scholarly journals On the representations of the braid group constructed by C. M. Egea and E. Galina

2021 ◽  
Author(s):  
Rana S. Kahil ◽  
Mohammad N. Abdulrahim
Keyword(s):  
Braid Group ◽  
Sufficient Condition ◽  
The Family

AbstractIn this paper, we determine a sufficient condition for the irreducibility of the family of representations of the braid group constructed by C. M. Egea and E. Galina without requiring that the representations are self-adjoint. Then, we construct a new subfamily of multi-parameter representations $$(\psi _m,V_m), $$ ( ψ m , V m ) , $$1\le m< n$$ 1 ≤ m < n , of dimension $$ V_m =\left( {\begin{array}{c}n\\ m\end{array}}\right) $$ V m = n m . Finally, we study the irreducibility of $$(\psi _m,V_m) $$ ( ψ m , V m ) .

Binomial subsampling

2006 ◽  
Vol 462 (2068) ◽  
pp. 1181-1195 ◽  
Author(s):  
Carsten Wiuf ◽  
Michael P.H Stumpf
Keyword(s):  
Mathematical Biology ◽  
Power Series ◽  
Generating Functions ◽  
Binomial Distribution ◽  
Random Variable ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Family ◽  
Necessary And Sufficient ◽  
Finite Moments

In this paper, we discuss statistical families with the property that if the distribution of a random variable X is in , then so is the distribution of Z ∼Bi( X ,  p ) for 0≤ p ≤1. (Here we take Z ∼Bi( X ,  p ) to mean that given X = x ,  Z is a draw from the binomial distribution Bi( x ,  p ).) It is said that the family is closed under binomial subsampling. We characterize such families in terms of probability generating functions and for families with finite moments of all orders we give a necessary and sufficient condition for the family to be closed under binomial subsampling. The results are illustrated with power series and other examples, and related to examples from mathematical biology. Finally, some issues concerning inference are discussed.

Quantum Feller semigroup in terms of quantum Bernoulli noises

2020 ◽  
pp. 2150015
Author(s):  
Jinshu Chen
Keyword(s):  
Local Structure ◽  
Identity Operator ◽  
Sufficient Condition ◽  
Markov Semigroups ◽  
Feller Semigroup ◽  
Abelian Subalgebra ◽  
Feller Property ◽  
The Family ◽  
Invariant States ◽  
Creation Operators

Quantum Bernoulli noises (QBN) are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anti-commutation relation in equal-time. In this paper, we aim to investigate quantum Feller semigroups in terms of QBN. We first investigate local structure of the algebra generated by identity operator and QBN. We then use our new results obtained here to construct a class of quantum Markov semigroups from QBN which enjoy Feller property. As an application of our results, we examine a special quantum Feller semigroup associated with QBN, when it reduced to a certain Abelian subalgebra, the semigroup gives rise to the semigroup generated by Ornstein–Uhlenbeck operator. Finally, we find a sufficient condition for the existence of faithful invariant states that are diagonal for the semigroup.

scholarly journals Dunkl harmonic analysis and fundamental sets of continuous functions on the unit sphere

2015 ◽  
Vol 6 (3) ◽  
Author(s):  
Roman A. Veprintsev
Keyword(s):  
Continuous Function ◽  
Harmonic Analysis ◽  
Unit Sphere ◽  
Continuous Functions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Family ◽  
Necessary And Sufficient

AbstractWe establish a necessary and sufficient condition on a continuous function on [-1,1] under which the family of functions on the unit sphere 𝕊

Comparison of density topologies on the real line

2018 ◽  
Vol 68 (1) ◽  
pp. 173-180
Author(s):  
Renata Wiertelak
Keyword(s):  
Real Line ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Real Numbers ◽  
The Real ◽  
Closed Intervals ◽  
The Family ◽  
Necessary And Sufficient

Abstract In this paper will be considered density-like points and density-like topology in the family of Lebesgue measurable subsets of real numbers connected with a sequence 𝓙= {Jn}n∈ℕ of closed intervals tending to zero. The main result concerns necessary and sufficient condition for inclusion between that defined topologies.

SYSTOLIC TREE WITH BASE AUTOMATA

1991 ◽  
Vol 02 (03) ◽  
pp. 221-236 ◽  
Author(s):  
A. MONTI ◽  
D. PARENTE
Keyword(s):  
Sufficient Condition ◽  
Tree Automata ◽  
Necessary And Sufficient Condition ◽  
The Family ◽  
Emptiness Problem ◽  
Necessary And Sufficient ◽  
Natural Way

Different systolic tree automata (STA) with base (T(b)−STA) are compared. This is a subclass of STA with interesting properties of modularity. We give a necessary and sufficient condition for the inclusion between classes of languages accepted by T(b)− STA, (L(T(b)−STA)), as b varies. We focus on T(b)−STA obtained by varying the base b in a natural way. We prove that for every base b within this framework there exists an a such that L(T(a)−STA) is not contained in L(T(b)−STA). We characterize the family of languages accepted by T(b)−STA when the input conditions are relaxed. Moreover we show that the emptiness problem is decidable for T(b)−STA.

