Linear superposition in nonlinear equations

Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of some remarkable new identities involving elliptic functions.     

An efficient one-pot synthesis of novel polysubstituted 4-amino-2,3-dihydropyridines

A convenient and efficient one-pot multi-component synthesis of novel polysubstituted 4-amino-2,3-dihydropyridines from carbonyl compounds, malononitrile and acetonitrile, using indium triflate is reported. Acetonitrile acts both as a solvent as well as a substrate.     

Tuning the Efficiency of Dendritic Nanocarriers using Conformational Constraints

A series of deoxycholic and cholic acid‐derived oligomers were synthesized and their ability to extract hydrophilic dye molecules of different structure, size, and functional groups into nonpolar media was studied. The structure of the dye and “dendritic effect” in the extraction process was examined using absorption spectroscopy and dynamic light scattering (DLS). The efficiency of structurally preorganized oligomers in the aggregation process was evaluated by 1‐anilinonaphthalene‐8‐sulfonic acid (ANS) fluorescence studies. The possible formation of globular structures for higher‐generation molecules was investigated by molecular modeling studies and the results were correlated with the anomaly observed in the extraction process with this molecule. The ability of these molecules for selective extraction of specific dyes from blended colors is also reported.     

Laser Induced Fluorescence of Biochemical for UV LIDAR Application

Laser induced fluorescence spectroscopy in the ultraviolet regime has been used for the detection of biochemical through a fiber coupled CCD detector from a distance of 2 m. The effect of concentration and laser excitation energy on the fluorescence spectra of nicotinamide adenine dinucleotide (NADH) has been investigated. The signature fluorescence peak of NADH was centred about 460 nm. At lower concentration Raman peak centred at 405 nm was also observed. The origin of this peak has been discussed. Detection limit with the proposed set up is found to be 1 ppm.     

Higher order stable generalized finite element method

The generalized finite element method (GFEM) is a Galerkin method, where the trial space is obtained by augmenting the trial space of the standard finite element method (FEM) by non-polynomial functions, called enrichments, that mimic the local behavior of the unknown solution of the underlying variational problem. The GFEM has excellent approximation properties, but its conditioning could be much worse than that of the FEM. However, if the enrichments satisfy certain properties, then the conditioning of the GFEM is not worse than that of the standard FEM, and the GFEM is referred to as the stable GFEM (SGFEM). In this paper, we address the higher order SGFEM that yields higher order convergence and suggest a specific modification of the enrichment function that guarantees the required conditioning, yielding a robust implementation of the higher order SGFEM.     

Isolation, structural, spectral, and thermal studies of imperatorin micro-crystals from Prangos pabularia

Imperatorin (mol. formula = C₁₆H₁₄O₄, mol. mass = 270) micro-crystals were isolated from ethyl acetate extract of the root parts of the plant Prangos pabularia. The composition related structural, spectral, and thermal properties were investigated. All the crystals were found to have single phase with orthorhombic structure. UV–Visible spectrum showed both direct forbidden transition and indirect allowed transition. The calculated optical band gaps (E _g) were 3.64 and 3.70 eV for direct forbidden and indirect allowed transitions, respectively. From the thermal studies of these crystals, melting point, stability, and other relevant information was obtained, ensuring the suitability of the material for application in any device where the crystals may have to withstand this range of temperature.     

Mechanistic approach for expeditious and solvent-free synthesis of α-hydroxy phosphonates using potassium phosphate as catalyst

An extremely simple, high yielding, highly rapid and solvent-free protocol has been described for hydrophosphylation of aldehydes using potassium phosphate as catalyst. Easy commercial availability of the reusable catalyst, operational simplicity at ambient temperature and avoidance of conventional work-up as well as purification procedure makes this solvent-free protocol a near-ideal synthesis.     

Direct C–H amination of benzothiazoles by magnetically recyclable CuFe2O4 nanoparticles under ligand-free conditions

A simple and highly practical method for the synthesis of 2-N-substituted benzothiazoles has been developed by using nano copper ferrite as a magnetically separable, recyclable catalyst. The present tandem process allows to get access to a wide range of 2-N-substituted benzothiazoles in good to excellent yields by the reaction of benzothiazole with nitrogen nucleophiles in the presence of Cs₂CO₃ as a base. The nano CuFe₂O₄ could be recovered and reused with no significant loss of catalytic activity.     

Catalytic reduction of organic dyes at gold nanoparticles impregnated silica materials: influence of functional groups and surfactants

Gold nanoparticles (Au NPs) in three different silica based sol–gel matrixes with and without surfactants are prepared. They are characterized by UV–vis absorbance and transmission electron microscopic (TEM) studies. The size and shape of Au NPs varied with the organo-functional group present in the sol–gel matrix. In the presence of mercaptopropyl functionalized organo-silica, large sized (200–280 nm) spherical Au NPs are formed whereas in the presence of aminopropyl functionalized organo-silica small sized (5–15 nm) Au NPs are formed inside the tube like organo-silica. Further, it is found that Au NPs act as efficient catalyst for the reduction of organic dyes. The catalytic rate constant is evaluated from the decrease in absorbance of the dye molecules. Presence of cationic or anionic surfactants greatly influences the catalytic reaction. The other factors like hydrophobicity of the organic dyes, complex formation of the dyes with anionic surfactants, repulsion between dyes and cationic surfactant, adsorption of dyes on the Au NPs also play important role on the reaction rate.