Filtrations of units of Viète field

Let [Formula: see text] be the [Formula: see text]th Viète field for any non-negative integer [Formula: see text]. We are interested in the relative unit group of [Formula: see text]. In this paper, we consider two filtrations of the relative unit group from Galois actions and from congruences and show that they are equal. And, as applications, we estimate the Mahler measure and the trace of square of relative units.

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Fake Galois actions

Journal of Algebra and Its Applications ◽

10.1142/s0219498821501334 ◽

2020 ◽

pp. 2150133

Author(s):

Niamh Farrell ◽

Lucas Ruhstorfer

Keyword(s):

Universal Covering ◽

Negative Integer ◽

Simple Groups ◽

Finite Simple Groups ◽

Universal Covering Group ◽

Covering Group ◽

Galois Action ◽

Galois Actions

We prove that for all non-abelian finite simple groups [Formula: see text], there exists a fake [Formula: see text]th Galois action on [Formula: see text] with respect to [Formula: see text], where [Formula: see text] is the universal covering group of [Formula: see text] and [Formula: see text] is any non-negative integer coprime to the order of [Formula: see text]. This is one of the two inductive conditions needed to prove an [Formula: see text]-modular analogue of the Glauberman–Isaacs correspondence.

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Early changes of lung function and structure in an elastase model of emphysema—a hyperpolarized 3He MRI study

Journal of Applied Physiology ◽

10.1152/japplphysiol.00482.2007 ◽

2008 ◽

Vol 104 (3) ◽

pp. 773-786 ◽

Cited By ~ 23

Author(s):

Kiarash Emami ◽

Robert V. Cadman ◽

John M. Woodburn ◽

Martin C. Fischer ◽

Stephen J. Kadlecek ◽

...

Keyword(s):

Lung Function ◽

Lung Ventilation ◽

Unit Group ◽

Sprague Dawley ◽

Sprague Dawley Rats ◽

Entire Lung ◽

Residual Capacity ◽

Regional Basis ◽

Mean Linear Intercept ◽

Mri Study

Early changes of lung function and structure were studied in the presence of an elastase-induced model of emphysema in 35 Sprague-Dawley rats at mild (5 U/100 g) and moderate (10 U/100 g) severities. Lung ventilation was measured on a regional basis (at a planar resolution of 3.2 mm) by hyperpolarized 3He MRI at 5 and 10 wk after model induction. Subsequent to imaging, average alveolar diameter was measured from histological slices taken from the centers of each lobe. Changes of mean fractional ventilation, mean linear intercept, and intrasubject heterogeneity of ventilation were studied during disease progression. Mean fractional ventilation was significantly different between healthy controls (0.23 ± 0.04) and emphysematous animals at both time points in the 10-unit group (0.06 ± 0.02 and 0.12 ± 0.05, respectively). Changes in average alveolar diameter were not statistically observable until the 10th wk between healthy (37 ± 10 μm) and emphysematous rats (73 ± 25 and 95 ± 31 μm, for 5 and 10 units, respectively). Assessment of function-structure correlation suggested that the majority of the decline in fractional ventilation occurred in the first 5 wk, while enlargement of alveolar diameters appeared primarily between the 5th and 10th wk. A thresholding metric, based on the 20th percentile of fractional ventilation over the entire lung, was utilized to detect the onset of the disease with confidence, independent of whether the regional ventilation measurements were normalized with respect to the delivered tidal volume and estimated functional residual capacity of each individual rat.

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On free products inside the unit group of integral group rings

Communications in Algebra ◽

10.1080/00927872.2021.1894167 ◽

2021 ◽

pp. 1-9

Author(s):

Feliks Rączka

Keyword(s):

Unit Group ◽

Group Rings ◽

Integral Group ◽

Free Products ◽

Integral Group Rings

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The Mahler measure of a three-variable family and an application to the Boyd–Lawton formula

Research in Number Theory ◽

10.1007/s40993-021-00237-1 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Jarry Gu ◽

Matilde Lalín

Keyword(s):

Mahler Measure

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Splanchnic Hypoperfusion-Directed Therapies in Trauma: A Prospective, Randomized Trial

The American Surgeon ◽

10.1177/000313480507100317 ◽

2005 ◽

Vol 71 (3) ◽

pp. 252-260 ◽

Cited By ~ 7

Author(s):

Stephen M. Cohn ◽

Orlando Kirton ◽

Margaret Brown ◽

S. Morad Hameed ◽

...

Keyword(s):

Randomized Trial ◽

Injury Severity ◽

Ischemia Reperfusion ◽

Unit Group ◽

Severe Trauma ◽

Prospective Randomized Trial ◽

Gastric Tonometry ◽

Trauma Patients ◽

Splanchnic Perfusion ◽

Splanchnic Hypoperfusion

Splanchnic hypoperfusion as reflected by gastric intramucosal acidosis has been recognized as an important determinant of outcome in shock. A comprehensive splanchnic hypoperfusion-ischemia reperfusion (IRP) protocol was evaluated against conventional shock management protocols in critical trauma patients. The study was a prospective randomized trial comparing three therapeutic approaches to hypoperfusion after severe trauma in 151 trauma patients admitted to the intensive care unit. Group 1 patients received hemodynamic support based on conventional indicators of hypoperfusion. In group 2, resuscitation was further guided by gastric tonometry-derived estimates of splanchnic hypoperfusion and included more invasive hemodynamic monitoring and additional administration of colloid or crystalloid solutions, or inotropic support. Group 3 patients additionally received therapies specifically aimed at optimizing splanchnic perfusion and minimizing oxidant-mediated damage from reperfusion. The three groups were similar based on age, Injury Severity Score, and Acute Physiology and Chronic Health Evaluation II Scores. There were no statistically significant differences in mortality rates, organ dysfunction, ventilator days, or length of stay between any of the interventions. Techniques of optimization of splanchnic perfusion and minimization of oxidant-mediated reperfusion injury evaluated in this study were not advantageous relative to standard resuscitation measures guided by conventional or tonometric measures of hypoperfusion in the therapy of occult and clinical shock in trauma patients.

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Smooth representations of unit groups of split basic algebras over non-Archimedean local fields

Journal of Group Theory ◽

10.1515/jgth-2019-0084 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Carlos A. M. André ◽

João Dias

Keyword(s):

Local Field ◽

Unit Group ◽

Basic Algebra ◽

Local Fields ◽

Dimensional Representation ◽

Smooth Representation ◽

One Dimensional ◽

Finite Dimensional

Abstract We consider smooth representations of the unit group G = A × G=\mathcal{A}^{\times} of a finite-dimensional split basic algebra 𝒜 over a non-Archimedean local field. In particular, we prove a version of Gutkin’s conjecture, namely, we prove that every irreducible smooth representation of 𝐺 is compactly induced by a one-dimensional representation of the unit group of some subalgebra of 𝒜. We also discuss admissibility and unitarisability of smooth representations of 𝐺.

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