On pp-filtrations of Weyl modules

This paper considers Weyl modules for a simple, simply connected algebraic group over an algebraically closed field $k$ of positive characteristic $p\not=2$. The main result proves, if $p\geq 2h-2$ (where $h$ is the Coxeter number) and if the Lusztig character formula holds for all (irreducible modules with) regular restricted highest weights, then any Weyl module $\Delta(\lambda)$ has a $\Delta^p$-filtration, namely, a filtration with sections of the form $\Delta^p(\mu_0+p\mu_1):=L(\mu_0)\otimes\Delta(\mu_1)^{[1]}$, where $\mu_0$ is restricted and $\mu_1$ is arbitrary dominant. In case the highest weight $\lambda$ of the Weyl module $\Delta(\lambda)$ is $p$-regular, the $p$-filtration is compatible with the $G_1$-radical series of the module. The problem of showing that Weyl modules have $\Delta^p$-filtrations was first proposed as a worthwhile ("w\"unschenswert") problem in Jantzen's 1980 Crelle paper.Comment: Latest version corrects minor mistakes in previous versions. A reference is made to Williamson's recent arXiv posting, providing some relevant discussion in a footnote. [Comments on earlier versions: Previous v. 1 with minor errors and statements corrected. Improved organization. Should replace v. 2 which is an older version (even older than v.1) and was mistakenly posted.

Complexity for Modules Over the Classical Lie Superalgebra gl(m|n)

Let $\mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus \mathfrak{g}_{\bar{1}}$ be a classical Lie superalgebra and $\mathcal{F}$ be the category of finite dimensional $\mathfrak{g}$-supermodules which are completely reducible over the reductive Lie algebra $\mathfrak{g}_{\bar{0}}$. In an earlier paper the authors demonstrated that for any module $M$ in $\mathcal{F}$ the rate of growth of the minimal projective resolution (i.e., the complexity of $M$) is bounded by the dimension of $\mathfrak{g}_{\bar{1}}$. In this paper we compute the complexity of the simple modules and the Kac modules for the Lie superalgebra $\mathfrak{gl}(m|n)$. In both cases we show that the complexity is related to the atypicality of the block containing the module.Comment: 32 page

Managing Variability in VLSI Circuits.

Over the last two decades, Design for Manufacturing (DFM) has emerged as an essential field within the semiconductor industry. The main objective of DFM is to reduce and, if possible, eliminate variability in integrated circuits (ICs). Numerous techniques for managing variation have emerged throughout IC design: manufacturers design instruments with minute tolerances, process engineers calibrate and characterize a given process throughout its lifetime, and IC designers strive to model and characterize variability within their devices, libraries, and circuits. This dissertation focuses on the last of these three techniques and presents material relevant to managing variability within IC design. Since characterization and modeling are essential to the analysis and reduction of variation in modern-day designs, this dissertation begins by studying various correlation models used within Statistical Static Timing Analysis (SSTA). In the end, the study shows that using complex correlation models does not necessarily result in significant error reduction within SSTA, and that simple models (which only include die-to-die and random variation) can therefore be used to achieve similar accuracy with reduced overhead and run-time. Next, the variation models, themselves, are explored and a new critical dimension (CD) model is proposed which reduces standard deviation error in SSTA by ~3X. Finally, the focus changes from the timing analysis level and moves lower in the design hierarchy to the libraries and devices that comprise the backbone of IC design. The final three chapters study mechanical stress enhancement and discuss how to fully exploit the layout dependencies of mechanically stressed silicon. The first of these three chapters presents an optimization scheme that uses the layout dependencies of stress in conjunction with dual-threshold-voltage (Vth) assignment to decrease leakage power consumption by ~24%. Next, the second of the three chapters proposes a new standard cell library design methodology, called “STEEL.” STEEL provides average delay improvements of 11% over equivalent single-Vth implementations, while consuming 2.5X less leakage than the dual-Vth alternative. Finally, the stress enhanced studies (and this document) are concluded by a new optimization scheme that combines stress enhancement with gate length biasing to achieve 2.9X leakage power savings in IC designs without modifying Vth.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/75947/1/btcline_1.pd

