scholarly journals Embedding subshifts of finite type into the Fibonacci–Dyck shift

2016 ◽  
Vol 37 (6) ◽  
pp. 1862-1886
Author(s):  
TOSHIHIRO HAMACHI ◽  
WOLFGANG KRIEGER
Keyword(s):  
Finite Type ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Subshift Of Finite Type ◽  
Subshifts Of Finite Type ◽  
Necessary And Sufficient

A necessary and sufficient condition is given for the existence of an embedding of an irreducible subshift of finite type into the Fibonacci–Dyck shift.

Automorphism Groups of Algebras of Finite Type

1972 ◽  
Vol 24 (6) ◽  
pp. 1065-1069 ◽  
Author(s):  
Matthew Gould
Keyword(s):  
Automorphism Group ◽  
Finite Number ◽  
Finite Type ◽  
Permutation Group ◽  
Universal Algebra ◽  
Automorphism Groups ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

By “algebra” we shall mean a finitary universal algebra, that is, a pair 〈A; F〉 where A and F are nonvoid sets and every element of F is a function, defined on A, of some finite number of variables. Armbrust and Schmidt showed in [1] that for any finite nonvoid set A, every group G of permutations of A is the automorphism group of an algebra defined on A and having only one operation, whose rank is the cardinality of A. In [6], Jónsson gave a necessary and sufficient condition for a given permutation group to be the automorphism group of an algebra, whereupon Plonka [8] modified Jonsson's condition to characterize the automorphism groups of algebras whose operations have ranks not exceeding a prescribed bound.

scholarly journals Friezes and continuant polynomials with parameters

2018 ◽  
Vol 36 (2) ◽  
pp. 57-81
Author(s):  
Véronique Bazier-Matte ◽  
David Racicot-Desloges ◽  
Tanna Sánchez McMillan
Keyword(s):  
Finite Type ◽  
Type A ◽  
Cluster Algebras ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
New Family ◽  
Laurent Phenomenon ◽  
Necessary And Sufficient ◽  
Positive Integers

Frieze patterns (in the sense of Conway and Coxeter) are related to cluster algebras of type A and to signed continuant polynomials. In view of studying certain classes of cluster algebras with coefficients, we extend the concept of signed continuant polynomial to define a new family of friezes, called c-friezes, which generalises frieze patterns. Having in mind the cluster algebras of finite type, we identify a necessary and sufficient condition for obtaining periodic c-friezes. Taking into account the Laurent phenomenon and the positivity conjecture, we present ways of generating c-friezes of integers and of positive integers. We also show some specific properties of c-friezes.

scholarly journals A note on a class of Banach algebra-valued polynomials

2002 ◽  
Vol 32 (3) ◽  
pp. 189-192
Author(s):  
Sin-Ei Takahasi ◽  
Osamu Hatori ◽  
Keiichi Watanabe ◽  
Takeshi Miura
Keyword(s):  
Banach Algebra ◽  
Finite Type ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Dimensional ◽  
Necessary And Sufficient

LetFbe a Banach algebra. We give a necessary and sufficient condition forFto be finite dimensional, in terms of finite typen-homogeneousF-valued polynomials.

scholarly journals A CHARACTERIZATION OF SATURATED C*-ALGEBRAIC BUNDLES OVER FINITE GROUPS

2010 ◽  
Vol 88 (3) ◽  
pp. 363-383
Author(s):  
KAZUNORI KODAKA ◽  
TAMOTSU TERUYA
Keyword(s):  
Finite Group ◽  
Finite Type ◽  
Finite Groups ◽  
Conditional Expectation ◽  
Crossed Product ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
A Finite Group ◽  
Necessary And Sufficient

AbstractLet A be a unital C*-algebra. Let (B,E) be a pair consisting of a unital C*-algebra B containing A as a C*-subalgebra with a unit that is also the unit of B, and a conditional expectation E from B onto A that is of index-finite type and of depth 2. Let B1 be the C*-basic construction induced by (B,E). In this paper, we shall show that any such pair (B,E) satisfying the conditions that A′∩B=ℂ1 and that A′∩B1 is commutative is constructed by a saturated C*-algebraic bundle over a finite group. Furthermore, we shall give a necessary and sufficient condition for B to be described as a twisted crossed product of A by its twisted action of a finite group under the condition that A′∩B1 is commutative.

scholarly journals Matrix characterization of multidimensional subshifts of finite type

2019 ◽  
Vol 20 (2) ◽  
pp. 407
Author(s):  
Puneet Sharma ◽  
Dileep Kumar
Keyword(s):  
Finite Type ◽  
Sufficient Conditions ◽  
Periodic Points ◽  
Alternative View ◽  
Subshift Of Finite Type ◽  
Shift Space ◽  
The Matrix ◽  
Subshifts Of Finite Type ◽  
Necessary And Sufficient

<p>Let X ⊂ A<sup>Zd </sup>be a 2-dimensional subshift of finite type. We prove that any 2-dimensional subshift of finite type can be characterized by a square matrix of infinite dimension. We extend our result to a general d-dimensional case. We prove that the multidimensional shift space is non-empty if and only if the matrix obtained is of positive dimension. In the process, we give an alternative view of the necessary and sufficient conditions obtained for the non-emptiness of the multidimensional shift space. We also give sufficient conditions for the shift space X to exhibit periodic points.</p>

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

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