Spectral factorization of rectangular rational matrix functions with application to discrete Wiener-Hopf equations

The properties of a discrete Wiener-Hopf equation are closely related to the factorization of the symbol of the equation. We give a necessary and sufficient condition for existence of a canonical Wiener-Hopf factorization of a possibly nonregular rational matrix function W relative to a contour which is a positively oriented boundary of a region in the finite complex plane. The condition involves decomposition of the state space in a minimal realization of W and, if it is satisfied, we give explicit formulas for the factors. The results are generalized by means of centered realizations to arbitrary rational matrix functions. The proposed approach can be used to solve discrete Wiener-Hopf equations whose symbols are rational matrix functions which admit canonical factorization relative to the unit circle.     

Differentiation of stereoisomers with electron impact mass spectrometry: (E)- and (Z)-α-hydroxyoximes

The electron impact mass spectra of 5,8-diethyl-7-hydroxydodecan-6-one (Z)-oxime and (E)-oxime provide a basis for distinguishing these stereoisomers.     

Ideal gas in a box — a numerical study

A numerical study of the ideal monoatomic gas in a rectangular box is presented. The spatial distribution of temperature, density, pressure and chemical potential is studied in detail with and without the presence of gravitational forces. Some conclusions are drawn regarding the importance of the particle-wall interaction.     

HPLC analysis of aliphatic sulfonate surfactants using ion-pair detection

A method was developed for the analysis of a number of surfactants which contained no UV-chromophores, using RP-HPLC with Indirect Photometric Detection, IPD. Pyridinium salts such as N-methylpyridinium iodide, N-methyl-2,2'-dipyridinium iodide and N,N'-dimethyl-2,2'-dipyridinium diiodide, were used as the visualization reagents, forming ion-pair complexes with the sulfonate surfactants. This allowed ordinary UV-detection. N-methylpyridinium iodide proved to be a suitable reagent, both with respect to ease of preparation and response. The eluents consisted of mixtures of acetonitrile and water, being 0.1 - 0.25 mM with respect to pyridinium salt. The method was sensitive and exhibited good signal to noise ratios, as well as linear responses over a wide concentration range. All of the analyzed surfactants were separated, including the diastereomeric forms of some of the surfactants.     

Concurrence of mixed bipartite quantum states in arbitrary dimensions

We derive a lower bound for the concurrence of mixed bipartite quantum states, valid in arbitrary dimensions. As a corollary, a weaker, purely algebraic estimate is found, which detects mixed entangled states with a positive partial transpose.     

Measurement of the flux of ultrahigh energy cosmic rays from monocular observations by the High Resolution Fly's Eye experiment

We have measured the cosmic ray spectrum above 10(17.2) eV using the two air-fluorescence detectors of the High Resolution Fly's Eye observatory operating in monocular mode. We describe the detector, phototube, and atmospheric calibrations, as well as the analysis techniques for the two detectors. We fit the spectrum to a model consisting of galactic and extragalactic sources.     

Photoreactions of 3-diazo-3H-benzofuran-2-one; dimerization and hydrolysis of its primary photoproduct, a quinonoid cumulenone: a study by time-resolved optical and infrared spectroscopy

Light-induced deazotization of 3-diazo-3H-benzofuran-2-one (1) in solution is accompanied by facile (CO)-O bond cleavage yielding 6-(oxoethenylidene)-2,4-cyclohexadien-1-one (3), which appears with a rise time of 28 ps. The expected Wolff-rearrangement product, 7-oxabicyclo[4.2.0]octa-1,3,5-trien-8-ylidenemethanone (4), is not formed. The efficient light-induced formation of the quinonoid cumulenone 3 opens the way to determine the reactivity of a cumulenone in solution. The reaction kinetics of 3 were monitored by nanosecond flash photolysis with optical (lambda(max) approximately 460 nm) as well as Raman (1526 cm(-1)) and IR detection (2050 cm(-)(1)). Remarkably, the reactivity of 3 is that expected from its valence isomer, the cyclic carbene 3H-benzofuran-2-one-3-ylidene, 2. In aqueous solution, acid-catalyzed addition of water forms the lactone 3-hydroxy-3H-benzofuran-2-one (5). The reaction is initiated by protonation of the cumulenone on its beta-carbon atom. In hexane, cumulenone 3 dimerizes to isoxindigo ((E)-[3,3']bibenzofuranylidene-2,2'-dione, 7), coumestan (6H-benzofuro[3,2-c][1]benzopyran-6-one, 8), and a small amount of dibenzonaphthyrone ([1]benzopyrano[4,3-][1]benzopyran-5,11-dione, 9) at a nearly diffusion-controlled rate. Ab initio calculations (G3) are consistent with the observed data. Carbene 2 is predicted to have a singlet ground state, which undergoes very facile, strongly exothermic (irreversible) ring opening to the cumulenone 3. The calculated barrier to formation of 4 (Wolff-rearrangement) is prohibitive. DFT calculations indicate that protonation of 3 on the beta-carbon is accompanied by cyclization to the protonated carbene 2H(+), and that dimerization of 3 to 7 and 9 takes place in a single step with negligible activation energy.     

A new synthesis of four diastereoisomeric 2,6-dideoxy-dl-hexoses

The synthesis of four diastereoisomeric 2,6-dideoxy-DL-hexoses from butyl E 2,3,4-trideoxy-aldehydo-DL-hex-2-enuronate (2) is described. The aldehyde 2 treated with MeMgBr affords a mixture of diastereoisomeric diols 6, which after hydroxylation and Ruff degradation gives 2,6-dideoxy-DL-hexoses 13,14, 15 and 16.