scholarly journals Dissipative conformal measures on locally compact spaces

2014 ◽  
Vol 36 (2) ◽  
pp. 649-670 ◽  
Author(s):  
KLAUS THOMSEN
Keyword(s):  
Operator Algebras ◽  
Sufficient Conditions ◽  
Locally Compact ◽  
Compact Spaces ◽  
Ruelle Operator ◽  
Conformal Measures ◽  
Continuous Potential ◽  
The One ◽  
Necessary And Sufficient ◽  
Uniformly Continuous

The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among other things, the method is used to give necessary and sufficient conditions for the existence of eigenmeasures for the dual Ruelle operator associated to a locally compact non-compact irreducible Markov shift equipped with a uniformly continuous potential function. As an application to operator algebras the results are used to determine for which ${\it\beta}$ there are gauge invariant ${\it\beta}$-KMS weights on a simple graph $C^{\ast }$-algebra when the one-parameter automorphism group is given by a uniformly continuous real-valued function on the path space of the graph.

scholarly journals Topological entropy in totally disconnected locally compact groups

2016 ◽  
Vol 37 (7) ◽  
pp. 2163-2186 ◽  
Author(s):  
ANNA GIORDANO BRUNO ◽  
SIMONE VIRILI
Keyword(s):  
Topological Entropy ◽  
Sufficient Conditions ◽  
Invariant Subgroup ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Image Position ◽  
Necessary And Sufficient ◽  
Totally Disconnected ◽  
Dynamical Interpretation

Let $G$ be a topological group, let $\unicode[STIX]{x1D719}$ be a continuous endomorphism of $G$ and let $H$ be a closed $\unicode[STIX]{x1D719}$-invariant subgroup of $G$. We study whether the topological entropy is an additive invariant, that is, $$\begin{eqnarray}h_{\text{top}}(\unicode[STIX]{x1D719})=h_{\text{top}}(\unicode[STIX]{x1D719}\restriction _{H})+h_{\text{top}}(\bar{\unicode[STIX]{x1D719}}),\end{eqnarray}$$ where $\bar{\unicode[STIX]{x1D719}}:G/H\rightarrow G/H$ is the map induced by $\unicode[STIX]{x1D719}$. We concentrate on the case when $G$ is totally disconnected locally compact and $H$ is either compact or normal. Under these hypotheses, we show that the above additivity property holds true whenever $\unicode[STIX]{x1D719}H=H$ and $\ker (\unicode[STIX]{x1D719})\leq H$. As an application, we give a dynamical interpretation of the scale $s(\unicode[STIX]{x1D719})$ by showing that $\log s(\unicode[STIX]{x1D719})$ is the topological entropy of a suitable map induced by $\unicode[STIX]{x1D719}$. Finally, we give necessary and sufficient conditions for the equality $\log s(\unicode[STIX]{x1D719})=h_{\text{top}}(\unicode[STIX]{x1D719})$ to hold.

scholarly journals Translation and the Dialectics of Difference and Equivalence: Some Theoretical Propositions for a Redefinition of the Source-Target Text Relation

2002 ◽  
Vol 45 (2) ◽  
pp. 210-227 ◽  
Author(s):  
Lieven Tack
Keyword(s):  
Social Relations ◽  
Communication Theory ◽  
Sufficient Conditions ◽  
General Question ◽  
Source Text ◽  
The Social ◽  
The One ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Level Of Analysis

Abstract At which level of analysis (descriptivist, empirical, epistemological), and along which perspective (sociological, linguistical, communicative), should we locate the distinctive criteria for the definition of translation? In other words, what are the necessary and sufficient conditions which constitute the object « translation,» exclusively this object and not any other object? This is the general question of this article. It will be developped in two steps. First, we shall try to demonstrate that the perspective adopted by translatology, in defining translation by its semantical and fonctional equivalence relation with a source text, is congenetically determined by the discursive exclusion of the theorisation of that which is the very condition of possibility of each translation: the disrupture and distancing by which humans structure their social relation. Consequently, it is by the critique of communication theory, where a large part of translatology has drawn its scientific foundations, that we can deliver sound arguments for the assessing of translation in the structure of social relations. A second step consists in the formulation of a working hypothesis: if translation may be caused by the social dialectics of distancing and negociation of meaning, it is not sufficiently specified by this logic. It could be hypothesized that translation finds its specificity in the hybridity of the linguistic referential relation it instaures with the mute universe to be conceptualized on the one hand, and with the source text to be reformulated on the other.

scholarly journals ON HYBRID SEQUENCES BUILT FROM NIEDERREITER–HALTON SEQUENCES AND KRONECKER SEQUENCES

2011 ◽  
Vol 84 (2) ◽  
pp. 238-254 ◽  
Author(s):  
ROSWITHA HOFER ◽  
PETER KRITZER
Keyword(s):  
Uniform Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Future Research ◽  
Short Summary ◽  
The One ◽  
Halton Sequences ◽  
Necessary And Sufficient

AbstractWe discuss the distribution properties of hybrid sequences whose components stem from Niederreiter–Halton sequences on the one hand, and Kronecker sequences on the other. In this paper, we give necessary and sufficient conditions on the uniform distribution of such sequences, and derive a result regarding their discrepancy. We conclude with a short summary and a discussion of topics for future research.

scholarly journals The nonsmoth optimal control problem for ensamble of trajectories of dynamic system under conditions of indeterminaci

2020 ◽  
Vol 5 ◽  
pp. 38-42
Author(s):  
Otakulov Salim ◽  
Rahimov Boykxuroz Shermuhamedovich ◽  
Haydarov Tulkinjon Turgunbayevich
Keyword(s):  
Optimal Control ◽  
Dynamic System ◽  
Control Problem ◽  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Value Analysis ◽  
Minimax Control ◽  
Informational Model ◽  
The One ◽  
Necessary And Sufficient