Local connectedness of the Julia set of the family $z^m(z^n-b)$

1998 ◽  
Vol 18 (2) ◽  
pp. 457-470 ◽  
Author(s):  
MARYAM RABII
Keyword(s):  
Julia Set ◽  
Sufficient Condition ◽  
Local Connectivity ◽  
Local Connectedness ◽  
The Family

We study the local connectedness of the Julia set of the family $f_b(z)=z^m(z^n-b)$. Assuming that the Julia set is connected and depending on whether $m=1$ or $m>1$, a sufficient condition for the local connectivity of the Julia set is obtained. This complements the known results of Yoccoz–Hubbard–Branner for $m=n=1$.

Atomic systems for operators

2019 ◽  
Vol 17 (01) ◽  
pp. 1850066 ◽  
Author(s):  
Khole Timothy Poumai ◽  
Shah Jahan
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Atomic System ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Bessel Sequence ◽  
Atomic Systems ◽  
The Family ◽  
Necessary And Sufficient

Gavruta [L. Gavruta, Frames for operators, Appl. Comput. Harmon. Anal. 32 (2012) 139–144] introduced the notion of [Formula: see text]-frame and atomic system for an operator [Formula: see text] in Hilbert spaces. We extend these notions to Banach spaces and obtain various new results. A necessary and sufficient condition for the existence of an atomic system for an operator [Formula: see text] in a Banach space is given. Also, a characterization for the family of local atoms of subspaces of Banach spaces has been given. Further, we give methods to construct an atomic system for an operator [Formula: see text] from a given Bessel sequence and an [Formula: see text]-Bessel sequence. Finally, a result related to stability of atomic system for an operator [Formula: see text] in a Banach space has been given.

scholarly journals Convective Cores in Stellar Models

1991 ◽  
Vol 130 ◽  
pp. 95-97
Author(s):  
I.W. Roxburgh ◽  
M. Monteiro
Keyword(s):  
Linear Function ◽  
Power Laws ◽  
Energy Generation ◽  
Polytropic Index ◽  
Sufficient Condition ◽  
The Family ◽  
Stellar Models

AbstractThe condition for homogeneous radiative stellar models to be marginally stable to convection at the centre is investigated for the family of models where the opacity к and energy generation ε are given by power laws in temperature and density κ = κo ρα T−β, ε = εo ρ Tη. The Naur-Osterbrock (1953) condition 6η > 6 + 10β − 15α is a necessary but not sufficient condition. A better estimate is obtained by taking the effective polytropic index n = dlogP/dlogT - 1 to be a linear function of temperature T throughout the model. This gives the conditionThe predictions of this condition agree well with results for a set of stellar models 0 ≤ α ≤ 1, 0≤ β ≤ 5.

scholarly journals Classifying Spaces for the Family of Virtually Cyclic Subgroups of Braid Groups

2018 ◽  
Vol 2020 (5) ◽  
pp. 1575-1600
Author(s):  
Ramón Flores ◽  
Juan González-Meneses
Keyword(s):  
Braid Group ◽  
Braid Groups ◽  
Classifying Spaces ◽  
Classifying Space ◽  
Cyclic Subgroups ◽  
Cyclic Groups ◽  
Pure Braid Group ◽  
Minimal Dimension ◽  
The Family

Abstract We prove that, for n ≥ 3, the minimal dimension of a model of the classifying space of the braid group $B_{n}$, and of the pure braid group $P_{n}$, with respect to the family of virtually cyclic groups is n.

scholarly journals NORMALIZED EIGENVECTORS OF A PERTURBED LINEAR OPERATOR VIA GENERAL BIFURCATION

2008 ◽  
Vol 50 (2) ◽  
pp. 303-318 ◽  
Author(s):  
RAFFAELE CHIAPPINELLI ◽  
MASSIMO FURI ◽  
MARIA PATRIZIA PERA
Keyword(s):  
Linear Operator ◽  
Bifurcation Point ◽  
Additional Assumption ◽  
Real Banach Space ◽  
Sufficient Conditions ◽  
Continuous Operator ◽  
Sufficient Condition ◽  
Bounded Linear ◽  
One Dimensional ◽  
The Family

AbstractLetXbe a real Banach space,A:X→Xa bounded linear operator, andB:X→Xa (possibly nonlinear) continuous operator. Assume that λ = 0 is an eigenvalue ofAand consider the family of perturbed operatorsA+ ϵB, where ϵ is a real parameter. Denote bySthe unit sphere ofXand letSA=S∩ KerAbe the set of unit 0-eigenvectors ofA. We say that a vectorx0∈SAis abifurcation pointfor the unit eigenvectors ofA+ ϵBif any neighborhood of (0,0,x0) ∈$\R$×$\R$×Xcontains a triple (ϵ, λ,x) with ϵ ≠ 0 andxa unit λ-eigenvector ofA+ ϵB, i.e.x∈Sand (A+ ϵB)x= λx.We give necessary as well as sufficient conditions for a unit 0-eigenvector ofAto be a bifurcation point for the unit eigenvectors ofA+ ϵB. These conditions turn out to be particularly meaningful when the perturbing operatorBis linear. Moreover, since our sufficient condition is trivially satisfied when KerAis one-dimensional, we extend a result of the first author, under the additional assumption thatBis of classC2.

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