scholarly journals Minimality for actions of abelian semigroups on compact spaces with a free interval

2018 ◽  
Vol 39 (11) ◽  
pp. 2968-2982
Author(s):  
MATÚŠ DIRBÁK ◽  
ROMAN HRIC ◽  
PETER MALIČKÝ ◽  
L’UBOMÍR SNOHA ◽  
VLADIMÍR ŠPITALSKÝ
Keyword(s):  
Topological Structure ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Hausdorff Spaces ◽  
Abelian Semigroup ◽  
Minimal Action ◽  
Compact Spaces ◽  
Free Interval ◽  
Continuous Actions ◽  
Necessary And Sufficient

We study minimality for continuous actions of abelian semigroups on compact Hausdorff spaces with a free interval. First, we give a necessary and sufficient condition for such a space to admit a minimal action of a given abelian semigroup. Further, for actions of abelian semigroups we provide a trichotomy for the topological structure of minimal sets intersecting a free interval.

The Topological Structure Code Permutation Group Method of Polyhedral Solid for Identification of Kinematic Chains Isomorphism

1998 ◽  
Author(s):  
Chuan-He Liu ◽  
Ting-Li Yang
Keyword(s):  
Permutation Group ◽  
Topological Structure ◽  
Group Method ◽  
Solid Model ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Kinematic Chains ◽  
Geometric Solids ◽  
Necessary And Sufficient ◽  
Structure Code

Abstract This paper puts forward a new method for identification of kinematic chains isomorphism, which is called the topological structure code permutation group method of polyhedral solid. It can be put into practice by means of computer, and it is exact, dependable, quick and efficient. When isomorphism of two kinematic chains is identified by the method, it only need determine whether one permutation can be found out or not between topological structure codes of the two kinematic chains, or determine whether adjoint codes of the two topological structure codes are equal or not, it need not find out a symmetry group at all. It applies to all kinds of non-separable closed kinematic chains that don’t contain compound hinges. In this paper, a new concept called polyhedral solid is put forward, the polyhedral solid model is given, and a theorem that describes the relation of faces, vertices, edges and geometric solids of a connected graph is given and proved. This paper expounds the definitions and general forms of the topological structure code and its adjoint code, the methods and rules of coding, the procedure of generating them. It also expounds and proves the beingness, accuracy and the uniqueness of the topological structure code and its adjoint code and the necessary and sufficient condition and criteria of kinematic chains isomorphism as well. The algorithm and some typical examples for identification of kinematic chains isomorphism are given.

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.

scholarly journals Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser
Keyword(s):  
Point Of View ◽  
Sufficient Condition ◽  
Use Of Self ◽  
Necessary And Sufficient Condition ◽  
Wigner Rotation ◽  
Inertial Frames ◽  
Explicit Formulae ◽  
Specific Implementation ◽  
Necessary And Sufficient ◽  
Lorentz Boosts

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

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