Diagram approach to character formulas for finite and compact groups

1979 ◽  
Vol 16 (6) ◽  
pp. 1161-1194 ◽  
Author(s):  
M. Kibler ◽  
E. Elbaz
Keyword(s):  
Compact Groups ◽  
Character Formulas ◽  
Diagram Approach

SETTING A DIAGRAM APPROACH TO CALCULATING VIBRATED, CENTRIFUGED AND VIBROCENTRIFUGED REINFORCED CONCRETE COLUMNS WITH A VARIATROPIC STRUCTURE

2020 ◽  
pp. 22-34
Author(s):  
Л. Р. Маилян ◽  
С. А. Стельмах ◽  
Е. М. Щербань ◽  
М. П. Нажуев
Keyword(s):  
Experimental Data ◽  
Reinforced Concrete ◽  
Bearing Capacity ◽  
Cross Section ◽  
Concrete Columns ◽  
Reinforced Concrete Columns ◽  
The Cross ◽  
Concrete Elements ◽  
Diagram Approach

Состояние проблемы. Железобетонные элементы изготавливаются, как правило, по трем основным технологиям - вибрированием, центрифугированием и виброцентрифугированием. Однако все основные расчетные зависимости для определения их несущей способности выведены, исходя из основного постулата - постоянства и равенства характеристик бетона по сечению, что реализуется лишь в вибрированных колоннах. Результаты. В рамках диаграммного подхода предложены итерационный, приближенный и упрощенный способы расчета несущей способности железобетонных вибрированных, центрифугированных и виброцентрифугированных колонн. Выводы. Расчет по диаграммному подходу показал существенно более подходящую сходимость с опытными данными, чем расчет по методике норм, а также дал лучшие результаты при использовании дифференциальных характеристик бетона, чем при использовании интегральных и, тем более, нормативных характеристик бетона. Statement of the problem. Reinforced concrete elements are typically manufactured according to three basic technologies - vibration, centrifugation and vibrocentrifugation. However, all the basic calculated dependencies for determining their bearing capacity were derived using the main postulate, i.e., the constancy and equality of the characteristics of concrete over the cross section, which is implemented only in vibrated columns. Results. Within the framework of the diagrammatic approach, iterative, approximate and simplified methods of calculating the bearing capacity of reinforced concrete vibrated, centrifuged and vibrocentrifuged columns are proposed. Conclusions. The calculation according to the diagrammatic approach showed a significantly better convergence with the experimental data than that using the method of norms, and also performs better when using differential characteristics of concrete than when employing integral and particularly standard characteristics of concrete.

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.

On the Lp-conjecture for locally compact groups

2007 ◽  
Vol 89 (3) ◽  
pp. 237-242 ◽  
Author(s):  
F. Abtahi ◽  
R. Nasr-Isfahani ◽  
A. Rejali
Keyword(s):  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact
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