Counting lifts of Brauer characters

In this paper we examine the behavior of lifts of Brauer characters in p-solvable groups where p is an odd prime. In the main result, we show that if \phi \in IBrp(G) is a Brauer character of a solvable group such that \phi has an abelian vertex subgroup Q, then the number of lifts of \phi in Irr(G) is at most |Q|. In order to accomplish this, we develop several results about lifts of Brauer characters in p-solvable groups that were previously only known to be true in the case of groups of odd order.Comment: A different proof of Theorem 1 is in the paper "The number of lifts of Brauer characters with a normal vertex" by J.P. Cossey, M.L.Lewis, and G. Navarro. Hence, we do not expect to try to publish this note. We feel that the proof in this paper is of independent interes

Lifts and vertex pairs in solvable groups

Suppose $G$ is a $p$-solvable group, where $p$ is odd. We explore the connection between lifts of Brauer characters of $G$ and certain local objects in $G$, called vertex pairs. We show that if $\chi$ is a lift, then the vertex pairs of $\chi$ form a single conjugacy class. We use this to prove a sufficient condition for a given pair to be a vertex pair of a lift and to study the behavior of lifts with respect to normal subgroups

Isomorphism in expanding families of indistinguishable groups

For every odd prime $p$ and every integer $n\geq 12$ there is a Heisenberg group of order $p^{5n/4+O(1)}$ that has $p^{n^2/24+O(n)}$ pairwise nonisomorphic quotients of order $p^{n}$. Yet, these quotients are virtually indistinguishable. They have isomorphic character tables, every conjugacy class of a non-central element has the same size, and every element has order at most $p$. They are also directly and centrally indecomposable and of the same indecomposability type. The recognized portions of their automorphism groups are isomorphic, represented isomorphically on their abelianizations, and of small index in their full automorphism groups. Nevertheless, there is a polynomial-time algorithm to test for isomorphisms between these groups.Comment: 28 page

NASA Docking System (NDS) Block 0 Configurations

The NASA Docking System (NDS) configuration descriptions and differences for NDS 301, NDS 302, NDS 303 and NDS 304 are presented

Advanced Mating System Development for Space Applications

This slide presentation reviews the development of space flight sealing and the work required for the further development of a dynamic interface seal for the use on space mating systems to support a fully androgynous mating interface. This effort has resulted in the advocacy of developing a standard multipurpose interface for use with all modern modular space architecture. This fully androgynous design means a seal-on-seal (SOS) system

Photoelectrochemical water splitting: silicon photocathodes for hydrogen evolution

The development of low cost, scalable, renewable energy technologies is one of today's most pressing scientific challenges. We report on progress towards the development of a photoelectrochemical water-splitting system that will use sunlight and water as the inputs to produce renewable hydrogen with oxygen as a by-product. This system is based on the design principle of incorporating two separate, photosensitive inorganic semiconductor/liquid junctions to collectively generate the 1.7-1.9 V at open circuit needed to support both the oxidation of H_2O (or OH^-) and the reduction of H^+ (or H_2O). Si microwire arrays are a promising photocathode material because the high aspect-ratio electrode architecture allows for the use of low cost, earth-abundant materials without sacrificing energy-conversion efficiency, due to the orthogonalization of light absorption and charge-carrier collection. Additionally, the high surfacearea design of the rod-based semiconductor array inherently lowers the flux of charge carriers over the rod array surface relative to the projected geometric surface of the photoelectrode, thus lowering the photocurrent density at the solid/liquid junction and thereby relaxing the demands on the activity (and cost) of any electrocatalysts. Arrays of Si microwires grown using the Vapor Liquid Solid (VLS) mechanism have been shown to have desirable electronic light absorption properties. We have demonstrated that these arrays can be coated with earth-abundant metallic catalysts and used for photoelectrochemical production of hydrogen. This development is a step towards the demonstration of a complete artificial photosynthetic system, composed of only inexpensive, earth-abundant materials, that is simultaneously efficient, durable, and scalable

Coordinate Confusion in Conformal Cosmology

A straight-forward interpretation of standard Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmologies is that objects move apart due to the expansion of space, and that sufficiently distant galaxies must be receding at velocities exceeding the speed of light. Recently, however, it has been suggested that a simple transformation into conformal coordinates can remove superluminal recession velocities, and hence the concept of the expansion of space should be abandoned. This work demonstrates that such conformal transformations do not eliminate superluminal recession velocities for open or flat matter-only FRLW cosmologies, and all possess superluminal expansion. Hence, the attack on the concept of the expansion of space based on this is poorly founded. This work concludes by emphasizing that the expansion of space is perfectly valid in the general relativistic framework, however, asking the question of whether space really expands is a futile exercise.Comment: 5 pages, accepted for publication in MNRAS Letter

EMI protection design guidance

This EMI Protection Design Guidelines report has been prepared as a guide for use by ALSEP experiment fabrication and subsystem designers.prepared by J. Whiteford, R. L. Lewis