On first-order quasi-variational inequalities with integral terms

This paper deals with first-order quasi-variational inequalities with integral terms associated with impulsive and switching control of piecewise-deterministic processes. Two formulations of quasi-variational inequalities are studied, characteristic and viscosity, and the relations between them are discussed. As a tool we apply convex analysis methods.     

Acid-catalyzed Hydrolysis of the cis-[Cr(1,10-phenanthroline)2(O2CO)]+ Ion Studied by the u.v.–vis Stopped Flow Method

The cis-[Cr(phen)₂(O₂CO)]⁺ ion was prepared through the displacement of two molecules of water from the cis-[Cr(phen)₂(OH₂)₂]³⁺ by the bidentate carbonate anion. It underwent two-phase hydrolysis reactions under acidic conditions (0.1 < [H⁺] < 2.7 m) at 5, 10, 15, 20 and 25 °C. Via slow carbonato chelate ring opening (first step k₁^slow) and a second fast decarboxylation(k₂^fast value). The first step was preceded by protonation of the coordinate bidentate carbonate ligand. The second step exhibited no pH dependence, while k₁^slow values increased with acid concentration that suggested the presence of both protonated and deprotonated reactant species. Based on these observations we have proposed a hydrolysis mechanism featuring H₂O-induced ring-opening of the coordinate CO₃²⁻ group in the first step k₁^slow followed by loss of CO₃²⁻ from two intermediates, [Cr(phen)₂(O₂COH)]²⁺ (k₁^slow) and [Cr(phen)₂(OH₂)(O₂COH)]²⁺ (k₂^fast).     

Representing homology classes by locally flat 2-spheres

We prove an existence result for topologically locally flat embeddings of 2-spheres in simply connected 4-manifolds. This topological result is deduced from a splitting theorem for pointed Hermitian modules over a cyclic group ring. A stability result for such modules is also proved. This applies to the isotopy classification of locally flat embeddings.Partially supported by the NSF.     

Rotational spectrum of trans-trans diethyl ether in the ground and three excited vibrational states

We report the results of a comprehensive reinvestigation of the rotational spectrum of diethyl ether based on broadband millimetre-wave spectra recently recorded at The Ohio State University and in Warsaw, covering the frequency region 108-366 GHz. The data set for the ground vibrational state of trans-trans diethyl ether has been extended to over 2000 lines and improved spectroscopic constants have been determined. Rotational spectra in the first excited vibrational states of the three lowest vibrational modes of trans-trans-diethyl ether, ν₂₀, ν₃₉, and ν₁₂ have been assigned. The v₂₀ = 1 and v₃₉ = 1 states are near 100 cm⁻¹ in vibrational term value and are coupled by a strong c-axis Coriolis interaction, which gives rise to many spectacular manifestations in the rotational spectrum. All of these effects have been successfully fitted for a dataset comprising over 3000 transitions, leading to precise determination of the energy difference between these states, (ΔE/hc)=10.400222(5) cm⁻¹. A newly developed software package for assignment and analysis of broadband spectra is described and made available.     

Conformational studies by nuclear magnetic resonance. VII—The direct observation of rotational isomers in some enamino carbonyl compounds and their thione derivatives by carbon magnetic resonance

Carbon-13 magnetic resonance spectra of the s-cis and s-trans rotamers of enamino ketones and thiones of the general formula \documentclass{article}\pagestyle{empty}\begin{document}${\rm X =}\mathop {\rm C}\limits^{\rm 1} {\rm (}\mathop {\rm R}\limits^{\rm 1} {\rm)}\mathop {\rm C}\limits^{\rm 2} {\rm H =}\mathop {\rm C}\limits^{\rm 3} {\rm HN}\mathop {{\rm R}_{\rm 2}}\limits^{\rm 4}$\end{document} (where × = O or S and R-1, R-4 = alkyl) have been obtained. With dimethylaminoacrolein and its thione analogue, restricted rotation could only be observed in the latter. The chemical shift differences between rotamers and homologues are attributed to changes in conjugation and to induced bond polarisation, both these factors resulting from steric strain. In particular, nonplanar deformations of the s-trans rotamers are deduced from their C-2 chemical shift values.     

Structural studies by 1H and 13C d.n.m.r.: I—barrier to trans-cis isomerization in aliphatic enamino ketones of the type R?CO?CHCH?NHR1

D.n.m.r. studies have been performed involving the measurement of rates of trans-cis isomerization of aliphatic enamino ketones of the type R? CO? CH?CH? NHR₁, by means of equilibration experiments and the method of finding the coalescence temperature. Simultaneous observation of the rates of dynamic N? H proton exchange and isomerization processes by the latter method has facilitated the assignment of the rate-determining reaction step in the title compounds studied in aprotic solvents. Thermodynamic parameters are discussed and the dipolar transition state to isomerization in a nonpolar solvent indicated. The dynamic behaviour of all protons undergoing exchange between the possible sites in the molecule are discussed in the light of our own experiments and other recent data.     

Structural studies by 1H and 13C DNMR—II°: Alternative protonation sites in carbonyl conjugated chain enamines of the type R1-C1O-C2HC3H-NR2R3. A method of synthesis of disubstituted pyridinium salts

O-Protonation of secondary enamino ketones in TFA or concentrated mineral acids in various solvents is the kinetically favoured course of reaction leading ultimately to stable 2,5- or 3,4-disubstituted pyridinium salts. The mechanism of formation of the salts involves electrophilic attack by the C-3 carbon atom on C-2 or N-nucleophilic centres of the O-protonated molecule.     

An aromatic iodination method, with iodic acid used as the only iodinating reagent

Benzene, halobenzenes, and a number of more or less deactivated arenes,including nitrobenzene, readily reacted in anhydrous HIO3/AcOH/Ac2O/conc. H2SO4 mixtures to probably give ArIO2 intermediates or other hypervalent species (not isolated). The final reaction mixtures were poured into excess aq. Na2SO3 solution (a reductant) to give the purified iodinated products in 39-83% yields.