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     

Aerobic alcohol oxidation catalyzed by a new, oxygen-bridged heterometallic compound [PPh4][Ru(N)Me2(μ2-O)2Pd((−)-sparteine)]

The reaction between the new hydroxy compound [PPh₄][Ru(N)(OH)₂Me₂] and Pd(OSiMe₃)₂((−)-sparteine) produces (Me₃Si)₂O, H₂O and a new heterobimetallic compound [PPh₄][Ru(N)Me₂(μ₂-O)₂Pd((−)-sparteine)] in good yield. The Ru/Pd bimetallic compound catalyzes the oxidation of aryl and allyl alcohols to the corresponding carbonyl compound in air and the rearrangement of allylic alcohols unsaturated aldehydes. It also oxidizes PPh₃ to O-PPh₃ under O₂.     

The equilibrium properties and folding kinetics of an all-atom Go model of the Trp-cage

The ultrafast-folding 20-residue Trp-cage protein is quickly becoming a new benchmark for molecular dynamics studies. Already several all-atom simulations have probed its equilibrium and kinetic properties. In this work an all-atom Go model is used to accurately represent the side-chain packing and native atomic contacts of the Trp-cage. The model reproduces the hallmark thermodynamics cooperativity of small proteins. Folding simulations observe that in the fast-folding dominant pathway, partial alpha-helical structure forms before hydrophobic core collapse. In the slow-folding secondary pathway, partial core collapse occurs before helical structure. The slow-folding rate of the secondary pathway is attributed to the loss of side-chain rotational freedom, due to the early core collapse, which impedes the helix formation. A major finding is the observation of a low-temperature kinetic intermediate stabilized by a salt bridge between residues Asp-9 and Arg-16. Similar observations [R. Zhou, Proc. Natl. Acad. Sci. U.S.A. 100, 13280 (2003)] were reported in a recent study using an all-atom model of the Trp-cage in explicit water, in which the salt-bridge stabilized intermediate was hypothesized to be the origin of the ultrafast-folding mechanism. A theoretical mutation that eliminates the Asp-9-Arg-16 salt bridge, but leaves the residues intact, is performed. Folding simulations of the mutant Trp-cage observe a two-state free-energy landscape with no kinetic intermediate and a significant decrease in the folding rate, in support of the hypothesis.     

The remarkable ability of lithium ion to reverse the stereoselectivity in the conjugate addition of Li[BuCuI] to a chiral N-crotonyl-2-oxazolidinone

[reaction: see text] The influence of lithium ions on the conjugate addition of the monoorganocuprate reagent, Li[BuCuI], to a chiral crotonate has been investigated. The results show that iodotrimethylsilane (TMSI) is crucial for the asymmetric conjugate addition of the copper reagent, but only in THF or when 12-crown-4 is used. The reaction is thought not to involve any halosilane in any critical steps in the organocopper mechanisms conducted in Et(2)O.     

Synthesis of some dibenzodiazepinone derivatives as potent and m2-selective antimuscarinic compounds

Two series of 5-[[4-[4-(dialkylamino)butyl]-l-cyclohexyl]acetyl], and 5-[(dialkylamino)acyl]-10,11-dihydro-5H- dibenzo[b,e][1,4]diazepin-11-ones were synthesized as potential m2-selective ligands 1,2. Their affinity and selectivity for the muscarinic cholinergic receptor m-AChR subtypes were determined. Replacing a nitrogen with CH in the piperidine ring of 5-[[4-[4-(dialkylamino)butyl]-l-piperidinyl]acetyl]-10,11-dihydro-5H-dibenzo-[b,e][1,4]diazepin-11-ones 3 significantly altered the affinity and selectivity to the muscarinic receptor subtypes.     

Propagating transverse electric and transverse magnetic modes in liquid crystal-clad planar waveguides

ABSTRACT

In a planar dielectric waveguide, weak confinement of a propagating mode in a high index core leads to a measurable evanescent interaction with the cladding. In this work, we study the effect of a reorientable anisotropic cladding on the behaviour of Transverse Electric (TE) and Transverse Magnetic (TM) mode polarisations using a liquid crystal (LC)-clad waveguide architecture. The polarised evanescent field of a guided mode interacts with a voltage-tunable birefringent LC cladding to deflect an out-coupled beam. Experimental measurements are coupled with a theoretical framework and show good consistency with simulation results. We isolate the effect of mode confinement by changing the thickness of the high index core. Interactions between the LC index ellipsoid and the mode polarisation are probed by changing the initial alignment of the LC. Finally, we examine the difference in deflection between TE and TM modes, which incorporates both a change in mode confinement and a difference in LC index components.     

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.     

Structure of strongly interacting polyelectrolyte diblock copolymer micelles

The structure of spherical micelles of the diblock poly(styrene-block-acrylic acid) [PS-b-PA] copolymer in water was investigated up to concentrations where the polyelectrolyte coronal layers have to shrink and/or interpenetrate in order to accommodate the micelles in the increasingly crowded volume. We obtained the partial structure factors pertaining to the core and corona density correlations with small angle neutron scattering and contrast matching in the water. The counterion structure factor was obtained with small angle x-ray scattering (SAXS) with a synchrotron radiation source. Furthermore, we have measured the flow curves and dynamic visco-elastic moduli. The functionality of the micelles is fixed with a 9 nm diameter PS core and a corona formed by around 100 PA arms. As shown by the SAXS intensities, the counterions are distributed in the coronal layer with the same density profile as the corona forming segments. Irrespective ionic strength and micelle charge, the corona shrinks with increasing packing fraction. At high charge and minimal screening conditions, the polyelectrolyte chains remain almost fully stretched and they interdigitate once the volume fraction exceeds the critical value 0.53+/-0.02. Interpenetration of the polyelectrolyte brushes also controls the fluid rheology: The viscosity increases by three orders of magnitude and the parallel frequency scaling behavior of the dynamic moduli suggests the formation of a physical gel. In excess salt, the coronal layers are less extended and they do not interpenetrate in the present concentration range.     

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.