biological activities. This work illustrates the synthesis of new N-benzylisatin Schiff bases and studies their biological activity. Firstly, Isatin and its analogs; 5-methoxyisatin, 5-fluoroisatin reacted with benzyl iodide to obtain N-benzylated derivatives of isatins 2 (ac). Secondly, these compounds were reacted with different amines (sulphanilamide and 4-methyl sulphonyl aniline) separately, to obtain Schiff bases compounds 3 (ac) and 4 (ac), respectively. The synthesized compounds were characterized by using FT-IR and 1HNMR spectroscopy. The s

The effect of the tensor term in the Skyrme interaction has been estimated in calculating the static and dynamic nuclear properties in sd and fp-shell model spaces nuclei. The nuclear shell gaps have been studied with different Skyrme parameterizations; Skxta and Skxtb with tensor interaction, SkX, SkM, and SLy4 without tensor interaction, and Skxcsb with consideration of the effect of charge symmetry breaking. We have examined the stability of N = 28 for 42Si and 48Ca. The results showed that the disappearance of the magicity occurs in the shell closure of 42Si. Furthermore, excitation energy, quadrupole deformation, neutron separation energy, pairing energy, and density profile have also been calculated. Quadrupole deformation indicates a

The nonlinear refractive (NLR) index and third order susceptibility (X3) of carbon quantum dots (CQDs) have been studied using two laser wavelengths (473 and 532 nm). The z-scan technique was used to examine the nonlinearity. Results showed that all concentrations have negative NLR indices in the order of 10−10 cm2/W at two laser wavelengths. Moreover, the nonlinearity of CQDs was improved by increasing the concentration of CQDs. The highest value of third order susceptibility was found to be 3.32*10−8 (esu) for CQDs with a concentration of 70 mA at 473 nm wavelength.

In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent method has null phase-lag and zero dissipation properties. The phase-lag or dispersion error is the angle between the real solution and the approximate solution. While the dissipation is the distance of the numerical solution from the basic periodic solution. Many of problems are tested over a long interval, and the numerical results have shown that the present method is more precise than the 4(5) Runge-Kutta-Fehlberg method.

A condense study was done to compare between the ordinary estimators. In particular the maximum likelihood estimator and the robust estimator, to estimate the parameters of the mixed model of order one, namely ARMA(1,1) model.

Simulation study was done for a varieties the model.  using: small, moderate and large sample sizes, were some new results were obtained. MAPE was used as a statistical criterion for comparison.

In this paper, we characterize normal composition operators induced by holomorphic self-map , when and .Moreover, we study other related classes of operators, and then we generalize these results to polynomials of degree n.