Synthesis of 5-alkylated barbituric acids and 3-alkylated indoles via microwave-assisted three-component reactions in solvent-free conditions using Hantzsch 1,4-dihydropyridines as reducing agents

Reaction of barbituric acids with aldehydes and dihydropyridines in one pot under microwave (MW) irradiation in the absence of solvent, affords 55–82% of the 5-benzylated barbituric acids. Use of alkyl nitriles or barbituric acids with indole-3-aldehyde and dihydropyridine (DHP) afforded 3-alkylated indoles in 57–76 % yield. In each case DHPs are converted to pyridines.     

First example of a Cu(I)-(η2-O,O)nitrite complex derived from Cu(II)-nitrosyl

Copper(II) complex, 1, of the bidentate ligand, L [L = bis(2-ethyl-4-methyl-imidazol-5yl)methane] has been synthesized and structurally characterized. Addition of nitric oxide gas to a degassed acetonitrile solution of 1 yielded the corresponding copper(ii)-nitrosyl complex, 2. In acetonitrile, complex 2 on reaction with water afforded the corresponding copper(I)-nitrite complex, 3. Single crystal structure of complex 3 reveals the bidentate nitrite (η(2)-O,O) bonding. This is the first example of a structurally characterized Cu(I)-(η(2)-O,O)nitrite complex with N-donor ligand. The sequence of the formation of these complexes is just the reverse of the key steps of the postulated nitrite reduction cycle by CuNiRs.     

On weighted directed graphs

The study of a mixed graph and its Laplacian matrix have gained quite a bit of interest among the researchers. Mixed graphs are very important for the study of graph theory as they provide a setup where one can have directed and undirected edges in the graph. In this article we present a more general structure, namely the weighted directed graphs and supply appropriate generalizations of several existing results for mixed graphs related to singularity of the corresponding Laplacian matrix. We also prove many new combinatorial results relating the Laplacian matrix and the graph structure.     

Direct synthesis of aqueous quantum dots through 4,4'-bipyridine-based twin ligand strategy

We report a new class of derivatized 4,4'-bipyridinium ligands for use in synthesizing highly fluorescent, extremely stable, water-soluble CdSe and CdTe quantum dots (QDs) for bioconjugation. We employed an evaporation-condensation technique, also known as solvated metal atom dispersion (SMAD), followed by a digestive ripening procedure. This method has been used to synthesize both metal nanoparticles and semiconductors in the gram scale with several stabilizing ligands in various solvents. The SMAD technique comprised evaporation condensation and stabilization of CdSe or CdTe in tetrahydrofuran. The as-prepared product was then digestively ripened in both water and dimethyl formamide, leading to narrowing of the particle size distributions. The ligands were synthesized by nucleophilic substitution (S(N)2) reactions using 4,4'-bipyridine as a nucleophile. Confocal microscopy images revealed the orange color of the nanocrystalline QDs with diameters of ~5 nm. The size has been confirmed by using transmission electron microscopy. As a part of our strategy, 85% of the 4,4'-bipyridinium salt was synthesized as propionic acid derivative and used to both stabilize the QDs in water and label basic amino acids and different biomarkers utilizing the carboxylic acid functional group. Fifteen percent of the 4,4'-bipyridinium salt was synthesized as N-propyl maleimide and used as a second ligand to label any protein containing the amino acid cysteine by means of a 1,4-Michael addition.     

Possibility of weakly charged nonlinear solitary dust clouds near the continuum threshold of dust population in a quasi-neutral dusty plasma

Considering the Boltzmann response of the plasma ions and electrons and inertial dynamics of the charged dust grains, the possibility of very weak compressive soliton near the continuum limit of the dust population has been inferred. It is concluded that the behaviour of such coherent structures could be well described by the numerical analysis of the derived nonlinear classical energy integral equation for bounded solutions. These seem to be higher order dispersive structures within acoustic limit of the nonlinear turbulence. It is observed that the dust density enhancement beyond the continuum threshold causes regular increment in width and amplitude of the soliton structures. It is found that the soliton amplitude sensitively depends on the massive impurity’s population. These coherent structures could be visualized as weakly charged solitary dust clouds of finite extension (∼ plasma Debye length) within Boltzmann environment of plasma particles in their local surroundings. The seeding mechanism of such clouds may be attributed to some plasma instabilities driven by either internal or external free energy sources. Numerical analysis of the problem concludes that the experimental observations of such clouds could be possible in low density plasma regime. It is deduced that for plasma density ∼ 10⁶ cm^-3 at temperatures of a few electron volts and for micron to l0nm sized dust grains, the observation of such structures could be possible within wide range variability of the dust population density.     

Exactness of the cordes condition of the Hölder property for the gradient of nondivergent elliptic systems

We give an example of a nondivergent elliptic system showing that the classical Cordes condition of the Hölder property for the gradient of solution of a nondivergent elliptic equation is exact if properly extended onto systems.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 2, pp. 292–294, February, 1995.     

Partial applicability of Moser's method to nonlinear elliptic systems

We consider nonlinear elliptic systems of divergent-type second-order partial differential equations with solutionsu W _p ¹ . It is proved thatDu L _q with someq (p; +) and it is explicitly shown howq depends on the ellipticity modulus of the system. Some conditions on the ellipticity modulus are obtained under which the solutions satisfy the Hölder conditions and the Liouville theorem holds.Translated fromMatematicheskie Zametki, Vol. 58, No. 4, pp. 547–557, October, 1995.