Holonomy and path structures in general relativity and Yang-Mills theory

This article is about a different representation of the geometry of the gravitational field, one in which the paths of test bodies play a crucial role. The primary concept is the geometry of the motion of a test body, and the relation between different such possible motions. Space-time as a Lorentzian manifold is regarded as a secondary construct, and it is shown how to construct it from the primary data. Some technical problems remain. Yang-Mills fields are defined by their holonomy in an analogous construction. I detail the development of this idea in the literature, and give a new version of the construction of a bundle and connection from holonomy data. The field equations of general relativity are discussed briefly in this context.     

Poincaré series and holomorphic averaging

Summary We provide an alternate proof of McMullen's theorem on contractive properties of the Poincaré series operator in the special case of the universal covering. This case includes in particular Kra's Theta Conjecture.Oblatum 16-X-1991 & 14-IV-1992First author supported in part by a grant from the National Science Foundation     

AUTOMATED WIND TUNNEL MEASUREMENTS

It is common practice in power transmission to use bundled overhead electrical conductors because the lower rate of corona discharge, compared with single conductors, makes the bundle attractive for high voltages. However, secondary problems may arise from the vibrations induced by the aerodynamic forces which act on the leeward conductors as a result of their immersion in the wake of a windward conductor. Thus, in addition to possible aeolian and galloping oscillations observed for a single conductor, bundle conductors may also be subjected to wake-induced oscillations. ^1,2 Although extensive research has been done on the aeroelastic behavior of single and bundled conductors which are bare, little is known about the galloping or wake oscillation characteristics of given bundle conductors which, depending upon the environmental conditions during the formation of ice, may have five or so representative shaped cross-sections. One important task involves the aerodynamic quasi-static force and moment measurements in a wind tunnel using full scale conductor cross-sections each of which must be rotated through many angles at different spacings. Such measurements are repetitive as well as tediously time consuming and, hence, are beneficially automated. A reliable, accurate and inexpensive automated apparatus is described in this paper which permits the aerodynamic measurements to be performed efficiently and without intervention. Most importantly, it relieves the operator of the usual responsibility for manually controlling the separation and orientation of the sections as well as the need to manually compensate fluctuations in the free stream air speed. For simplicity, the apparatus is detailed in the context of a twin bundle conductor.     

Inhomogeneous Cosmologies, the Copernican Principle and the Cosmic Microwave Background: More on the EGS Theorem

We discuss inhomogeneous cosmological models which satisfy the Copernican principle. We construct some inhomogeneous cosmological models starting from the ansatz that the all the observers in the models view an isotropic cosmic microwave background. We discuss multi-fluid models, and illustrate how more general inhomogeneous models may be derived, both in General Relativity and in scalar-tensor theories of gravity. Thus we illustrate that the cosmologicalprinciple, the assumption that the Universe we live in is spatially homogeneous, does not necessarily follow from the Copernican principle and the high isotropy of the cosmic microwave background. We also present some new conformally flat two-fluid solutions of Einstein's field equations.     

Stoichiometry-dependent formation of quantum dot-antibody bioconjugates: a complementary atomic force microscopy and agarose gel electrophoresis study

The unique advantages of quantum dot (QD) bioconjugates have motivated their application in biological assays. However, physical characterization of bioconjugated QDs after surface modification has often been overlooked. Here, biotinylated antibodies (biotin-IgG) were attached to commercial streptavidin-conjugated quantum dots (strep-QDs) at different stoichiometric ratios, and these QD bioconjugates were characterized with atomic force microscopy and discontinuous sodium dodecyl sulfate agarose gel electrophoresis (SDS-AGE). The results from these complementary analytical techniques showed that the molar ratio determined the relative sizes, molecular weights and morphologies of the QD bioconjugates. Additionally, the novel discontinuous SDS-AGE analysis confirmed specific binding between biotin-IgG and strep-QDs. Researchers who design QD bioconjugates for cell-based assays should consider stoichiometry-dependent differences in the physical properties of their QD bioconjugates.     

Bismuth-catalyzed benzylic oxidations with tert-butyl hydroperoxide

[reaction: see text] Oxidation of alkyl and cycloalkyl arenes with tert-butyl hydroperoxide catalyzed by bismuth and picolinic acid in pyridine and acetic acid gave the corresponding benzylic ketones (48-99%). Alternatively, oxidation of methyl arenes gave the corresponding substituted benzoic acids (50-95%). Preliminary mechanistic studies were consistent with a radical mechanism rather than a bismuth(III)-bismuth(V) cycle.