Some dynamical properties of a two-dimensional Wigner crystal

Results for the static part of the ground state energy of the square and hexagonal two-dimensional Wigner lattices are given. The hexagonal lattice has the lower energy. Phonon dispersion curves and the vibrational zeropoint energy are calculated for the hexagonal lattice. The dielectric susceptibility tensor of a two-dimensional Wigner crystal χ_αβ(q) has been determined in the long wavelength limit in the presence of a static magnetic field perpendicular to the crystal, and explicit expressions have been obtained for the hexagonal lattice. Applying the analysis developed by Chiu and Quinn, the results for the susceptibility have been used to obtain the dispersion relation for the plasma oscillations in the electron crystal on the assumption that the crystal is embedded in a dielectric medium. The dispersion curves have been calculated for differing magnitudes of the applied magnetic field.     

On the existence of oscillatory solutions to nonlinear differential equations

Summary A general change of variable technique is combined with appropriate energy functions to show the existence of oscillatory solutions to nonlinear ordinary second order differential equations. Entrata in Redazione il 21 marzo 1974. Research supported by National Research Council of Canada grants NRC-A-7673 and NRC-A-7197 and Defence Research Board of Canada grand DRB-9540-28.     

Probing local environments in paramagnetic europium-substituted Keggin solids by 31P magic angle spinning NMR spectroscopy

Paramagnetic Eu-substituted Keggin oxopolytungstates crystallize in different forms, determined by the nature of the counterions. The crystal packing is in turn responsible for the variations in the geometry of paramagnetic Eu sites with respect to the anion core. We probed the paramagnetic environments in a series of Eu-substituted Keggin solids, by 31P magic angle spinning NMR spectroscopy. 31P spinning sideband envelopes are dominated by the electron-nuclear dipolar interaction. For the compounds under investigation, both the magnitude and the asymmetry parameter of the electron-nuclear dipolar coupling tensor are sensitive to the mutual arrangements of paramagnetic Eu sites in the crystal lattice. and also report on the stoichiometry of the anion. The electron-nuclear dipolar coupling tensors were calculated from the crystallographic coordinates and the experimentally determined effective magnetic moments, assuming a point dipole approximation. The computed tensors are in very good agreement with the experimental spectra. Furthermore, the P-Eu distance estimates, accurate to within 0.06-0.12 A, can be obtained directly from the magnitude of the electron-nuclear dipolar coupling. This work demonstrates that 31P MAS NMR spectroscopy is a useful probe for investigating local environments in paramagnetic Keggin solids.     

Existence and Uniqueness Theorem of the Solution to a Class of Nonlinear Nabla Fractional Difference System with a Time Delay

In this paper, we investigate an existence and uniqueness theorem of the solution to a class of nonlinear nabla fractional difference system with a time delay. More precisely, observing \(\nu (t-k)^{\overline{\nu -1}}\le {t^{\bar{\nu }}}\), we get the evaluation of \(\nabla _{a+k}^{-\nu } ||z(t-k)||\), which allows us to apply the generalized Gronwall’s inequality for the solutions of nonlinear nabla fractional difference system. The theorems we establish fill the gaps in some existing papers.     

Emission from the working and counter electrodes under co-reactant electrochemiluminescence conditions

We present a new approach to explore the potential-dependent multi-colour co-reactant electrochemiluminescence (ECL) from multiple luminophores. The potentials at both the working and counter electrodes, the current between these electrodes, and the emission over cyclic voltammetric scans were simultaneously measured for the ECL reaction of Ir(ppy)₃ and either [Ru(bpy)₃]²⁺ or [Ir(df-ppy)₂(ptb)]⁺, with tri-n-propylamine as the co-reactant. The counter electrode potential was monitored by adding a differential electrometer module to the potentiostat. Plotting the data against the applied working electrode potential and against time provided complementary depictions of their relationships. Photographs of the ECL at the surface of the two electrodes were taken to confirm the source of the emissions. This provided a new understanding of these multifaceted ECL systems, including the nature of the counter electrode potential and the possibility of eliciting ECL at this electrode, a mechanism-based rationalisation of the interactions of different metal-complex luminophores, and a previously unknown ECL pathway for the Ir(ppy)₃ complex at negative potentials that was observed even in the absence of the co-reactant.

Exploration of potential-dependent, multi-colour co-reactant electrochemiluminescence from multiple luminophores at the working and counter electrodes reveals new pathways to emission.     

Gas Chromatographic-mass Spectrometric Analysis Of Methaqualone,Phendimetrazine And Phenmetrazine

Gas chromatographic - mass spectrometric techniques are gaining acceptance as a tool for drug identification. Standard techniques for the analysis of street drugs are still based upon infrared and ultraviolet spetra in conjunction with specific chemical test. These standard methods are adequate for the identification of a majority of confiscated drugs; but due to the increasing diversification of street drugs, these methods are becoming less conclusive.