Spin-orbit matrix elements in the atomic f shell from automorphisms of SO(8)

A scrutiny of the matrix elements within the f shell of the spin-other-orbit interaction H(soo) has revealed many unexpected proportionalities that go beyond an application of the Wigner-Eckart theorem to Racah's groups G2 and SO(7). An explanation is sought by using the automorphisms of SO(8) by means of which the states of the atomic f shell are generated by two alternative SO(7) bases of the type (1 / 21 / 21 / 2)(4), each augmented by two parity labels. Transformations between the bases can be made by reversing the relative phases of the two angular-momentum states 3 and 0 that comprise any one of the four SO(7) spinors. The method is exemplified by the single-electron spin-orbit interaction H(so), for which a component can be found that is invariant under the phase reversal. The extension from H(so) to H(soo) is described for the component z(6) of H(soo), and several examples drawn from the comparatively inaccessible configurations near the middle of the f shell are presented.     

A photo-optical technique for measuring flow-induced vibrations in cantilevered tube bundles

A photo-optical technique has been developed for monitoring the dynamic displacement of cantilevered tubes in fluid flow. The technique employs an optical fiber to transmit light through the tube and a phototransistor array to measure the motion of the light beam that is projected from the end of the tube. The device is simple, inexpensive, and very sensitive to small displacements. Details are given for the development of the technique, analysis of performance, and static calibration. The device was tested by monitoring the dynamic response of a bundle of cantilevered tubes in both single-phase and two-phase Freon 11 flows. The results are compared with those of a standard strain gauge bridge.     

Trichlorophenol (TCP) sulfonate esters: a selective alternative to pentafluorophenol (PFP) esters and sulfonyl chlorides for the preparation of sulfonamides

2,4,6-Trichlorophenol (TCP) sulfonate esters undergo effective aminolysis under conventional heating and microwave irradiation; the reactivity of these species is such that chemoselective transformations of PFP sulfonate esters can be achieved.     

Constructing dynamical systems with specified symbolic dynamics

In this paper we demonstrate how to construct signals (time series) of continuous-time dynamical systems that exhibit a given symbolic dynamics. This is achieved without construction of the ordinary differential equations that generate the flow. This construction is of theoretical interest and is useful as a source of dynamical data that can be used to test various data analysis algorithms.     

The Szlenk index and local ℓ<Subscript>1</Subscript>-indices

We introduce two new local ₁-indices of the same type as the Bourgain ₁-index; the ⁺₁-index and the ⁺₁-weakly null index. We show that the ⁺₁-weakly null index of a Banach space X is the same as the Szlenk index of X, provided X does not contain ₁. The ⁺₁-weakly null index has the same form as the Bourgain ₁-index: if it is countable it must take values for some <₁. The different ₁-indices are closely related and so knowing the Szlenk index of a Banach space helps us calculate its ₁-index, via the ⁺₁-weakly null index. We show that I(C(^{))=^1++1}.     

Interaction with Brian Garner Wybourne

Quotations from personal letters and other sources are used to give an account of an interaction with Brian Wybourne over the course of a career in theoretcial rare-earth spectroscopy spanning nearly a half-century.