Intramolecular hemiacetals. The acid-base-catalyzed ring-chain interconversion of 2-substituted 2-hydroxy-4,4-dimethylmorpholinium cations in aqueous solution.

The ring-chain tautomerism in aqueous solution of some aryl-substituted morpholinium salts (bromides), has been studied and equilibrium constants are reported. In the crystals the substrates exist entirely in their cyclic forms as hemiacetals, but in aqueous solution NMR measurements reveal that an equilibrium is established between the cyclic (hemiacetal) and the noncyclic (ketone) form, the degree of ring-opening being more pronounced with electron-donating aryl substituents at the carbonyl carbon. The kinetics of the ring-chain interconversion in water has been investigated spectrophotometrically by a 'pH jump' stopped-flow technique. General base catalysis is observed with a Br?nsted beta value apparently independent of substituent and equal to 0.60. The Hammett rho values for various base catalysts are close to those for very similar intermolecular reactions involving hemiacetal breakdown, leading to the suggestion of a 'normal' class n mechanism for base catalysis. For acid catalysis, however, a quite different situation is encountered, since no general acid but only (weak) catalysis by the hydronium ion can be detected. We believe this deviation from 'normal' general acid catalysis is caused by an electrostatic interaction, and we suggest that it might result from a change in the usual class e mechanism for general acid catalysis by a situation in which rate-limiting concerted proton transfer is replaced by rate-limiting preprotonation. This is supported by the observed drastic change in Hammett rho value for catalysis by the hydronium ion, compared with the 'normal' case. An interesting case is encountered for the 4-aminophenyl-substituted substrate, in which the amino group becomes protonated in acid solution, thus representing a new substituent. Despite this complication, the various equilibrium and rate constants may also be evaluated experimentally for this substrate.     

Surface tension and density measurements for indium and uranium using a sessile-drop apparatus with glow discharge cleaning

The sessile-drop method is used to measure the surface tension and density of liquid indium and uranium under high vacuum. Measurements are made over the temperature range 156–500°C for In and at the melting point for U. Surface oxides are efficiently removed with a glow discharge system. Drop profiles are captured by photograph and processed using nonlinear regression to yield the surface tension and density. In this regression procedure, normal distances from calculated profiles to data points are minimized. For indium, the density and surface tension measurements yield _mp = 7.05 × 10³kg/m³, d/dT = −0.776 kg/m³·°C, and γ_mp = 0.568 N/m, dγ/dT = −9.45 × 10⁻⁵ N/m·°C. The results for uranium at the melting point are _mp = 17.47 × 10³ kg/m³ and γ_mp = 1.653 N/m.     

Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution

Collocation type methods are studied for the numerical solutionof the weakly singular Volterra integral equation of the secondkind: where the solution (t) is assumedto have the form f(t) = x(t)+r^?(t), x and being sufficientlysmooth. The solution is approximated near zero by a linear combinationof powers of t?, and away from zero by the usual polynomialrepresentation. Convergence is proved and many numerical experimentsare carried out with examples from the literature. A comparisonis made with a method of Brunner & Norsett (1981), originallydeveloped for (1) with a smooth solution. Special attentionis paid to the numerical approximation of the so-called momentintegrals which emerge in the collocation scheme.     

Suppression of classic and quantum radiation pressure noise by electro-optic feedback

We present theoretical results that demonstrate a new technique that can be used to improve the sensitivity of thermal noise measurements: intracavity intensity stabilization. It is demonstrated that electro-optic feedback can be used to reduce intracavity intensity fluctuations, and the consequent radiation pressure fluctuations, by a factor of 2 below the quantum-noise limit. We show that this reduction is achievable in the presence of large classic intensity fluctuations in the incident laser beam. The benefits of this scheme are a consequence of the sub-Poissonian intensity statistics of the field inside a feedback loop and the quantum nondemolition nature of radiation pressure noise as a readout system for the intracavity intensity fluctuations.