Gas‐phase tautomerism in 1‐phenylazonaphthalene‐4‐ol: verification of the responses of individual tautomers

Gas‐phase tautomerism in 1‐phenylazonaphthalene‐4‐ol (1) was studied by using electron ionization (EI) mass spectrometry on the basis of the fragmentations of the model enol and keto tautomers, where the movable proton is replaced by a methyl group. These fixed tautomers were obtained as an easy separable mixture by simple methylation of the cheap and easily accessible diazene (1). It was found that their EI mass spectral fragmentations are in full congruence with the already published theoretical predictions. The relative energies required for bond cleavage in 1 and its fixed tautomers were estimated by stepwise increasing of the electron energy of the ion source of the mass spectrometer. A simple equation for the approximate estimation of the molar fractions of the individual tautomers was suggested. It was shown that the enol form is dominant in the temperature range of 200–300°C. Copyright © 2009 John Wiley & Sons, Ltd.     

Novel surface tension isotherm for surfactants based on local density functional theory

In this Letter we report a new general method for calculating of surface tension isotherms in the presence of surfactants, based on a local density functional. We illustrate this method by deriving the interfacial tension isotherm for nonionic surfactants at an air-water or oil-water interface by using the self-consistent field theory of polymer brushes. We consider a particular case of local density functional to calculate explicitly how the interfacial tension and the surfactant adsorption depend on the surfactant bulk concentration. Experimental data for the surface tension and the surfactant adsorption isotherm for nonionic surfactants were interpreted with the help of the new isotherm. Very good agreement between the adsorption of n-dodecyl pentaoxyethylene glycol ether (C12E5) at an air-water interface, calculated from the surface tension isotherm and small-angle neutron-scattering is obtained.     

Local times of stochastic processes with positive definite bivariate densities

A new class of stochastic processes, called processes of positive bivariate type, is defined. Such a process is typically one whose bivariate density functions are positive definite, at least for pairs of time points which are sufficiently mutually close. The class includes stationary Gaussian processes and stationary reversible Markov processes, and is closed under the operations of composition and convolution. The purpose of this work is to show that the local times of such processes can be investigated in a natural way. One of the main contributions is an orthogonal expansion of the local time which is new even in the well-studied stationary Gaussian case. The basic tool in its construction is the Lancaster-Sarmanov expansion of a bivariate density in a series of canonical correlations and canonical variables.     

Extension problems for accretive sets in Banach spaces

This paper contains both negative and positive results concerning the possibility of extending accretive sets in Banach spaces to m-accretive sets. On the one hand, it is shown that if a closed convex subset C of a reflexive strictly convex Banach space E is not a nonexpansive retract of E, then no accretive A such that clco(D(A)) = C can be extended to an m-accretive set B with D(B) ?C, and that if a non-Hilbert E is reflexive and smooth, then there is an accretive set A ?E × E which has no m-accretive extension. On the other hand, we establish positive results and then apply them to the study of the asymptotic behavior of nonlinear semigroups, the construction of zeros of accretive sets, and the characterization of invariant sets for nonlinear semigroups.     

Gaussian processes with biconvex covariances

Let R(s, t) be a continuous, nonnegative, real valued function on a ≤ s ≤ t ≤ b. Suppose $\text{?R}\text{?s}\text{≥ 0}$, $\text{?R}\text{?t}\text{≤ 0}$, and $\text{?}{}^2\text{R}\text{?t}\text{?t ≤ 0}$ in the interior of the domain. Then the extension of R to a symmetric function on [a, b] × [a, b] is a covariance function. Such a covariance is called biconvex. Let X(t) be a Gaussian process with mean 0 and biconvex covariance. X has a representation as a sum of simple moving averages of white noises on the line and plane. The germ field of X at every point t is generated by X(t) alone. X is locally nondeterministic. Under an additional assumption involving the partial derivatives of R near the diagonal, the local time of the sample function exists and is jointly continuous almost surely, so that the sample function is nowhere differentiable.     

Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces

LetA be anm-accretive operator in a Banach spaceE. Suppose thatA ⁻¹0 is not empty and that bothE andE ^* are uniformly convex. We study a general condition onA that guarantees the strong convergence of the semigroup generated by—A and of related implicit and explicit iterative schemes to a zero ofA. Rates of convergence are also obtained. In Hilbert space this condition has been recently introduced by A. Pazy. We also establish strong convergence under the assumption that the interior ofA ⁻¹0 is not empty. In Hilbert space this result is due to H. Brezis. Sponsored by the United States Army under Contract No. DAAG29-75-C-0024.