Classification of Demushkin Groups

1967 ◽  
Vol 19 ◽  
pp. 106-132 ◽  
Author(s):  
John P. Labute
Keyword(s):  
Topological Group ◽  
Normal Subgroup ◽  
Bilinear Form ◽  
Minimal System ◽  
List Type ◽  
Type Number ◽  
Cup Product ◽  
Minimal System Of Generators ◽  
Closed Normal Subgroup

A pro-p-group G is said to be a Demushkin group if(1)dimFp H1(G, Z/pZ) < ∞,(2)dimFp H2(G, Z/pZ) = 1,(3)the cup product H1(G, Z/pZ) × H1(G, Z/pZ) → H2(G, Z/pZ) is a non-degenerate bilinear form. Here FP denotes the field with p elements. If G is a Demushkin group, then G is a finitely generated topological group with n(G) = dim H1(G, Z/pZ) as the minimal number of topological generators; cf. §1.3. Condition (2) means that there is only one relation among a minimal system of generators for G; that is, G is isomorphic to a quotient F/(r), where F is a free pro-p-group of rank n = n(G) and (r) is the closed normal subgroup of F generated by an element r ∈ F9 (F, F); cf. §1.4.

Regular Homeomorphisms of Finite Order on Countable Spaces

2009 ◽  
Vol 61 (3) ◽  
pp. 708-720 ◽  
Author(s):  
Yevhen Zelenyuk
Keyword(s):  
Topological Group ◽  
Abelian Group ◽  
Finite Order ◽  
Free Product ◽  
Structure Theorem ◽  
Broad Class ◽  
List Type ◽  
Type Number ◽  
Countably Infinite ◽  
Infinite Abelian Group

Abstract.We present a structure theorem for a broad class of homeomorphisms of finite order on countable zero dimensional spaces. As applications we show the following.(a) Every countable nondiscrete topological group not containing an open Boolean subgroup can be partitioned into infinitely many dense subsets.(b) If G is a countably infinite Abelian group with finitely many elements of order 2 and βG is the Stone–Čech compactification of G as a discrete semigroup, then for every idempotent p ∈ βG\﹛0﹜, the subset ﹛p,−p﹜ ⊂ βG generates algebraically the free product of one-element semigroups ﹛p﹜ and ﹛−p﹜.

Authority

1974 ◽  
Vol 3 (4) ◽  
pp. 563-583 ◽  
Author(s):  
Gary Young
Keyword(s):  
Subject Matter ◽  
List Type ◽  
Type Number ◽  
Personal Authority ◽  
In Virtue Of

Philosophers often contrast personal authority to authority vested in offices. Some such distinction is traditional and sometimes useful. But it does not provide us with an exhaustive classification of the types of authority, for there is a third type of authority that I shall argue is more fundamental than these two. Let us start with the types marked out by the usual distinction.Consider first the sort of authority illustrated by the following sentences:(1)Smith is an authority on physics.(2)Smith has (some) authority as a physicist.(3)Smith's views (utterances) on physics have (some) authority.(4)O.K., I believe you—after all, you're the authority on physics!A person is an authority in virtue of possessing extensive knowledge of a field or subject-matter. There seem to be no limits on what the field or subject-matter can be—for instance, one can be an authority on trivia.

scholarly journals A VLBA 15 GHz Small Separation Gravitational Lens Survey

1996 ◽  
Vol 173 ◽  
pp. 405-406
Author(s):  
A.R. Patnaik ◽  
M.A. Garrett ◽  
A. Polatidis ◽  
D. Bagri
Keyword(s):  
High Frequency ◽  
Gravitational Lens ◽  
Radio Sources ◽  
List Type ◽  
Type Number ◽  
Morphological Classification ◽  
Small Separation

We have embarked on a 15 GHz VLBA survey of 1000 flat spectrum sources. We present the results from a 24 hour pilot observing run in which 72 sources were mapped. The primary aims of this project are: –to search for small separation (1-150 mas) gravitational lens systems–to identify targets for current mm and anticipated Space VLBI programs–a morphological classification of compact radio sources at relatively high frequency with sub-mas resolution.

Similarity Classification of Cowen-Douglas Operators

2004 ◽  
Vol 56 (4) ◽  
pp. 742-775 ◽  
Author(s):  
Chunlan Jiang
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Linear Operators ◽  
List Type ◽  
Type Number ◽  
Bounded Linear ◽  
Similarity Classification ◽  
Strongly Irreducible ◽  
Connected Open Subset

AbstractLet ℋ be a complex separable Hilbert space and ℒ(ℋ) denote the collection of bounded linear operators on ℋ. An operator A in ℒ(ℋ) is said to be strongly irreducible, if , the commutant of A, has no non-trivial idempotent. An operator A in ℒ(ℋ) is said to be a Cowen-Douglas operator, if there exists Ω, a connected open subset of C, and n, a positive integer, such that(a)Ω ⊂ σ(A) = ﹛z ∈ C | A – z not invertible﹜;(b)ran(A – z) = ℋ, for z in Ω;(c)Vz∈Ω ker(A – z) = ℋ and(d)dim ker(A – z) = n for z in Ω.In the paper, we give a similarity classification of strongly irreducible Cowen-Douglas operators by using the K0-group of the commutant algebra as an invariant.

