Irreducible character degrees and normal subgroups

Let N be a normal subgroup of a finite group G and consider the set cd(G|N) of degrees of irreducible characters of G whose kernels do not contain N. A number of theorems are proved relating the set cd(G|N) to the structure of N. For example, if N is solvable, its derived length is bounded above by a function of |cd(G|N)|. Also, if |cd(G|N)| is at most 2, then N is solvable and its derived length is at most |cd(G|N)|. If G is solvable and |cd(G|N)| = 3, then the derived length of N is at most 3

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Tropical cyclones and climate change

Recent research has strengthened the understanding of the links between climate and tropical cyclones (TCs) on various timescales. Geological records of past climates have shown century-long variations in TC numbers. While no significant trends have been identified in the Atlantic since the late 19th century, significant observed trends in TC numbers and intensities have occurred in this basin over the past few decades, and trends in other basins are increasingly being identified. However, understanding of the causes of these trends is incomplete, and confidence in these trends continues to be hampered by a lack of consistent observations in some basins. A theoretical basis for maximum TC intensity appears now to be well established, but a climate theory of TC formation remains elusive. Climate models mostly continue to predict future decreases in global TC numbers, projected increases in the intensities of the strongest storms and increased rainfall rates. Sea level rise will likely contribute toward increased storm surge risk. Against the background of global climate change and sea level rise, it is important to carry out quantitative assessments on the potential risk of TC-induced storm surge and flooding to densely populated cities and river deltas. Several climate models are now able to generate a good distribution of both TC numbers and intensities in the current climate. Inconsistent TC projection results emerge from modeling studies due to different downscaling methodologies and warming scenarios, inconsistencies in projected changes of large-scale conditions, and differences in model physics and tracking algorithms

A Clear View of a Cloudy Brown Dwarf Companion from High-Resolution Spectroscopy

Direct imaging studies have mainly used low-resolution spectroscopy ($R\sim20-100$) to study the atmospheres of giant exoplanets and brown dwarf companions, but the presence of clouds has often led to degeneracies in the retrieved atmospheric abundances (e.g. C/O, metallicity). This precludes clear insights into the formation mechanisms of these companions. The Keck Planet Imager and Characterizer (KPIC) uses adaptive optics and single-mode fibers to transport light into NIRSPEC ($R\sim35,000$ in $K$ band), and aims to address these challenges with high-resolution spectroscopy. Using an atmospheric retrieval framework based on petitRADTRANS, we analyze KPIC high-resolution spectrum ($2.29-2.49~\mu$m) and archival low-resolution spectrum ($1-2.2~\mu$m) of the benchmark brown dwarf HD 4747 B ($m=67.2\pm1.8~M_{\rm{Jup}}$, $a=10.0\pm0.2$ au, $T_{\rm eff}\approx1400$ K). We find that our measured C/O and metallicity for the companion from the KPIC high-resolution spectrum agree with that of its host star within $1-2\sigma$. The retrieved parameters from the $K$ band high-resolution spectrum are also independent of our choice of cloud model. In contrast, the retrieved parameters from the low-resolution spectrum are highly sensitive to our chosen cloud model. Finally, we detect CO, H$_2$O, and CH$_4$ (volume mixing ratio of log(CH$_4$)=$-4.82\pm0.23$) in this L/T transition companion with the KPIC data. The relative molecular abundances allow us to constrain the degree of chemical disequilibrium in the atmosphere of HD 4747 B, and infer a vertical diffusion coefficient that is at the upper limit predicted from mixing length theory.Comment: 33 pages, 16 figures, Accepted to Ap

Role of tides in Arctic ocean/ice climate

Author Posting. © American Geophysical Union, 2007. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 112 (2007): C04S06, doi:10.1029/2006JC003643.A three-dimensional coupled ocean/ice model, intended for long-term Arctic climate studies, is extended to include tidal effects. From saved output of an Arctic tides model, we introduce parameterizations for (1) enhanced ocean mixing associated with tides and (2) the role of tides fracturing and mobilizing sea ice. Results show tides enhancing loss of heat from Atlantic waters. The impact of tides on sea ice is more subtle as thinning due to enhanced ocean heat flux competes with net ice growth during rapid openings and closings of tidal leads. Present model results are compared with an ensemble of nine models under the Arctic Ocean Model Intercomparison Project (AOMIP). Among results from AOMIP is a tendency for models to accumulate excessive Arctic Ocean heat throughout the intercomparison period 1950 to 2000 which is contrary to observations. Tidally induced ventilation of ocean heat reduces this discrepancy.This research is supported by the National Science Foundation Office of Polar Programs under cooperative agreements OPP-0002239 and OPP-0327664 with the International Arctic Research Center, University of Alaska Fairbanks

The development of HISPEC for Keck and MODHIS for TMT: science cases and predicted sensitivities

HISPEC is a new, high-resolution near-infrared spectrograph being designed for the W.M. Keck II telescope. By offering single-shot, R=100,000 between 0.98 - 2.5 um, HISPEC will enable spectroscopy of transiting and non-transiting exoplanets in close orbits, direct high-contrast detection and spectroscopy of spatially separated substellar companions, and exoplanet dynamical mass and orbit measurements using precision radial velocity monitoring calibrated with a suite of state-of-the-art absolute and relative wavelength references. MODHIS is the counterpart to HISPEC for the Thirty Meter Telescope and is being developed in parallel with similar scientific goals. In this proceeding, we provide a brief overview of the current design of both instruments, and the requirements for the two spectrographs as guided by the scientific goals for each. We then outline the current science case for HISPEC and MODHIS, with focuses on the science enabled for exoplanet discovery and characterization. We also provide updated sensitivity curves for both instruments, in terms of both signal-to-noise ratio and predicted radial velocity precision.Comment: 25 pages, 9 figures. To appear in the Proceedings of SPIE: Techniques and Instrumentation for Detection of Exoplanets XI, vol. 12680 (2023

Mucedorus: the last ludic playbook, the first stage Arcadia

This article argues that two seemingly contradictory factors contributed to and sustained the success of the anonymous Elizabethan play Mucedorus (c. 1590; pub. 1598). First, that both the initial composition of Mucedorus and its Jacobean revival were driven in part by the popularity of its source, Philip Sidney's Arcadia. Second, the playbook's invitation to amateur playing allowed its romance narrative to be adopted and repurposed by diverse social groups. These two factors combined to create something of a paradox, suggesting that Mucedorus was both open to all yet iconographically connected to an elite author's popular text. This study will argue that Mucedorus pioneered the fashion for “continuations” or adaptations of the famously unfinished Arcadia, and one element of its success in print was its presentation as an affordable and performable version of Sidney's elite work. The Jacobean revival of Mucedorus by the King's Men is thus evidence of a strategy of engagement with the Arcadia designed to please the new Stuart monarchs. This association with the monarchy in part determined the cultural functions of the Arcadia and Mucedorus through the Interregnum to the close of the seventeenth century