GENERAL ENTROPY OF GENERAL MEASURES

2002 ◽  
Vol 10 (03) ◽  
pp. 213-225 ◽  
Author(s):  
ALEXANDER DUKHOVNY
Keyword(s):  
Sufficient Condition ◽  
Independence Property ◽  
General Entropy ◽  
Definition Of ◽  
Additive Measures ◽  
Countable Case

The concept of entropy is an important part of the theory of additive measures. In this paper, a definition of entropy is introduced for general (not necessarily additive) measures as the infinum of the Shannon entropies of "subordinate" additive measures. Several properties of the general entropy are discussed and proved. Some of the properties require that the measure belongs to the class of so-called "equientropic" general measures introduced and studied in this paper. The definition of general entropy is extended to the countable case for which a sufficient condition of convergence is proved. We introduce a method of "conditional combination" of general measures and prove that in that case the general entropy possesses the "subset independence" property.

scholarly journals A generalized inversion formula for the continuous Jacobi transform

1987 ◽  
Vol 10 (4) ◽  
pp. 671-692 ◽  
Author(s):  
Ahmed I. Zayed
Keyword(s):  
Analytic Function ◽  
Inversion Formula ◽  
Generalized Functions ◽  
Generalized Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generalized Inversion ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Jacobi Transform

In this paper we extend the definition of the continuous Jacobi transform to a class of generalized functions and obtain a generalized inversion formula for it. As a by-product of our technique we obtain a necessary and sufficient condition for an analytic functionF(λ)inReλ>0to be the continuous Jacobi transform of a generalized function.

INTERTWINED BASINS OF ATTRACTION

2012 ◽  
Vol 22 (06) ◽  
pp. 1250130
Author(s):  
CHANGMING DING
Keyword(s):  
Dynamical Systems ◽  
Metric Space ◽  
Basins Of Attraction ◽  
General Definition ◽  
Sufficient Condition ◽  
Topological Equivalence ◽  
Definition Of

This paper deals with intertwined basins of attraction for dynamical systems in a metric space. After giving a general definition of intertwining property, which is preserved by a topological equivalence between dynamical systems, we present a sufficient condition to guarantee the existence of intertwined basins for dynamical systems in ℝn.

On the Indispensability of Intentionality

1972 ◽  
Vol 2 (1) ◽  
pp. 127-133
Author(s):  
Harold Morick
Keyword(s):  
Recent Literature ◽  
Essential Property ◽  
Sufficient Condition ◽  
Conceptual Scheme ◽  
Necessary And Sufficient Condition ◽  
Definition Of ◽  
Necessary And Sufficient

In the last two decades, there has been a great deal of interest in providing an intentional criterion of the psychological. Of the various ones proferred, it seems to me that the best was the earliest, which was Chisholm’s initial criterion in his 1955 essay “Sentences about Believing.” In this present paper I first single out a basic misconception pervading the recent literature on intentionality and suggest that a consequence of this misconception has been the futile attempt to use the notion of intentionality to provide a kind of definition of “mind”; that is, to use intentionality to provide a necessary and sufficient condition for the psychological. Secondly, I point out how intentionality as captured by my own criterion is indispensable in that it is an essential property of certain particulars (persons) which are basic to our conceptual scheme and apparently basic to any conceptual scheme whatsoever.

scholarly journals Some results concerning frames in Banach spaces

2007 ◽  
Vol 38 (3) ◽  
pp. 267-276 ◽  
Author(s):  
S. K. Kaushik
Keyword(s):  
Finite Number ◽  
Banach Spaces ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Linearly Independent ◽  
Banach Frame ◽  
Minimal Sequence ◽  
Definition Of ◽  
Necessary And Sufficient

A necessary and sufficient condition for the associated sequence of functionals to a complete minimal sequence to be a Banach frame has been given. We give the definition of a weak-exact Banach frame, and observe that an exact Banach frame is weak-exact. An example of a weak-exact Banach frame which is not exact has been given. A necessary and sufficient condition for a Banach frame to be a weak-exact Banach frame has been obtained. Finally, a necessary condition for the perturbation of a retro Banach frame by a finite number of linearly independent vectors to be a retro Banach frame has been given.

