The discussion in this paper gives several theorems and lemmas on the Sums of Squares of  consecutive Carol Numbers. These theorems are proved by using the definition of carol numbers and mathematical induction method. Here the matrix form and the recursive form of sum of squares of  consecutive Carol numbers is also given. The properties of the Carol numbers are also derived.

The aim of the present investigation was to develop a microsponge delivery system of acyclovir to control its release when applied topically thereby reducing dosing frequency and enhancement patient compliance. The microsponges were produced by the oil in oil emulsion solvent diffusion method. The effect of different formulation and process variables such as internal phase volume, polymer type, drug-polymer ratio, stirring speed and stirring duration on microsponge production yield, loading efficiency, particle size and in-vitro drug release was evaluated. The result showed that the microsponge F2 prepared from Eudrajet RS polymer had optimum physical properties regarding the loading efficiency of 99.71_+ 0.7% and product

A

A new series of bases of Schiff (H₂-H₄) derived from phthalic anhydrideweresynthesized. These Schiff bases were prepared by the reaction of different amines (tyrosine methyl ester, phenylalanine methyl ester, and isoniazid) with the phthalimide derived aldehyde with the aid of glacial acetic acid or triethylamine ascatalysts. All the synthesized compounds were characterized by (FT-IR and ¹HNMR) analyses and were in vitro evaluated for their antimicrobial activity against six various kinds of microorganisms. All the synthesized compounds had been screened for their antimicrobial activity against two Gram-positive bacteria “Staph. Aureus, and Bacillus subtilis

Heterocyclic systems, which are essential in medicinal chemistry due to their promising cytotoxic activity, are one of the most important families of organic molecules found in nature or produced in the laboratory. As a result of coupling N-(4-nitrophenyl)-3-oxo-butanamide (3) using thiourea, indole-3-carboxaldehyde, or piperonal, the pyrimidine derivatives (5a and 5b) were produced. Furthermore, pyrimidine 9 was synthesized by reacting thiophene-2-carboxaldehyde with ethyl cyanoacetate and urea with potassium carbonate as a catalyst. The chalcones 11a and 11b were synthesized by reacting equal molar quantities of 1-naphthaldehy

A new Schiff bases ligand 4- ((2-hyolroxy phenylimino) methyl) -2, 6-dimethoxyphenol  derived from condensation of 2- amino phenol with 4-hydroxy -3, 5-dimethoxy benzaldehyde have been synthesized and characterized by  spectroscopy,  spectra, Mass spectrum and elemental microanalysis (C.H.N). Metal Complexes with ions have been also synthesized and characterized spectroscopic methods  spectroscopy, flame atomic absorption, molar conductivity measurements and magnetic susceptibility. These studies indicate that the moler ratio  for the complexes. The complexes  showed characteristics octahedral geometry with the (O,N) ligand coordinated in bidentate mode while with  showed square planer. The enzyme activity of the ligand and i

In the current study, new derivatives were synthesized by reaction of N-hydroxyphthalimide with chloro acetyl chloride in the presence of Et3N as a base to form 1,3-dioxoisoindolin-2-yl 2-chloroacetate (B1), which in turn enters several reactions with different amines where it interacts with primary amines to give 1,3-dioxoisoindolin-2-yl acetate derivatives (B2-B4) in basic medium, in the same way it interacts with these amines but with adding KNCS to form thiourea derivatives (B5-B7). It also reacts with diamines to give bis(azanediyl) derivatives (compounds B8-B10). The prepared derivatives were diagnosed using infrared FTIR and 1HNMR,13CNMR for some derivatives. Compounds B4, B5 and B9 were measured as corrosion inhibitors the inhibitio

Nanoparticles of Pb_1-xCd_xS within the composition of 0≤x≤1 were prepared from the reaction of aqueous solution of cadmium acetate, lead acetate, thiourea, and NaOH by chemical co-precipitation. The prepared samples were characterized by UV-Vis spectroscopy(in the range 300-1100nm) to study the optical properties, AFM and SEM to check the surface morphology(Roughness average and shape) and the particle size. XRD technique was used to determine the crystalline structure, XRD technique was used to determine the purity of the phase and the crystalline structure, The crystalline size average of the nanoparticles have been found to be 20.7, 15.48, 11.9, 11.8, and 13.65 nm for PbS, Pb_0.75Cd_0.25S,

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

Kinetics and mechanism studies of oxidation of some α-amino acids (Proline, Arginine, Alanine) (AA) by N-Bromosuccinimide (NBS) by using conductivity method was carried out. The kinetic study showed that the reaction was first order with respect to NBS and AA. The effect of addition of HClO4 to the reaction was negative on the rate of reaction. The reaction was carried out at different temperatures in which  * * *   , S , G were calculated. The rate of reaction of AA was as follows: Proline > Arginine > Alanine