Neutralisation and Fusion of Vocalic Phonemes in Canadian English as Spoken in the Vancouver Area

1957 ◽  
Vol 3 (2) ◽  
pp. 78-83 ◽  
Author(s):  
R. J. Gregg
Keyword(s):  
Real World ◽  
List Type ◽  
Type Number ◽  
Canadian English ◽  
The Real ◽  
Younger Generation

1.In the last issue of the JCLA (March 1957) I made a tentative phonetic analysis of the English spoken by the younger generation in the Vancouver area. On the basis of that analysis I propose in this article to go on to the examination of one of the problems that face us in the phonemic classification of the Vancouver vowels.2.I should like to stress from the beginning that this problem is distributional, for whatever our views on the nature of the phoneme — whether we regard it as a concrete, practical unit, useful in the description of languages and dialects known or hitherto unknown, or whether we consider it as an abstract Platonic idea whose translation to the real world involves a series of Protean adaptations or adjustments to the phonological environment — in either case, the most important factor to be considered is distribution.

scholarly journals The Amygdala in Neurodegeneration

2021 ◽  
Vol 48 (s1) ◽  
pp. S5-S6
Author(s):  
JT Joseph
Keyword(s):  
Alzheimer Disease ◽  
Neurodegenerative Diseases ◽  
Lewy Body ◽  
Lewy Body Disease ◽  
Learning Objectives ◽  
List Type ◽  
Type Number ◽  
Anatomic Structure ◽  
Critical Aspects

The amygdala is a key anatomic structure that has multiple different nuclei and is involved in several critical aspects of cognition and systemic functions. Several different neurodegenerative diseases have major pathological effects on distinct amygdala nuclei. This presentation will describe the classic and characteristic anatomic distributions in the amygdala of “pure” Alzheimer disease and “pure” Lewy body disease, as well as “normal aging”. In addition, data will be presented on how these classic distributions are altered in either “mixed dementias” or in some atypical forms of neurodegeneration. Amygdala pathology will also be illustrated in several other neurodegenerative diseases. The implications of the differing anatomic distributions in different neurodegenerative diseases will be discussed.LEARNING OBJECTIVESThis presentation will enable the learner to:Recognize key anatomic divisions of the amygdala 1.Describe how different neurodegenerative diseases affect the amygdala2.Consider how anatomic specificity of protein aggregation is important in the classification of neurodegenerative diseases

The texture between grains

1994 ◽  
Vol 52 ◽  
pp. 616-617
Author(s):  
V. Randle
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Boundary Surface ◽  
Coincident Site Lattice ◽  
Electron Back Scatter Diffraction ◽  
List Type ◽  
Type Number ◽  
Grain Orientations ◽  
Boundary Properties

The ‘texture between grains’, sometimes called mesotexture, refers to the distribution of geometry/crystallography at grain boundaries and grain junctions (edges). These parameters can be accessed from measurements of individual grain orientations, and the most efficient means of collecting such data is by electron back-scatter diffraction (EBSD) in a scanning electron microscope. The reason for studying the texture at grain boundaries and junctions, on an individual basis, is that the properties of these defects (e.g. energy, mobility, diffusivity, resistivity etc) is geometry-dependent. It is desirable to investigate the nature of this relationship and how improved grain boundary properties might be achieved.The following information can be obtained:1.Misorientation across grain boundaries, allowing them to be classified as low/high angle, and according to the coincident site lattice model.2.The orientation of the grain boundary surface (plane) itself with respect to the lattice of each neighbouring grain.3.Classification of grain junctions as I-lines (dislocation balance) or U-lines (dislocation imbalance).4.The connectivity between grain boundaries, or between the grain boundary/junction networks.

Supersoluble Immersion

1959 ◽  
Vol 11 ◽  
pp. 353-369 ◽  
Author(s):  
Reinhold Baer
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Minimal Normal Subgroup ◽  
Independent Interest ◽  
List Type ◽  
Type Number ◽  
Group Of Automorphisms ◽  
A Finite Group ◽  
Subgroup J

Supersoluble immersion of a normal subgroup K of a finite group G shall be defined by the following property:If σ is a homomorphism of G, and if the minimal normal subgroup J of Gσ is part of Kσ then J is cyclic (of order a prime).Our principal aim in the present investigation is the proof of the equivalence of the following three properties of the normal subgroup K of the finite group G:(i)K is supersolubly immersed in G.(ii)K/ϕK is supersolubly immersed in G/ϕK.(iii)If θ is the group of automorphisms induced in the p-subgroup U of K by elements in the normalizer of U in G, then θ' θp-1 is a p-subgroup of θ.Though most of our discussion is concerned with the proof of this theorem, some of our concepts and results are of independent interest.

scholarly journals SOME COMMENTS ON A CATALOGUE OF ATMOSPHERIC PARAMETERS AND [Fe/H] DETERMINATIONS

1976 ◽  
Vol 72 ◽  
pp. 29-46
Author(s):  
G. Cayrel de Strobel
Keyword(s):  
Detailed Analysis ◽  
High Dispersion ◽  
Physical Parameters ◽  
List Type ◽  
Type Number ◽  
Spectral Classification ◽  
Atmospheric Parameters ◽  
Nearby Stars ◽  
The Impact

A few examples are given showing the utility of the catalogue of iron/hydrogen determinations for astrophysical researches. These are: (a)Histograms of dwarfs and giants analyzed in detail with spectral type between O and M.(b)Logarithmic abundances diagrams of given stars.(c)The impact on spectral classification of high-dispersion-detailed-analysis results.(d)The use of well-determined chemical and physical parameters of nearby stars for the construction of HR diagrams in the (Mbol –log Teff) plane.The spectra of F, G and K stars having the iron lines at their best visibility, special emphasis has been given to the results concerning these stars.

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