scholarly journals Dense images of the power maps for a disconnected real algebraic group

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Arunava Mandal
Keyword(s):  
Algebraic Group ◽  
Exponential Map ◽  
The Real ◽  
Power Maps

Abstract Let 𝐺 be a complex algebraic group defined over ℝ, which is not necessarily Zariski-connected. In this article, we study the density of the images of the power maps g → g k g\to g^{k} , k ∈ N k\in\mathbb{N} , on real points of 𝐺, i.e., G ⁢ ( R ) G(\mathbb{R}) equipped with the real topology. As a result, we extend a theorem of P. Chatterjee on surjectivity of the power map for the set of semisimple elements of G ⁢ ( R ) G(\mathbb{R}) . We also characterize surjectivity of the power map for a disconnected group G ⁢ ( R ) G(\mathbb{R}) . The results are applied in particular to describe the image of the exponential map of G ⁢ ( R ) G(\mathbb{R}) .

scholarly journals Unitary Representations with Dirac Cohomology: Finiteness in the Real Case

2019 ◽  
Vol 2020 (24) ◽  
pp. 10277-10316 ◽  
Author(s):  
Chao-Ping Dong
Keyword(s):  
Convex Hull ◽  
Algebraic Group ◽  
Unitary Representations ◽  
Real Case ◽  
Finiteness Theorem ◽  
Real Form ◽  
Simple Algebraic Group ◽  
The Real ◽  
Dirac Cohomology

Abstract Let $G$ be a complex connected simple algebraic group with a fixed real form $\sigma $. Let $G({\mathbb{R}})=G^\sigma $ be the corresponding group of real points. This paper reports a finiteness theorem for the classification of irreducible unitary Harish-Chandra modules of $G({\mathbb{R}})$ (up to equivalence) having nonvanishing Dirac cohomology. Moreover, we study the distribution of the spin norm along Vogan pencils for certain $G({\mathbb{R}})$, with particular attention paid to the unitarily small convex hull introduced by Salamanca-Riba and Vogan.

scholarly journals Algebraic families of groups and commuting involutions

2018 ◽  
Vol 29 (04) ◽  
pp. 1850030 ◽  
Author(s):  
Dan Barbasch ◽  
Nigel Higson ◽  
Eyal Subag
Keyword(s):  
Algebraic Group ◽  
Algebraic Groups ◽  
Projective Line ◽  
Real Structure ◽  
The Real ◽  
The Family ◽  
Complex Projective Line ◽  
Complex Projective ◽  
Real Forms

Let [Formula: see text] be a complex affine algebraic group, and let [Formula: see text] and [Formula: see text] be commuting anti-holomorphic involutions of [Formula: see text]. We construct an algebraic family of algebraic groups over the complex projective line and a real structure on the family that interpolates between the real forms [Formula: see text] and [Formula: see text].

scholarly journals The real Chevalley involution

2014 ◽  
Vol 150 (12) ◽  
pp. 2127-2142 ◽  
Author(s):  
Jeffrey Adams
Keyword(s):  
Irreducible Representation ◽  
Algebraic Group ◽  
Semisimple Element ◽  
Closed Field ◽  
Reductive Algebraic Group ◽  
Algebraically Closed Field ◽  
The Real ◽  
Chevalley Involution

AbstractThe Chevalley involution of a connected, reductive algebraic group over an algebraically closed field takes every semisimple element to a conjugate of its inverse, and this involution is unique up to conjugacy. In the case of the reals we prove the existence of a real Chevalley involution, which is defined over $\mathbb{R}$, takes every semisimple element of $G(\mathbb{R})$ to a $G(\mathbb{R})$-conjugate of its inverse, and is unique up to conjugacy by $G(\mathbb{R})$. We derive some consequences, including an analysis of groups for which every irreducible representation is self-dual, and a calculation of the Frobenius Schur indicator for such groups.

scholarly journals Chaotic Behaviour in Two-parameter Family of Transcendental Functions Associated with Exponential Map

2020 ◽  
Vol 5 (6) ◽  
pp. 1191-1209
Author(s):  
Mohammad Sajid ◽  
Abdullah S. Alsuwaiyan
Keyword(s):  
Numerical Simulations ◽  
Period Doubling ◽  
Periodic Points ◽  
Parameter Family ◽  
Exponential Map ◽  
Bifurcation Diagrams ◽  
The Real ◽  
Transcendental Functions ◽  
Parameter Values ◽  
Two Parameter

This article is devoted to the study of chaos and bifurcation in the real dynamics of a newly proposed two-parameter family of transcendental functions. We assume that one parameter is continuous and other parameter is discrete. For certain parameters, the theoretical computations of the real fixed points of a family of functions are given. The numerical simulations of the real periodic points of functions are described. The bifurcation diagrams of the real dynamics of these functions for some selected parameter values are provided. In these bifurcation diagrams, the period-doubling occurs which proceeds to a pathway toward chaos in the dynamics of functions. Further, the periodic-three window is visible in the bifurcation diagrams which implies chaos. Lastly, chaos is quantified in the dynamics of functions by calculating Lyapunov exponents.

