scholarly journals On the Fourier Transformability of Strongly Almost Periodic Measures

2019 ◽  
Vol 72 (4) ◽  
pp. 900-927
Author(s):  
Nicolae Strungaru
Keyword(s):  
Fourier Transform ◽  
Large Class ◽  
Integrability Condition ◽  
Sufficient Condition ◽  
Almost Periodic ◽  
Necessary And Sufficient Condition ◽  
Periodic Measure ◽  
Tempered Distribution ◽  
The Fourier Transform ◽  
Necessary And Sufficient

AbstractIn this paper we characterize the Fourier transformability of strongly almost periodic measures in terms of an integrability condition for their Fourier–Bohr series. We also provide a necessary and sufficient condition for a strongly almost periodic measure to be the Fourier transform of a measure. We discuss the Fourier transformability of a measure on $\mathbb{R}^{d}$ in terms of its Fourier transform as a tempered distribution. We conclude by looking at a large class of such measures coming from the cut and project formalism.

scholarly journals Vector fields with transverse foliations, II

1986 ◽  
Vol 6 (2) ◽  
pp. 193-203 ◽  
Author(s):  
Sue Goodman
Keyword(s):  
Large Class ◽  
Periodic Orbits ◽  
Vector Fields ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complete Answer ◽  
Necessary And Sufficient ◽  
Singular Flow ◽  
Chain Recurrent Set ◽  
Recurrent Set

AbstractWhen does a non-singular flow on a 3-manifold have a 2-dimensional foliation everywhere transverse to it? A complete answer is given for a large class of flows, those with 1-dimensional hyperbolic chain recurrent set. We find a simple necessary and sufficient condition on the linking of periodic orbits of the flow.

An Oscillation Result for Singular Neutral Equations

1994 ◽  
Vol 37 (1) ◽  
pp. 54-65
Author(s):  
István Gyori ◽  
Janos Turi
Keyword(s):  
Large Class ◽  
Difference Operator ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Neutral Equations ◽  
Oscillation Result ◽  
The Difference ◽  
Necessary And Sufficient

AbstractIn this paper, extending the results in [ 1 ], we establish a necessary and sufficient condition for oscillation in a large class of singular (i.e., the difference operator is nonatomic) neutral equations.

scholarly journals On the Equationally Artinian Groups

2020 ◽  
pp. 583-595
Author(s):  
Mohammad Shahryari ◽  
Javad Tayyebi
Keyword(s):  
Abelian Group ◽  
Normal Subgroup ◽  
Large Class ◽  
Finite Extension ◽  
Finite Union ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Closed Sets ◽  
Necessary And Sufficient

In this article, we study the property of being equationally Artinian in groups. We define the radical topology corresponding to such groups and investigate the structure of irreducible closed sets of these topologies. We prove that a finite extension of an equationally Artinian group is again equationally Artinian. We also show that a quotient of an equationally Artinian group of the form G[t] by a normal subgroup which is a finite union of radicals, is again equationally Artnian. A necessary and sufficient condition for an Abelian group to be equationally Artinian will be given as the last result. This will provide a large class of examples of equationally Artinian groups

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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