A Lie theoretic galois theory for the spectral curves of an integrable system: I

In the study of integrable systems of ODE's arising from a Lax pair with a parameter, the constants of the motion occur as spectral curves. The specific curves depend upon the representation of the Lie algebra. In this paper a Galois theory of spectral curves is given that classifies the spectral curves from an integrable system. The spectral curves correspond to conjugacy classes of certain subgroups of the Weyl group for the Lie algebra. The theory is illustrated with the periodic Toda lattice.Partially supported by a Louisiana Education Quality Support Fund grant LEQSF (87-89)-RD-A-8     

Synthesis of two new crown ethers containing selenium and the complexation of one of them with silver and lead

Two new macrocyclic crown ethers containing one or two selenium donor atoms have been prepared. Diselena-18-crown-6 (2) was found to transport silver ions through a methylene chloride bulk membrane at about the same rate as the analogous dithia- (3) and diaza-18-crown-6 (4) compounds and transported lead ions about the same as dithia-18-crown-6 but better than diaza-18-crown-6.     

Metal salt catalyzed carbenoid—XIII: On the mechanisms of cyclopropanation and allylic CH insertions by diazo esters in the presence of olefins and homogeneous copper catalysts

Evidence is presented demonstrating the existence of two paths to the title processes which arise from a common intermediate. A rationale involving catalyzed addition of the diazo compound to the olefin and carbenoid addition to the olefin is proposed. The penultimate intermediate has one new CC bond formed. It is partitioned between products by forming the second CC bond or formation of a hydrocarbenoid allyl complex which collapses to the allylic CH insertion products. Cyclopropanation occurs stereospecifically. The proposed mechanism accounts for the stereospecificity of cyclopropanation, the variance of syn/anti ratios with catalyst concentration when diazoacetic ester is employed and optical inductions with chiral catalysts. The question of whether the alleged carbenoid and/or the penultimate intermediate contain N₂ is not answered although it is felt that a cupro-cyclobutane intermediate is the most probable intermediate before product partitioning.     

Mixed-metal uranium(VI) iodates: hydrothermal syntheses,structures, and reactivity of Rb[UO(2)(CrO(4))(IO(3))(H(2)O)], A(2)[UO(2)(CrO(4))(IO(3))(2)] (A = K,Rb, Cs), and K(2)[UO(2)(MoO(4))(IO(3))(2)

The reactions of the molecular transition metal iodates A[CrO(3)(IO(3))] (A = K, Rb, Cs) with UO(3) under mild hydrothermal conditions provide access to four new, one-dimensional, uranyl chromatoiodates, Rb[UO(2)(CrO(4))(IO(3))(H(2)O)] (1) and A(2)[UO(2)(CrO(4))(IO(3))(2)] (A = K (2), Rb (3), Cs (4)). Under basic conditions, MoO(3), UO(3), and KIO(4) can be reacted to form K(2)[UO(2)(MoO(4))(IO(3))(2)] (5), which is isostructural with 2 and 3. The structure of 1 consists of one-dimensional[UO(2)(CrO(4))(IO(3))(H(2)O)](-) ribbons that contain uranyl moieties bound by bridging chromate and iodate anions as well as a terminal water molecule to create [UO(7)] pentagonal bipyramidal environments around the U(VI) centers. These ribbons are separated from one another by Rb(+) cations. When the iodate content is increased in the hydrothermal reactions, the terminal water molecule is replaced by a monodentate iodate anion to yield 2-4. These ribbons can be further modified by replacing tetrahedral chromate anions with MoO(4)(2)(-) anions to yield isostructural, one-dimensional [UO(2)(MoO(4))(IO(3))(2)](2)(-) ribbons. Crystallographic data: 1, triclinic, space group P(-)1, a = 7.3133(5) A, b = 8.0561(6) A, c = 8.4870(6) A, alpha = 88.740(1) degrees, beta = 87.075(1) degrees, gamma = 71.672(1) degrees, Z = 2; 2, monoclinic, space group P2(1)/c, a = 11.1337(5) A, b = 7.2884(4) A, c = 15.5661(7) A, beta = 107.977(1) degrees, Z = 4; 3, monoclinic, space group P2(1)/c, a = 11.3463(6) A, b = 7.3263(4) A, c = 15.9332(8) A, beta = 108.173(1) degrees, Z = 4; 4, monoclinic, space group P2(1)/n, a = 7.3929(5) A, b = 8.1346(6) A, c = 22.126(2) A, beta = 90.647(1) degrees, Z = 4; 5, monoclinic, space group P2(1)/c, a = 11.3717(6) A, b = 7.2903(4) A, c = 15.7122(8) A, beta = 108.167(1) degrees, Z = 4.     

