scholarly journals Dimensions of slowly escaping sets and annular itineraries for exponential functions

2015 ◽  
Vol 36 (7) ◽  
pp. 2273-2292 ◽  
Author(s):  
D. J. SIXSMITH
Keyword(s):  
Entire Function ◽  
Hausdorff Dimension ◽  
Exponential Family ◽  
Transcendental Entire Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Exponential Functions ◽  
Dynamical Properties ◽  
Necessary And Sufficient

We study the iteration of functions in the exponential family. We construct a number of sets, consisting of points which escape to infinity ‘slowly’, and which have Hausdorff dimension equal to$1$. We prove these results by using the idea of anannular itinerary. In the case of a general transcendental entire function we show that one of these sets, theuniformly slowly escaping set, has strong dynamical properties and we give a necessary and sufficient condition for this set to be non-empty.

scholarly journals Dynamical properties of some adic systems with arbitrary orderings

2016 ◽  
Vol 37 (7) ◽  
pp. 2131-2162 ◽  
Author(s):  
SARAH FRICK ◽  
KARL PETERSEN ◽  
SANDI SHIELDS
Keyword(s):  
Probability Measure ◽  
Fixed Points ◽  
Invariant Probability Measure ◽  
Random Order ◽  
Periodic Points ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Weakly Mixing ◽  
Dynamical Properties ◽  
Necessary And Sufficient

We consider arbitrary orderings of the edges entering each vertex of the (downward directed) Pascal graph. Each ordering determines an adic (Bratteli–Vershik) system, with a transformation that is defined on most of the space of infinite paths that begin at the root. We prove that for every ordering the coding of orbits according to the partition of the path space determined by the first three edges is essentially faithful, meaning that it is one-to-one on a set of paths that has full measure for every fully supported invariant probability measure. We also show that for every$k$the subshift that arises from coding orbits according to the first$k$edges is topologically weakly mixing. We give a necessary and sufficient condition for any adic system to be topologically conjugate to an odometer and use this condition to determine the probability that a random order on a fixed diagram, or a diagram constructed at random in some way, is topologically conjugate to an odometer. We also show that the closure of the union over all orderings of the subshifts arising from codings of the Pascal adic by the first edge has superpolynomial complexity, is not topologically transitive, and has no periodic points besides the two fixed points, while the intersection over all orderings consists of just four orbits.

Observability and Observer Design of a Class of Switched Linear Systems

2021 ◽  
Vol 69 (2) ◽  
pp. 68-75
Author(s):  
Noureddine GAZZAM ◽  
Kaouthar HADDADI ◽  
Atallah BENALIA
Keyword(s):  
Real Time ◽  
Switched Systems ◽  
State Observer ◽  
Observer Design ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Switching Sequence ◽  
Continuous State ◽  
Dynamical Properties ◽  
Necessary And Sufficient

This paper addresses the observability analysis and the observer design of the continuous state for a particular class of linear switched systems. Using some dynamical properties of considered systems, we give a simple necessary and sufficient condition of the observability for a predetermined switching sequence. The obtained observability condition leads us to design a new real time state observer. This latter is based on the exact accumulation of the information provided from the switching sequence of modes, and it convergences once the observability condition is verified. Some examples with simulation show the efficiency of the obtain observability condition and the proposed state observer.

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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