In the paper we consider the one model of dynamic system under conditions of indeterminacy – linear controllable differential inclusions. For the informational model of the control system the minimax control problem for ensemble trajectories is researched. This control problem is study with a methods nonsmooth and multi-value analysis. The necessary and sufficient conditions of optimality are obtained.

scholarly journals A Hybrid Inversive Congruential Pseudorandom Number Generator with High Period

2021 ◽  
Vol 14 (1) ◽  
pp. 1-18
Author(s):  
Constanza Riera ◽  
Tapabrata Roy ◽  
Santanu Sarkar ◽  
Pantelimon Stanica
Keyword(s):  
Binary Sequence ◽  
Sufficient Conditions ◽  
Stochastic Simulations ◽  
Pseudorandom Number Generator ◽  
Pseudorandom Numbers ◽  
Congruential Generator ◽  
Congruential Pseudorandom Number ◽  
Full Period ◽  
The One ◽  
Necessary And Sufficient

Though generating a sequence of pseudorandom numbers by linear methods (Lehmer generator) displays acceptable behavior under some conditions of the parameters, it also has undesirable  features, which makes the sequence unusable for various stochastic simulations. An extension which showed promise for such applications is a generator obtained by using a first-order recurrence based upon the inversive modulo a prime or a prime power, called inversive congruential generator (ICG). A lot of work has been dedicated to investigate the periods (under some conditions of the parameters), the lattice test passing, discrepancy  and other statistical properties of such a generator. Here, we propose a new method, which we call hybrid inversive congruential generator (HICG), based upon a second order recurrence using the inversive modulo $M$, a power of 2. We investigate the period of this  pseudorandom numbers generator (PRNG) and give necessary and sufficient conditions for our PRNG to have periods $M$ (thereby doubling the period of the classical ICG) and $M/2$ (matching the one of the ICG). Moreover, we show that the lattice test complexity for a binary sequence associated to (a full period) HICG is precisely M/2.

Answerability

2018 ◽  
Author(s):  
Natalie Stoljar
Keyword(s):  
Moral Responsibility ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Alternative Approach ◽  
The One ◽  
Necessary And Sufficient

This chapter defends externalist or “constitutively relational” conceptions of autonomy through an examination of an alternative approach developed by Andrea Westlund. Westlund develops her approach in response to what has been called the “agency dilemma.” On the one hand, constraining external circumstances seem to undermine autonomy; on the other, the claim that people are nonautonomous because of their circumstances seems to erase their agency and disrespect their evaluative commitments. This chapter distinguishes the necessary and sufficient conditions of several interrelated aspects of agency: autonomy, authentic agential perspective, and moral responsibility. I argue that whereas answerability may be sufficient for moral responsibility, it is not sufficient for autonomy. Objections to externalist conceptions of autonomy, including the agency dilemma, wrongly assume that denying autonomy implies erasing agency. Once it is recognized that autonomy does not always overlap with authentic agential perspective or moral responsibility, the objections lose their force.

Essentials of General Topology

2021 ◽  
pp. 191-244
Author(s):  
Adel N. Boules
Keyword(s):  
Topological Spaces ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Compact Spaces ◽  
Section 8 ◽  
Finite Products ◽  
The One ◽  
One Point Compactification ◽  
Locally Compact Spaces ◽  
Metrization Theorem

The first eight sections of this chapter constitute its core and are generally parallel to the leading sections of chapter 4. Most of the sections are brief and emphasize the nonmetric aspects of topology. Among the topics treated are normality, regularity, and second countability. The proof of Tychonoff’s theorem for finite products appears in section 8. The section on locally compact spaces is the transition between the core of the chapter and the more advanced sections on metrization, compactification, and the product of infinitely many spaces. The highlights include the one-point compactification, the Urysohn metrization theorem, and Tychonoff’s theorem. Little subsequent material is based on the last three sections. At various points in the book, it is explained how results stated for the metric case can be extended to topological spaces, especially locally compact Hausdorff spaces. Some such results are developed in the exercises.

scholarly journals Maximal topologies

1973 ◽  
Vol 15 (3) ◽  
pp. 279-290 ◽  
Author(s):  
Asit Baran Raha
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Compact Spaces ◽  
Other Hand ◽  
Countably Compact ◽  
Countably Compact Spaces ◽  
Necessary And Sufficient

This article is devoted to studying maximal π spaces where π = Lindelöf, countably compact, connected, lightly compact or pseudocompact. Necessary and sufficient conditions for Lindelöf or countably compact spaces to be maximal Lindelöf or maximal countably compact have been obtained. On the other hand only necessary conditions for maximal π spaces have been deduced where π = connected, lightly compact or pseudocompact.

scholarly journals Condensor Principle and the Unit Contraction

1967 ◽  
Vol 30 ◽  
pp. 9-28 ◽  
Author(s):  
Masayuki Itô
Keyword(s):  
Positive Measure ◽  
Hausdorff Space ◽  
Sufficient Conditions ◽  
Dirichlet Space ◽  
Functional Space ◽  
Dirichlet Spaces ◽  
Locally Compact ◽  
Necessary And Sufficient ◽  
Regular Functional ◽  
Locally Compact Hausdorff Space

Deny introduced in [4] the notion of functional spaces by generalizing Dirichlet spaces. In this paper, we shall give the following necessary and sufficient conditions for a functional space to be a real Dirichlet space.Let be a regular functional space with respect to a locally compact Hausdorff space X and a positive measure ξ in X. The following four conditions are equivalent.

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