Cauchy’s Functional Equation, Schur’s Lemma, One-Dimensional Special Relativity, and Möbius’s Functional Equation

2018 ◽  
pp. 389-396 ◽  
Author(s):  
Teerapong Suksumran
Keyword(s):  
Functional Equation ◽  
Special Relativity ◽  
One Dimensional ◽  
Cauchy’S Functional Equation ◽  
Schur’S Lemma ◽  
Schur's Lemma

scholarly journals A Remark on the Orthogonality Relations in the Representation Theory of Finite Groups

1959 ◽  
Vol 11 ◽  
pp. 59-60 ◽  
Author(s):  
Hirosi Nagao
Keyword(s):  
Finite Group ◽  
Irreducible Representation ◽  
Representation Theory ◽  
Finite Groups ◽  
Characteristic Zero ◽  
Orthogonality Relations ◽  
Schur’S Lemma ◽  
Image Position ◽  
A Finite Group ◽  
Schur's Lemma

Let G be a finite group of order g, andbe an absolutely irreducible representation of degree fμ over a field of characteristic zero. As is well known, by using Schur's lemma (1), we can prove the following orthogonality relations for the coefficients :1It is easy to conclude from (1) the following orthogonality relations for characters:whereand is 1 or 0 according as t and s are conjugate in G or not, and n(t) is the order of the normalize of t.

scholarly journals Family Symmetries and Multi Higgs Doublet Models

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 156
Author(s):  
Bartosz Dziewit ◽  
Jacek Holeczek ◽  
Sebastian Zając ◽  
Marek Zrałek
Keyword(s):  
Standard Model ◽  
Higgs Doublet ◽  
Family Symmetry ◽  
The Standard Model ◽  
Schur’S Lemma ◽  
Finite Subgroups ◽  
Free Parameters ◽  
Schur's Lemma

Imposing a family symmetry on the Standard Model in order to reduce the number of its free parameters, due to the Schur’s Lemma, requires an explicit breaking of this symmetry. To avoid the need for this symmetry to break, additional Higgs doublets can be introduced. In such an extension of the Standard Model, we investigate family symmetries of the Yukawa Lagrangian. We find that adding a second Higgs doublet (2HDM) does not help, at least for finite subgroups of the U ( 3 ) group up to the order of 1025.

UNBOUNDED SETS OF ATTRACTION

2000 ◽  
Vol 10 (06) ◽  
pp. 1437-1469 ◽  
Author(s):  
GIAN-ITALO BISCHI ◽  
CHRISTIAN MIRA ◽  
LAURA GARDINI
Keyword(s):  
Functional Equation ◽  
Two Dimensional ◽  
Elementary Functions ◽  
Theoretical Methods ◽  
One Dimensional ◽  
Zero Measure ◽  
Analytical Expressions

In this paper we show that unbounded chaotic trajectories are easily observed in the iteration of maps which are not defined everywhere, due to the presence of a denominator which vanishes in a zero-measure set. Through simple examples, obtained by the iteration of one-dimensional and two-dimensional maps with denominator, the basic mechanisms which are at the basis of the existence of unbounded chaotic trajectories are explained. Moreover, new kinds of contact bifurcations, which mark the transition from bounded to unbounded sets of attraction, are studied both through the examples and by general theoretical methods. Some of the maps studied in this paper have been obtained by a method based on the Schröoder functional equation, which allows one to write closed analytical expressions of the unbounded chaotic trajectories, in terms of elementary functions.

Breaking of relativistic simple waves

1988 ◽  
Vol 196 ◽  
pp. 223-239 ◽  
Author(s):  
O. Muscato
Keyword(s):  
Special Relativity ◽  
Critical Time ◽  
Space Time ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Simple Waves ◽  
Magnetoacoustic Waves

The breaking of relativistic simple waves, for one-dimensional flow in the space-time of special relativity, is investigated. The cases of relativistic acoustic and magnetoacoustic waves are treated in detail and the critical time for breaking is evaluated.

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