Determination of signs of hyperfine coupling constants for an S = ½ system through E.P.R., ENDOR and double ENDOR

A systematic method of obtaining relative signs of hyperfine coupling constants is described. It applies to systems consisting of (a) a set of one or more nuclei coupled fairly strongly to the electron spin, and possessing a two-fold (or higher) axis of symmetry, together with (b) a set of weakly coupled nuclei defining superhyperfine transitions. ENDOR measurements for several E.P.R. hyperfine transitions, with the field oriented along the symmetry axis, give relative signs of hyperfine components for this direction. Signs for the other directions can then be obtained through ENDOR measurements on a single hyperfine transition at various field orientations. Additional double ENDOR measurements may be necessary for very weakly coupled nuclei. This method can complement double ENDOR studies in favourable cases. It is illustrated by the determination of signs of coupling constants of protons and of ⁷⁵As in the AsO₄ ^4- radical in KH₂AsO₄.     

The preparation of a new "safety catch" ester linker for solid-phase synthesis

A new "safety catch" linker for esters has been synthesized on polystyrene resin. This 2-tert-butoxyphenol resin 10 may be acylated to give a relatively stable ester that will allow nucleophilic chemistry without reaction at the linking ester group. Removal of the tert-butyl group with acid unmasks a highly reactive 2-hydroxyphenyl ester that reacts readily with nucleophiles to cause release of the product from the resin. This sequence has been exemplified by acylating the resin with various bromo acids, carrying out nucleophilic displacements with thiols, phenols, or amines, activating the ester with trifluoroacetic acid and cleaving from the resin with amines to give the (nucleophile) substituted carboxamides in high yield and purity. Kinetic studies with a model ester revealed half-lives for reaction with morpholine of 119 h for the tert-butoxyphenyl ester and 1 min for the corresponding phenol.     

Frame-Based Ray Search Algorithms in Unconstrained Optimization

This paper describes a class of frame-based direct search methods for unconstrained optimization without derivatives. A template for convergent direct search methods is developed, some requiring only the relative ordering of function values. At each iteration, the template considers a number of search steps which form a positive basis and conducts a ray search along a step giving adequate decrease. Various ray search strategies are possible, including discrete equivalents of the Goldstein–Armijo and one-sided Wolfe–Powell ray searches. Convergence is shown under mild conditions which allow successive frames to be rotated, translated, and scaled relative to one another.     

On the calculation of minimum variance estimators for unobservable dependent variables

The determination of minimum variance estimators in an unusual context is considered. The problem arises from an attempt to perform a regression with an unobservable dependent variable. The required minimum variance estimator is shown to satisfy a linear system of equations where the coefficient matrix has a simple structure. Uniqueness of the estimator is established by determining necessary and sufficient conditions on the data which guarantee positive definiteness of this coefficient matrix. Numerical aspects of the method of computation are also briefly explored.