香港の衛星都市

textabstractThe Drosophila protein Sex-lethal (Sxl) contains two RNP consensus-type RNA-binding domains (RBDs) separated by a short linker sequence. Both domains are essential for high-affinity binding tO the single-stranded polypyrimidine tract (PPT) within the regulated 3' splice site of the transformer (tra) pre- mRNA. In this paper, the effect of RNA binding to a protein fragment containing both RBDs from Sxl (Sxl-RBD1+2) has been characterized by heteronuclear NMR. Newly complete (85-90%) backbone resonance assignments have been obtained for unbound and RNA-bound states of Sxl-RBD1+2. A comparison of amide 1H and 15N chemical shifts between free and bound states has highlighted residues which respond to RNA binding. The β-sheets in both RBDs (RBD1 and RBD2) form an RNA interaction surface, as has been observed in other RBDs. A significant number of residues display different behavior when comparing RBD1 and RBD2. This argues for a model in which RBD1 and RBD2 of Sxl have different or nonanalogous points of interaction with the tra PPT. R142 (in RBD2) exhibits the largest chemical shift change upon RNA binding. The role of R142 in RNA binding was tested by measuring the K(d) of a mutant of Sxl-RBD1+2 in which R142 was replaced by alanine. This mutant lost the ability to bind RNA, showing a correlation with the chemical shift difference data. The RNA-binding affinities of two other mutants, F146A and T138I, were also shown to correlate with the NMR observations

A Search for Early Optical Emission from Short and Long Duration Gamma-ray Bursts

Gamma-ray bursts of short duration may harbor vital clues to the range of phenomena producing bursts. However, recent progress from the observation of optical counterparts has not benefitted the study of short bursts. We have searched for early optical emission from six gamma-ray bursts using the ROTSE-I telephoto array. Three of these events were of short duration, including GRB 980527 which is among the brightest short bursts yet observed. The data consist of unfiltered CCD optical images taken in response to BATSE triggers delivered via the GCN. For the first time, we have analyzed the entire 16 degree by 16 degree field covered for five of these bursts. In addition, we discuss a search for the optical counterpart to GRB 000201, a well-localized long burst. Single image sensitivities range from 13th to 14th magnitude around 10 s after the initial burst detection, and 14 - 15.8 one hour later. No new optical counterparts were discovered in this analysis suggesting short burst optical and gamma-ray fluxes are uncorrelated.Comment: 8 pages, 2 figures, subm. to ApJ Let

An Effect of α′\alpha' Corrections on Racetrack Inflation

We study the effects of $\alpha '$ corrections to the K\"ahler potential on volume stabilisation and racetrack inflation. In a region where classical supergravity analysis is justified, stringy corrections can nevertheless be relevant for correctly analyzing moduli stabilisation and the onset of inflation.Comment: 13 pages, 4 figures. Typos corrected, references added, this version to appear in JHE

Prompt Optical Observations of Gamma-ray Bursts

The Robotic Optical Transient Search Experiment (ROTSE) seeks to measure simultaneous and early afterglow optical emission from gamma-ray bursts (GRBs). A search for optical counterparts to six GRBs with localization errors of 1 square degree or better produced no detections. The earliest limiting sensitivity is m(ROTSE) > 13.1 at 10.85 seconds (5 second exposure) after the gamma-ray rise, and the best limit is m(ROTSE) > 16.0 at 62 minutes (897 second exposure). These are the most stringent limits obtained for GRB optical counterpart brightness in the first hour after the burst. Consideration of the gamma-ray fluence and peak flux for these bursts and for GRB990123 indicates that there is not a strong positive correlation between optical flux and gamma-ray emission.Comment: 4 pages, 3 figures, submitted to ApJ Letter