The Continuing Need to Distinguish Between Myth and Reality: Remarks of Edward B. Miller before the Commission on the Future of Worker-Management Relations

Testimony_Miller_090894.pdf: 117 downloads, before Oct. 1, 2020

Overview of Ka-band communications technology requirements for the space exploration initiative

In the Space Exploration Initiative, Ka-band frequencies are likely to carry the bulk of the communications traffic both in the vicinity of and on the return links from the moon and Mars. The four exploration architectures identified by the Synthesis Group are examined and Ka-band technology requirements to meet the data traffic needs and schedule are identified. Specific Ka-band technology requirements identified are: transmitters - 0.5 to 200 W with high efficiency; antennas - 5m and 9m diameter, with multiple beams and/or scanning beams; and spacecraft receivers - noise figure of 2 dB. For each component, the current state of technology is assessed and needed technology development programs are identified. It is concluded that to meet the schedules of lunar and Mars precursor missions beginning in approximately the year 2000, aggressive technology development and advanced development programs are required immediately for Ka-band communications systems components. Additionally, the greater data transmission rates for the cargo and piloted phases of the exploration program require further Ka-band communications technology developments targeted for operations beginning in about 2010

Witt differentials in the h-topology

Recent important and powerful frameworks for the study of differential forms by Huber-Joerder and Huber-Kebekus-Kelly based on Voevodsky's h-topology have greatly simplified and unified many approaches. This article builds towards the goal of putting Illusie's de Rham-Witt complex in the same framework by exploring the h-sheafification of the rational de Rham-Witt differentials. Assuming resolution of singularities in positive characteristic one recovers a complete cohomological h-descent for all terms of the complex. We also provide unconditional h-descent for the global sections and draw the expected conclusions. The approach is to realize that a certain right Kan extension introduced by Huber-Kebekus-Kelly takes the sheaf of rational de Rham-Witt forms to a qfh-sheaf. As such, we state and prove many results about qfh-sheaves which are of independent interest

On Lower Bounds for ss-multiplicities

A recent continuous family of multiplicity functions on local rings was introduced by Taylor interpolating between Hilbert-Samuel and Hilbert-Kunz multiplicities. The obvious goal is to use this as a tool for deforming results from one to the other. The values in this family which do not match these classic variants however are not known yet to be well-behaved. This article explores lower bounds for these intermediate multiplicities as well as gives evidence for analogies of the Watanabe-Yoshida minimality conjectures for unmixed singular rings.Comment: 10 page