Scanning electron microscopy of human iliac bone by a simple preparation method

1990 ◽  
Vol 48 (3) ◽  
pp. 226-227
Author(s):  
Toshihiko Takita ◽  
Tomonori Naguro ◽  
Toshio Kameie ◽  
Akihiro Iino ◽  
Kichizo Yamamoto
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Preparation Method ◽  
Specimen Preparation ◽  
Real Surface ◽  
Public Attention ◽  
Preparation Methods ◽  
The Real ◽  
Simple Preparation ◽  
Scanning Electron

Recently with the increase in advanced age population, the osteoporosis becomes the object of public attention in the field of orthopedics. The surface topography of the bone by scanning electron microscopy (SEM) is one of the most useful means to study the bone metabolism, that is considered to make clear the mechanism of the osteoporosis. Until today many specimen preparation methods for SEM have been reported. They are roughly classified into two; the anorganic preparation and the simple preparation. The former is suitable for observing mineralization, but has the demerit that the real surface of the bone can not be observed and, moreover, the samples prepared by this method are extremely fragile especially in the case of osteoporosis. On the other hand, the latter has the merit that the real information of the bone surface can be obtained, though it is difficult to recognize the functional situation of the bone.

Personal Audio System: Hearing Symptoms, Habits, and Sound Pressure Levels Measured in Real Ear and a Manikin

2020 ◽  
Vol 63 (6) ◽  
pp. 2016-2026
Author(s):  
Tamara R. Almeida ◽  
Clayton H. Rocha ◽  
Camila M. Rabelo ◽  
Raquel F. Gomes ◽  
Ivone F. Neves-Lobo ◽  
...  
Keyword(s):  
Sound Pressure ◽  
Daily Basis ◽  
Cross Sectional Study ◽  
Normal Hearing ◽  
Chi Square ◽  
Cross Sectional ◽  
The Real ◽  
Significant Difference ◽  
Sound Pressure Levels ◽  
Audio System

Purpose The aims of this study were to characterize hearing symptoms, habits, and sound pressure levels (SPLs) of personal audio system (PAS) used by young adults; estimate the risk of developing hearing loss and assess whether instructions given to users led to behavioral changes; and propose recommendations for PAS users. Method A cross-sectional study was performed in 50 subjects with normal hearing. Procedures included questionnaire and measurement of PAS SPLs (real ear and manikin) through the users' own headphones and devices while they listened to four songs. After 1 year, 30 subjects answered questions about their usage habits. For the statistical analysis, one-way analysis of variance, Tukey's post hoc test, Lin and Spearman coefficients, the chi-square test, and logistic regression were used. Results Most subjects listened to music every day, usually in noisy environments. Sixty percent of the subjects reported hearing symptoms after using a PAS. Substantial variability in the equivalent music listening level (Leq) was noted ( M = 84.7 dBA; min = 65.1 dBA, max = 97.5 dBA). A significant difference was found only in the 4-kHz band when comparing the real-ear and manikin techniques. Based on the Leq, 38% of the individuals exceeded the maximum daily time allowance. Comparison of the subjects according to the maximum allowed daily exposure time revealed a higher number of hearing complaints from people with greater exposure. After 1 year, 43% of the subjects reduced their usage time, and 70% reduced the volume. A volume not exceeding 80% was recommended, and at this volume, the maximum usage time should be 160 min. Conclusions The habit of listening to music at high intensities on a daily basis seems to cause hearing symptoms, even in individuals with normal hearing. The real-ear and manikin techniques produced similar results. Providing instructions on this topic combined with measuring PAS SPLs may be an appropriate strategy for raising the awareness of people who are at risk. Supplemental Material https://doi.org/10.23641/asha.12431435

Current Issues: Evidence-Based Practice for the Real World: Thoughts on Clinical Education in Communication Disorders

2010 ◽  
Vol 20 (3) ◽  
pp. 100-105 ◽  
Author(s):  
Anne K. Bothe
Keyword(s):  
Clinical Education ◽  
Real World ◽  
Evidence Based Practice ◽  
Communication Disorders ◽  
University Faculty ◽  
Evidence Based ◽  
Speech Language Pathology ◽  
Basic Principles ◽  
The Real ◽  
Language Pathology

This article presents some streamlined and intentionally oversimplified ideas about educating future communication disorders professionals to use some of the most basic principles of evidence-based practice. Working from a popular five-step approach, modifications are suggested that may make the ideas more accessible, and therefore more useful, for university faculty, other supervisors, and future professionals in speech-language pathology, audiology, and related fields.

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