Synthesis and characterization of stable organosols of silver nanoparticles by electrochemical dissolution of silver in DMSO

Stable organosols of silver nanoparticles (AgNPs) without any capping agents have been synthesized by an electrochemical dissolution of a sacrificing silver electrode in dimethyl sulfoxide (DMSO). The peak at 425 +/- 5 nm observed in the UV-vis spectra was attributed to the surface plasmon resonance for silver. The formation of nanoparticles of silver was confirmed by X-ray diffraction analysis (XRD). In TEM, three ranges of particle size were observed, namely, 3.75 +/- 0.8, 6.25 +/- 0.5, and 9.25 +/- 0.3 nm. The correlation among these sizes was explained by a new model based on a droplet coalition. Based on that, sizes correlation fits very well in the empirical formula 5d(1)(3)n' + (3 - n')d(2)(3) = d(3)(3) where d(1), d(2), and d(3) are three sizes of particles and n' is an integer having values 0, 1, 2, 3, .... The sols prepared in DMSO were stable against flocculation for months. An unusual solution stability without any capping agents was attributed to the formation of Ag(I)DMSO complex on particle surface, which was confirmed by FTIR, fluorescence spectroscopy, and thermal analysis.     

Isospectrality of conventional and new extended potentials,second-order supersymmetry and role of $$ \mathcal{P}\mathcal{T} $$ symmetry

We develop a systematic approach to construct novel completely solvable rational potentials. Second-order supersymmetric quantum mechanics dictates the latter to be isospectral to some well-studied quantum systems. $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} symmetry may facilitate reconciling our approach to the requirement that the rationally extended potentials be singularity free. Some examples are shown.     

Optical rotatory dispersion of rare earth crystal

The ORD spectrum of optically active single crystal of praseodymium oxydiacetate has been studied in the visible range at 77 K. The results have been compared with those obtained in the cases of transition metal complexes and other RE complexes with optically active ligands, and correlated with the site symmetry of the RE ion in the crystal. The optical activity has been related to the magnetic dipole strengths of the transitions.     

Molybdenum(VI)-peroxo complex catalyzed oxidation of alkylbenzenes with hydrogen peroxide

The molybdenum(VI) peroxo complex 1, synthesized from the reaction of MoO₃ with H₂O₂ and 3,5-dimethylpyrazole (dmpz), selectively oxidizes benzylic C-H bonds of alkylbenzenes to the corresponding alcohols and ketones in moderate to good yields in the presence of H₂O₂ in acetonitrile under reflux (ca. 80°C).     

A proof of Howard's conjecture in homogeneous parallel shear flows—II: Limitations of Fjortoft's necessary instability criterion

The present paper on the linear instability of nonviscous homogeneous parallel shear flows mathematically demonstrates the correctness of Howard's [4] prediction, for a class of velocity distributions specified by a monotone functionU of the altitudey and a single point of inflexion in the domain of flow, by showing not only the existence of a critical wave numberk _c>0 but also deriving an explicit expression for it, beyond which for all wave numbers the manifesting perturbations attain stability. An exciting conclusion to which the above result leads to is that the necessary instability criterion of Fjortoft has the seeds of its own destruction in the entire range of wave numbersk>k _c—a result which is not at all evident either from the criterion itself or from its derivation and has thus remained undiscovered ever since Fjortoft enunciated [3].     

A solution to the distribution problems arising in the studies of a two-sex population process

Given a population of two sexes, the birth rate of one sex of which depends upon the population size of the other, it is very difficult to find an explicit expression for the probability distribution of the former. In this paper we have explicitly found the probability generating function of the joint distribution from which individual probability distributions and, in particular, moments of all orders in each case can be obtained in principle. As an example, using this probability generating function we have worked out explicitly the first and second order moments of the male and female populations and the explicit expression for the distribution of the male population in a particular case. This method can be successfully applied for the same purpose in the studies of chemical and biological processes where the synthesis or production of one species depends upon the concentration of another species.     

On the principle of exchange of stabilities in the magnetohydrodynamic simple Bénard problem

The present paper establishes a new result which was long sought after in the field of magnetoconvection, namely, the validity of the principle of exchange of stabilities for the magnetohydrodynamic simple Bénard problem in the regime Qσ₁ ? π² where Q is the Chandrasekhar number and σ₁ is the magnetic Prandtl number. This result is applicable for quite general boundary conditions and provides a natural extension of A. Pellew and R. V. Southwell's (Proc. Roy. Soc. London Ser. A176 (1940), 312–343) result for the simple Bénard problem. A corresponding result for rotatory magnetohydrodynamic simple Bénard problem is also given.