Intelligibility ratings of continuous discourse: application to hearing aid selection

Twelve normal-hearing subjects rated the intelligibility of 35-s, hearing-aid-processed continuous discourse (CD) passages. Three talkers (two male, one female), four hearing aids, and two signal-to-babble (S/B) ratios were used in a completely crossed design. Research questions concerned: (1) ability of listeners to rate intelligibility, (2) sensitivity of hearing aid rankings were based on intelligibility ratings for three CD passages per instrument, and (3) dependence of hearing aid rankings on (a) S/B ratio, and (b) talker characteristics. Results were: (1) listeners were able to rate intelligibility, (2) rankings based on intelligibility ratings of three CD passages per hearing aid were capable of identifying two superior instruments within a group of four hearing aids that were similar in frequency/gain function, (3) listening in a more difficult S/B ratio substantially decreased the sensitivity of the hearing aid rankings for the female talker but had only minor effects on the rankings for the male talkers, and (4) hearing aid intelligibility rankings were found to be different for different talkers. Applications to hearing aid selection are discussed.     

Esterification of decanoic acid during supercritical fluid extraction employing either methanol-modified carbon dioxide or a methanol trap.

The methylation of decanoic acid during the supercritical fluid extraction process was investigated. It was found that the majority of the methylation occurred not during the extraction, but during the collection step, in the presence of methanol. Increasing dynamic extraction time (and hence collection time) from 0 to 60 min increased acid to ester conversions from 2% to 4%. The addition of HCl as a catalyst to the reaction increased the reaction rate 10-fold, and resulted in 88% conversion to the methyl ester within 30 min, without any detrimental effects on the chromatographic system. Higher collection temperatures appeared to increase conversion, but decreased methyl ester collection efficiency.     

Curvature operators which preserve normal spaces

This paper characterizes the invertible algebraic curvature operators that satisfy the Bianchi identity and also preserve normal spaces to the action of SO(n) on the space of bivectors.     

Identification of the intercalant species in SbCl5-graphite using Mössbauer spectroscopy

¹²¹Sb Mössbauer spectra of SbCl₅-graphite have been obtained. The spectra provide clear evidence for the presence of the acceptor molecular ion SbCl₆^-(Sb⁵⁺ and neutral SbCl₃(Sb³⁺ in the intercalate layers, with weak evidence for neutral intercalated SbCl₅. Lineshape analyses of the Sb³⁺ region of the spectra further indicate that two chemical Sb³⁺ sites fit the data significantly better than one site. We attribute the second Sb³⁺ site to SbCl₄^- and find the concentration ratio [SbCl₄^-]/[SbCl₃] 0.25. Samples prepared by the reaction of graphite with vapor mixtures of SbCl₅ and SbCl₃ were found to exhibit dramatically higher concentrations of SbCl₃ than those samples prepared from a reaction with SbCl₅ alone. This latter result is interesting in view of the fact that the reaction of graphite with SbCl₃ vapor does not lead to an intercalation compound.     

Dynamics of bi-periodic structures

Many structures considered for space applications are bi-periodic in their construction. Bi-periodicity means that two types of structural subassemblies, alternating in one or more directions, make up the structure. To gain insight into the dynamics of bi-periodic space structures a variety of one and two dimensional bi-periodic structures are considered. Results indicate that bands in which natural frequencies lie for periodic structures are further subdivided as a consequence of the bi-periodicity. Analytical solutions for the modes and frequencies of finite length one dimensional bi-periodic structures are obtained for general boundary conditions. A transmission method is developed to simplify the application of boundary conditions. It is found that some modes occur at frequencies which are outside the frequency bands predicted for bi-periodic structures. Two dimensional bi-periodic crossed beam grillage and truss structures are considered in this study. For cases where a separation of variables solution is possible the two dimensional structures exhibit similar properties to the one dimensional bi-periodic structures. Analytical solutions for the one and two dimensional bi-periodic structures considered above lead to a compact solution form similar to that of periodic structures analysis.