On extendability of group actions on compact Riemann surfaces

The question of whether a given group which acts faithfully on a compact Riemann surface of genus is the full group of automorphisms of (or some other such surface of the same genus) is considered. Conditions are derived for the extendability of the action of the group in terms of a concrete partial presentation for associated with the relevant branching data, using Singerman's list of signatures of Fuchsian groups that are not finitely maximal. By way of illustration, the results are applied to the special case where is a non-cyclic abelian group.

     

Precise measurement of the positive muon anomalous magnetic moment

A precise measurement of the anomalous g value, a(mu) = (g-2)/2, for the positive muon has been made at the Brookhaven Alternating Gradient Synchrotron. The result a(mu+) = 11 659 202(14) (6) x 10(-10) (1.3 ppm) is in good agreement with previous measurements and has an error one third that of the combined previous data. The current theoretical value from the standard model is a(mu)(SM) = 11 659 159.6(6.7) x 10(-10) (0.57 ppm) and a(mu)(exp) - a(mu)(SM) = 43(16) x 10(-10) in which a(mu)(exp) is the world average experimental value.     

Generalized optical theorem for scatterers having inversion symmetry: applications to acoustic backscattering

The far-field acoustic scattering amplitudes for the scattering of plane waves by targets having inversion symmetry obey a generalized optical theorem in the absence of dissipation. The theorem allows a component of the complex scattering amplitude in an arbitrary direction to be expressed in terms of an angular integration involving scattering amplitudes evaluated at different angles. The result reduces to the usual optical theorem in the case of forward scattering. The theorem is applied to the backscattering by a perfectly soft sphere as a numerical example. The relevant integrand is shown to be oscillatory. Some potential applications to inverse problems, multiple scattering, and the verification of numerical algorithms are noted.     

A new 5-arc-transitive cubic graph

A connected cubic graph having 75,600 vertices is shown to exist, with the symmetric group S₁₀ as a group of automorphisms acting transitively on its 5-arcs. This graph is not bipartite, nor is it a covering of any other known 4- or 5-arc-transitive graph.     

Uncinatone,a New Antifungal Hydroquinone Diterpenoid from Clerodendrum uncinatum SCHINZ

A new hydroquinone diterpenoid was isolated from Clerodendrum uncinatum SCHINZ (Verbenaceae) by flash chromatography on silica gel. The structure was established as 7,11-dihydroxy-3,4,9,11b-tetramethyl-1,2,8,9,11b-pentahydrophenanthro[3,2-b]furan-6(2H)-one by spectroscopic methods and X-ray analysis. The diterpene was strongly fungitoxic to spores of Cladosporium cucumerinum.     

Microscopic calculation of cross sections for the reactions 12C(p, 2p) and 16O(p, 2p): U. Wille and R. Lipperheide Nucl. Phys. A189 (1972) 113

Isomeric states of ⁶⁹Se were produced via the heavy-ion compound-nucleus process and from the positon decay of ⁶⁹Br, the former producing a high-spin state and the latter preferentially populating a low-spin state. Ge(Li) detectors as well as scintillation counting showed that the high-spin state decays with T_{$\text{1}\text{2}$} = 14.0 ± 1.0 min to levels in ⁶⁹As, giving rise to γ-rays of 116, 166 and 282 keV. The low-spin state decays predominantly to a state giving rise to a 145 keV γ-ray with T_{$\text{1}\text{2}$} = 1.8 ± 0.2 min. The beta end-point energy of both isomers is 5.2 ± 0.2 MeV. It is deduced that the high-spin state, assigned J^π = $\text{9}\text{2}$⁺, is the ground state; the isomeric state had J^π = $\text{3}\text{2}$^?. The angular momentum inversion as compared to neutron-excess Se isotopes is attributed to Coriolis coupling to a deformed core as described by Malik and Scholz.