Noncommutative geometry, topology and the standard model vacuum

As a ramification of a motivational discussion for previous joint work, in which equations of motion for the finite spectral action of the Standard Model were derived, we provide a new analysis of the results of the calculations herein, switching from the perspective of Spectral triple to that of Fredholm module and thus from the analogy with Riemannian geometry to the pre-metrical structure of the Noncommutative geometry. Using a suggested Noncommutative version of Morse theory together with algebraic $K$-theory to analyse the vacuum solutions, the first two summands of the algebra for the finite triple of the Standard Model arise up to Morita equivalence. We also demonstrate a new vacuum solution whose features are compatible with the physical mass matrix.Comment: 24 page

Calculation of energy levels and transition amplitudes for barium and radium

The radium atom is a promising system for studying parity and time invariance violating weak interactions. However, available experimental spectroscopic data for radium is insufficient for designing an optimal experimental setup. We calculate the energy levels and transition amplitudes for radium states of significant interest. Forty states corresponding to all possible configurations consisting of the $7s$, $7p$ and $6d$ single-electron states as well as the states of the $7s8s$, $7s8p$ and $7s7d$ configurations have been calculated. The energies of ten of these states corresponding to the $6d^2$, $7s8s$, $7p^2$, and $6d7p$ configurations are not known from experiment. Calculations for barium are used to control the accuracy.Comment: 12 pages, 4 table

Simple pressure-tuned Fabry–Pérot interferometer

A simple, compact and inexpensive pressure-tuned Fabry–Pérot interferometer is presented. It is used as a laser locking reference for optical frequencies where the use of an atomic reference is impractical. The scanning range is several GHz. Absolute positioning of the interferometer with an accuracy of 7 MHz7MHz rms over a range of 2 GHz2GHz is possible. The instrument is temperature stabilized and shows long-term drift of 16 MHz16MHz rms over 48 h48h.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87892/2/033105_1.pd

Magellan: Preliminary description of Venus surface geologic units

Observations from approximately one-half of the Magellan nominal eight-month mission to map Venus are summarized. Preliminary compilation of initial geologic observations of the planet reveals a surface dominated by plains that are characterized by extensive and intensive volcanism and tectonic deformation. Four broad categories of units have been identified: plains units, linear belts, surficial units, and terrain units

Evidence for two protein-lipoylation activities in Escherichia coli

AbstractThe lipoate acyltransferase subunits of the 2-oxo acid dehydrogenase complexes are post-translationally modified with one or more covalently-bound lipoyl cofactors. Two distinct lipoate-protein ligase activities, LPL-A and LPL-B, have been detected in E. coli by their ability to modify purified lipoyl apo-domains of the bacterial pyruvate dehydrogenase complex. Both enzymes require ATP and Mg2+, use L-lipoate, 8-methyllipoate, lipoyl adenylate and octanoyl adenylate as substrates, and both activate lipoyl-deficient pyruvate dehydrogenase complexes. In contrast, only LPL-B uses D-lipoate and octanoate and there are differences in the metal-ion and phosphate requirements. It is suggested that LPL-B may be responsible for the octanoylation of lipoyl domains observed previously under lipoate-deficient conditions

The orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure