Vacuum ultraviolet photolysis of CClF2CH2Cl

Photolysis of CClF₂CH₂Cl was studied by 147 nm vacuum ultraviolet irradiation. In the presence of NO; CF₂CH₂, CF₂CHCl, and CClF₂CN were produced. These products represent three different reaction paths; the molecular dechlorination, molecular dehydrochlorination, and chlorine radical elimination reactions. The reactant pressure and the addition gas (He or NO) pressure effects upon the product yield were studied. © 1994 John Wiley & Sons, Inc.     

An alternative theorem for set-valued maps via set relations and its application to robustness of feasible sets

Abstract

This paper contains a generalized Gordan-type alternative theorem for set-valued maps which characterizes set relations without any convexity assumptions using certain evaluation functions. As a direct consequence and as a good example, we discuss robustness (or stability) of linear programming problems for modelling error. Moreover, this theorem can be utilized for that of general vector optimization problems in special cases due to reformation of the evaluation functions.     

Regularity of harmonic maps from polyhedra to CAT(1) spaces

We determine regularity results for energy minimizing maps from an n-dimensional Riemannian polyhedral complex X into a CAT(1) space. Provided that the metric on X is Lipschitz regular, we prove Hölder regularity with Hölder constant and exponent dependent on the total energy of the map and the metric on the domain. Moreover, at points away from the \((n-2)\)-skeleton, we improve the regularity to locally Lipschitz. Finally, for points \(x \in X^{(k)}\) with \(k \le n-2\), we demonstrate that the Hölder exponent depends on geometric and combinatorial data of the link of \(x \in X\).     

Photoluminescence spectral change in layered titanate oxide intercalated with hydrated Eu3+

A number of interesting photoluminescence properties of titanate layered oxide intercalated with hydrated Eu3+ have been demonstrated. Photoluminescence intensity of Eu3+ decreased rapidly with time during irradiation by UV light having energy higher than the band gap energy of the host TiO (Ti(1.81)O4) layer. This is presumably due to the decrease in energy transfer from the host TiO layer to Eu3+ as a result of the change in the hydration state of water molecules surrounding Eu3+, which is caused by the hole produced in the TiO valence band. When irradiation was discontinued, the emission intensity gradually recovered. The recovery time increased when the water in the interlayer is removed by heat treatment. This indicates that the state of interlayer water changes during irradiation and returns to its initial state after discontinuation of irradiation. The excitation spectra changed drastically at any given wavelength upon irradiation with UV light. A comparison of the excitation spectra before and after irradiation reveals that only the excitation peak at around the irradiation wavelength decreased upon irradiation, as in the case of spectral hole burning. The hydration state of water molecules surrounding Eu3+ presumably changes depending on the irradiation wavelength, leading to the above spectral change because the Eu/TiO film has a superlattice structure producing holes with different energies.     

Inference for vast dimensional elliptical distributions

We propose a quantile–based method to estimate the parameters of an elliptical distribution, and a battery of tests for model adequacy. The method is suitable for vast dimensions as the estimators for location and dispersion have closed–form expressions, while estimation of the tail index boils down to univariate optimizations. The tests for model adequacy are for the null hypothesis of correct specification of one or several level contours. A Monte Carlo study to three distributions (Gaussian, Student–t and elliptical stable) for dimensions 20, 200 and 2000 reveals the goodness of the method, both in terms of computational time and finite samples. An empirical application to financial data illustrates the method.