Metric properties of endomorphisms of compact groups

1968 ◽  
pp. 63-98 ◽  
Author(s):  
S. A. Juzvinskiĭ
Keyword(s):  
Compact Groups ◽  
Metric Properties

scholarly journals Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 80
Author(s):  
Sergey Kryzhevich ◽  
Viktor Avrutin ◽  
Nikita Begun ◽  
Dmitrii Rachinskii ◽  
Khosro Tajbakhsh
Keyword(s):  
Risk Management ◽  
Invariant Measure ◽  
Invariant Measures ◽  
Interval Exchange ◽  
Management Model ◽  
Closing Lemma ◽  
Symbolic Model ◽  
Metric Properties ◽  
Ergodic Measures ◽  
Maximal Invariant

We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and demonstrated that an ITM, endowed with such a measure, is metrically conjugated to an interval exchange map (IEM). This allowed us to extend some properties of IEMs (e.g., an estimate of the number of ergodic measures and the minimality of the symbolic model) to ITMs. Further, we proved a version of the closing lemma and studied how the invariant measures depend on the parameters of the system. These results were illustrated by a simple example or a risk management model where interval translation maps appear naturally.

scholarly journals Compact groups with a set of positive Haar measure satisfying a nilpotent law

2021 ◽  
pp. 1-4
Author(s):  
ALIREZA ABDOLLAHI ◽  
MEISAM SOLEIMANI MALEKAN
Keyword(s):  
Compact Group ◽  
Haar Measure ◽  
Positive Answer ◽  
Nilpotent Subgroup ◽  
Compact Groups

Abstract The following question is proposed by Martino, Tointon, Valiunas and Ventura in [4, question 1·20]: Let G be a compact group, and suppose that \[\mathcal{N}_k(G) = \{(x_1,\dots,x_{k+1}) \in G^{k+1} \;|\; [x_1,\dots, x_{k+1}] = 1\}\] has positive Haar measure in $G^{k+1}$ . Does G have an open k-step nilpotent subgroup? We give a positive answer for $k = 2$ .

scholarly journals Tracing interactions in HCGs through the H I

2000 ◽  
Vol 174 ◽  
pp. 167-173 ◽  
Author(s):  
L. Verdes-Montenegro ◽  
M. S. Yun ◽  
B. A. Williams ◽  
W. K. Huchtmeier ◽  
A. Del Olmo ◽  
...  
Keyword(s):  
Velocity Dispersion ◽  
Group Velocity Dispersion ◽  
Dynamical Evolution ◽  
Compact Groups ◽  
High Group ◽  
X Ray ◽  
Hot Gas ◽  
Isolated Galaxies ◽  
Global Study ◽  
Hickson Compact Groups

AbstractWe present a global study of Hɪ spectral line mapping for 16 Hickson Compact Groups (HCGs) combining new and unpublished VLA data, plus the analysis of the Hɪ content of individual galaxies. Sixty percent of the groups show morphological and kinematical signs of perturbations (from multiple tidal features to concentration of the Hɪ in a single enveloping cloud) and sixty five of the resolved galaxies are found to be Hɪ deficient with respect to a sample of isolated galaxies. In total, 77% of the groups suffer interactions among all its members which provides strong evidence of their reality. We find that dynamical evolution does not always produce Hɪ deficiency, but when this deficiency is observed, it appears to correlate with a high group velocity dispersion and in some cases with the presence of a first-ranked elliptical. The X-ray data available for our sample are not sensitive enough for a comparison with the Hɪ mass; however this study does suggest a correlation between Hɪ deficiency and hot gas since velocity dispersions are known from the literature to correlate with X-ray luminosity.

scholarly journals Characters and group invariant polynomials of (super)fields: road to “Lagrangian”

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
Upalaparna Banerjee ◽  
Joydeep Chakrabortty ◽  
Suraj Prakash ◽  
Shakeel Ur Rahaman
Keyword(s):  
Standard Model ◽  
Explicit Construction ◽  
Effective Field ◽  
Compact Groups ◽  
Group Invariant ◽  
Fundamental Particles ◽  
Quantum Numbers ◽  
The Standard Model ◽  
Mass Dimension ◽  
Complete Set

AbstractThe dynamics of the subatomic fundamental particles, represented by quantum fields, and their interactions are determined uniquely by the assigned transformation properties, i.e., the quantum numbers associated with the underlying symmetry of the model under consideration. These fields constitute a finite number of group invariant operators which are assembled to build a polynomial, known as the Lagrangian of that particular model. The order of the polynomial is determined by the mass dimension. In this paper, we have introduced an automated $${\texttt {Mathematica}}^{\tiny \textregistered }$$ Mathematica ® package, GrIP, that computes the complete set of operators that form a basis at each such order for a model containing any number of fields transforming under connected compact groups. The spacetime symmetry is restricted to the Lorentz group. The first part of the paper is dedicated to formulating the algorithm of GrIP. In this context, the detailed and explicit construction of the characters of different representations corresponding to connected compact groups and respective Haar measures have been discussed in terms of the coordinates of their respective maximal torus. In the second part, we have documented the user manual of GrIP that captures the generic features of the main program and guides to prepare the input file. We have attached a sub-program CHaar to compute characters and Haar measures for $$SU(N), SO(2N), SO(2N+1), Sp(2N)$$ S U ( N ) , S O ( 2 N ) , S O ( 2 N + 1 ) , S p ( 2 N ) . This program works very efficiently to find out the higher mass (non-supersymmetric) and canonical (supersymmetric) dimensional operators relevant to the effective field theory (EFT). We have demonstrated the working principles with two examples: the standard model (SM) and the minimal supersymmetric standard model (MSSM). We have further highlighted important features of GrIP, e.g., identification of effective operators leading to specific rare processes linked with the violation of baryon and lepton numbers, using several beyond standard model (BSM) scenarios. We have also tabulated a complete set of dimension-6 operators for each such model. Some of the operators possess rich flavour structures which are discussed in detail. This work paves the way towards BSM-EFT.

scholarly journals The Walking Index for Spinal Cord Injury (WISCI/WISCI II): nature, metric properties, use and misuse

Spinal Cord ◽  
2013 ◽  
Vol 51 (5) ◽  
pp. 346-355 ◽  
Author(s):  
J F Ditunno ◽  
P L Ditunno ◽  
G Scivoletto ◽  
M Patrick ◽  
M Dijkers ◽  
...  
Keyword(s):  
Spinal Cord ◽  
Spinal Cord Injury ◽  
Metric Properties ◽  
Cord Injury
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