Effect of the twisted alignment on the liquid crystal wave-front corrector

The effect of twisted alignment on the phase modulation of a liquid crystal wave-front corrector was investigated. First, the effect of twisted alignment is discussed in terms of the modulation principle of the liquid crystal molecule. Only partial incident light can be modulated because of the effect of the twisted alignment. Other unmodulated light will affect the correction accuracy and the resolution of the image. The blazed grating method is proposed to solve this problem. Adaptive correction was performed without the blazed grating method and the correction results are poor. A similar adaptive correction experiment was performed with the blazed grating method and a better correction result is obtained. The residual averaged wave-front errors are PV = 0.101λ and RMS = 0.015λ and a resolvable image is obtained.     

On the Spaltenstein correspondence

In the article [Spa1], N. Spaltenstein has established a bijection between the irreducible components of _χ, the space of full flags fixed by a nilpotent element χ ? M(n, k), where k is an algebraically closed field, and the standard tableaux associated to the Young diagram of χ. In this present work we determine, when χ is of hook type, for each irreducible component X of _χ, the unique Schubert cell _X of the full flag manifold = (V) (where V is vector space of dimension n over k), such that X ∩ _X is a dense subspace in X. This result will allow us to optimize the computation of _χ and when k = is the complex field, to see that the graph resolution of the partition (2, 1, …, 1) of n is related to the Dynkin diagram of sl(n, ).     

1H-1H dipolar couplings provide a unique probe of RNA backbone structure

A NMR method is described that permits simultaneous measurement of the geminal 2JH1H2 + 2DH1H2 splitting and the sum of the 1JCH1 + 1DCH1 + 1JCH2 + 1DCH2 couplings for methylene groups, where 2DH1H2 and 1DCH are residual dipolar couplings, occurring when molecules are weakly oriented relative to the magnetic field. By suppressing either the upfield or downfield half of the 1H-1H geminal doublet, the experiment yields improved resolution relative to regular two-dimensional 1H-13C correlation spectra, making it applicable to systems of considerable complexity. The method is demonstrated for measurement of all 2DH5'H5' couplings in a 24-nucleotide 13C-enriched RNA stem loop structure, weakly aligned in liquid crystalline Pf1. The method is equally applicable to methylene groups in 13C-labeled proteins and to natural abundance samples of smaller molecules.     

Matricial norms

A generalization of the concept of matrix norm is investigated. It is defined to be a mapping from the algebra of complexn × n matrices into the set of nonnegativek × k matrices and which satisfies certain axioms.Taken from the dissertation submitted to the Faculty of the Polytechnic Institute of Brooklyn in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Mathematics), 1969.     

Microscopic approaches to liquid nitromethane detonation properties

In this paper, thermodynamic and chemical properties of nitromethane are investigated using microscopic simulations. The Hugoniot curve of the inert explosive is computed using Monte Carlo simulations with a modified version of the adaptative Erpenbeck equation of state and a recently developed intermolecular potential. Molecular dynamic simulations of nitromethane decomposition have been performed using a reactive potential, allowing the calculation of kinetic rate constants and activation energies. Finally, the Crussard curve of detonation products as well as thermodynamic properties at the Chapman-Jouguet (CJ) point are computed using reactive ensemble Monte Carlo simulations. Results are in good agreement with both thermochemical calculations and experimental measurements.     

On the spread of matrices and polynomials

The spread of a matrix (polynomial) is defined as the maximum distance between two of its eigenvalues (zeros). In this note upper bounds are found for the spread of matrices and polynomials.     

On-line monitoring of composite nanoparticles synthesized in a pre-industrial laser pyrolysis reactor using Laser-Induced Breakdown Spectroscopy

Laser-Induced Breakdown Spectroscopy (LIBS) was employed for on-line and real time process monitoring during nanoparticle production by laser pyrolysis. Laser pyrolysis has proved to be a reliable and versatile method for nanoparticle production. However, an on-line and real time monitoring system could greatly enhance the process optimization and accordingly improve its performances. For this purpose, experiments aiming at demonstrating the feasibility of an on-line monitoring system for silicon carbide nanoparticle production using the LIBS technique were carried out. Nanosecond laser pulses were focused into a cell through which part of the nanoparticle flux diverted from the production process was flowed for LIBS analysis purposes. The nanoparticles were vaporized within the laser-induced plasma created in argon used as background gas in the process. Temporally-resolved emission spectroscopy measurements were performed in order to monitor nanoparticle stoichiometry. Promising results were obtained and on-line Si/C_x stoichiometry was successfully observed. These results put forward the possibility of real time correction of the nanoparticle stoichiometry during the production process.     

Anisotropic united-atoms (AUA) potential for alcohols

An anisotropic united-atom (AUA4) intermolecular potential has been derived for the family of alkanols by first optimizing a set of charges to reproduce the electrostatic potential of the isolated molecules of methanol and ethanol and then by adjusting the parameters of the OH group to fit selected equilibrium properties. In particular, the proposed potential includes additional extra-atomic charges in order to improve the matching to the electrostatic field. Gibbs ensemble Monte Carlo simulations were performed to determine the phase equilibria, while the critical region was explored by means of grand canonical Monte Carlo simulations combined with histogram reweighting techniques. In order to increase the transferability of the model, only the parameters of the Lennard-Jones OH group have been fitted, the parameters of the other AUA groups are taken from previous works. Nevertheless, a good level of agreement was obtained for all compounds considered in this work. In particular, excellent results were obtained for the Henry constants calculation of different gases in alkanols.     

The variation of the eigenvalues of a real symmetric tridiagonal matrix upon the variation of some of its elements

Separation, monotonicity, and growth rate theorems are obtained for the eigenvalues of a real symmetric tridiagonal matrix when some of its elements are varying.