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

COMPTEL solar flare measurements

We review some of the highlights of the COMPTEL measurements of solar flares. These include images of the Sun in γ rays and neutrons. One of the important features of the COMPTEL instrument is its capability to measure weak fluxes of γ rays and neutrons in the extended phase of flares. These data complement the spectra taken with the COMPTEL burst spectrometer and the telescope during the impulsive phase of flares. We focus our attention on some of these general capabilities of the instrument and the latest results of two long‐duration γ‐ray flares, i.e., 11 and 15 June 199

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

Noncontact true temperature measurement, 2

A laser pyrometer was developed for acquiring the true temperature of a levitated sample. The reflectivity is measured by first expanding the laser beam to cover the entire cross-sectional surface of the diffuse target. The reflectivity calibration of this system is determined from the surface emissivity of a target with a blackbody cavity. The emissivity of the real target can then be calculated. The overall system constant is obtained by passively measuring the radiance of the blackbody cavity (emissivity = 1.0) at a known, arbitrary temperature. Since the photosensor used is highly linear over the entire operating temperature range, the true temperature of the target can then be computed. The latest results available from this on-going research indicate that true temperatures thus obtained are in very good quantitative agreement with thermocouple measured temperatures

Noncontact temperature pattern measuring device

Laser pyrometer techniques are utilized to accurately image a true temperature distribution on a given target without touching the target and without knowing the localized emissivity of the target. The pyrometer utilizes a very high definition laser beam and photodetector, both having a very narrow focus. The pyrometer is mounted in a mechanism designed to permit the pyrometer to be aimed and focused at precise localized points on the target surface. The pyrometer is swept over the surface area to be imaged, temperature measurements being taken at each point of focus

Artificial intelligence for multi-mission planetary operations

A brief introduction is given to an automated system called the Spacecraft Health Automated Reasoning Prototype (SHARP). SHARP is designed to demonstrate automated health and status analysis for multi-mission spacecraft and ground data systems operations. The SHARP system combines conventional computer science methodologies with artificial intelligence techniques to produce an effective method for detecting and analyzing potential spacecraft and ground systems problems. The system performs real-time analysis of spacecraft and other related telemetry, and is also capable of examining data in historical context. Telecommunications link analysis of the Voyager II spacecraft is the initial focus for evaluation of the prototype in a real-time operations setting during the Voyager spacecraft encounter with Neptune in August, 1989. The preliminary results of the SHARP project and plans for future application of the technology are discussed