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.

scholarly journals Killing Vector Fields in Generalized Conformalβ-Change of Finsler Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Mallikarjun Yallappa Kumbar ◽  
Narasimhamurthy Senajji Kampalappa ◽  
Thippeswamy Komalobiah Rajanna ◽  
Kavyashree Ambale Rajegowda
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Finsler Space ◽  
Killing Vector ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finsler Spaces ◽  
Killing Vector Fields ◽  
Necessary And Sufficient

We consider a Finsler space equipped with a Generalized Conformalβ-change of metric and study the Killing vector fields that correspond between the original Finsler space and the Finsler space equipped with Generalized Conformalβ-change of metric. We obtain necessary and sufficient condition for a vector field Killing in the original Finsler space to be Killing in the Finsler space equipped with Generalized Conformalβ-change of metric.

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 Differential Equation Governing Torqued Vector Fields on a Riemannian Manifold

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1941
Author(s):  
Sharief Deshmukh ◽  
Nasser Bin Turki ◽  
Haila Alodan
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Euclidean Space ◽  
Riemannian Manifolds ◽  
Vector Fields ◽  
Compact Riemannian Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Rigidity Results ◽  
Necessary And Sufficient

In this article, we show that the presence of a torqued vector field on a Riemannian manifold can be used to obtain rigidity results for Riemannian manifolds of constant curvature. More precisely, we show that there is no torqued vector field on n-sphere Sn(c). A nontrivial example of torqued vector field is constructed on an open subset of the Euclidean space En whose torqued function and torqued form are nowhere zero. It is shown that owing to topology of the Euclidean space En, this type of torqued vector fields could not be extended globally to En. Finally, we find a necessary and sufficient condition for a torqued vector field on a compact Riemannian manifold to be a concircular vector field.

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

STABILIZING HIGHER PERIODIC ORBITS

1994 ◽  
Vol 04 (02) ◽  
pp. 457-460 ◽  
Author(s):  
M. PASKOTA ◽  
A.I. MEES ◽  
K.L. TEO
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
State Feedback ◽  
State Feedback Control ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Chaotic Dynamical Systems ◽  
Linear State ◽  
Necessary And Sufficient ◽  
Bounded Perturbations

In this paper, we consider stabilization of chaotic dynamical systems onto higher periodic orbits. We give a necessary and sufficient condition for using local linear state feedback control for this purpose. The control is achieved using small, bounded perturbations, and the method proposed is shown to be effective even in the presence of relatively small random dynamical noise.

Absolutely continuous conjugacy of expanding endomorphisms

1993 ◽  
Vol 13 (2) ◽  
pp. 225-230
Author(s):  
Carlos Arteaga
Keyword(s):  
Periodic Orbits ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Expanding Maps ◽  
Absolutely Continuous ◽  
Necessary And Sufficient

AbstractIn this article we consider conjugacies between differentiable expanding maps. We give a necessary and sufficient condition for a conjugating map to be absolutely continuous, in terms of the Jacobian around periodic orbits.

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.

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.

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