Dropping 'E's: the missing link in quality assurance for disabled people

1995 ◽  
Vol 15 (44-45) ◽  
pp. 7-21 ◽  
Author(s):  
Mark Priestley
Keyword(s):  
Quality Assurance ◽  
Service Quality ◽  
Community Care ◽  
Sufficient Condition ◽  
Disabled People ◽  
Missing Link ◽  
Definition Of ◽  
Is Value

Community Care reforms have revived interest in service quality. It is argued that the definition of service quality is value-led and that domi nant ideologies have contributed to the continued oppression of disabled people. The design of quality assurance systems is considered and it is suggested that organisations controlled by disabled people have a central role to play in providing disablement services. Two conclusions are drawn. First, service quality cannot on its own be a sufficient condition for disabled people's emancipation. Second, 'quality' has been used as a policy substitute for the necessary con dition of 'equality'.

Properties and Constructing of a Kind of Four-Dimensional Vector Wavelet Packets According to a Dilation Matrix

2010 ◽  
Vol 439-440 ◽  
pp. 920-925
Author(s):  
Yu Min Yu ◽  
Yu Qing Zhu
Keyword(s):  
Functional Analysis ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Sufficient Condition ◽  
Subdivision Scheme ◽  
Dimensional Vector ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Matrix ◽  
Definition Of

In this paper, we introduce a sort of vector four-dimensional wavelet packets according to a dilation matrix, which are generalizations of univariate wavelet packets. The definition of biortho- gonal vector four-dimensional wavelet packets is provided and their biorthogonality quality is researched by means of time-frequency analysis method, vector subdivision scheme and functional analysis method. Three biorthogonality formulas regarding the wavelet packets are established. Finally, it is shown how to draw new Riesz bases of space from these wavelet packets. The sufficient condition for the existence of four-dimensional wavelet packets is established based on the multiresolution analysis method.

scholarly journals Logicality and Invariance

2008 ◽  
Vol 14 (1) ◽  
pp. 29-68 ◽  
Author(s):  
Denis Bonnay
Keyword(s):  
Similarity Relation ◽  
Necessary Condition ◽  
General Notion ◽  
Sufficient Condition ◽  
Logical Constants ◽  
Similarity Relations ◽  
Definition Of

AbstractThis paper deals with the problem of giving a principled characterization of the class of logical constants. According to the so-called Tarski–Sher thesis, an operation is logical iff it is invariant under permutation. In the model-theoretic tradition, this criterion has been widely accepted as giving a necessary condition for an operation to be logical. But it has been also widely criticized on the account that it counts too many operations as logical, failing thus to provide a sufficient condition.Our aim is to solve this problem of overgeneration by modifying the invariance criterion. We introduce a general notion of invariance under a similarity relation and present the connection between similarity relations and classes of invariant operations. The next task is to isolate a similarity relation well-suited for a definition of logicality. We argue that the standard arguments in favor of invariance under permutation, which rely on the generality and the formality of logic, should be modified. The revised arguments are shown to support an alternative to Tarski's criterion, according to which an operation is logical iff it is invariant under potential isomorphism.

scholarly journals Derivatives, Products, and Pullbacks in Forman's Combinatorial Differential Forms

2020 ◽  
Vol 3 (1) ◽  
pp. 7-16
Author(s):  
Vu Quang Huynh ◽  
Thach Phu Nguyen ◽  
Phuong Van Phan
Keyword(s):  
Connected Domain ◽  
Differential Forms ◽  
Sufficient Condition ◽  
Simply Connected Domain ◽  
Definition Of ◽  
Simply Connected

We study derivatives, closedness, and exactness of 0-forms and 1-forms in the theory of combinatorial differential forms constructed by Robin Forman. We give an example of a closed but not exact 1-form on a non-simply connected domain. We give a sufficient condition on the domain for a closed 1-form to be exact. We show that the product of forms proposed by Forman is not anti-commutative. We propose a definition of pullbacks of forms and show that this operation has several properties analogous to pullbacks on smooth forms.

Analysis on Degree of Freedom and Singularity of Mechanism Based on Topological Graph Theory

2011 ◽  
Vol 393-395 ◽  
pp. 20-23
Author(s):  
Jian Guo Luo ◽  
Mao Yan He
Keyword(s):  
Graph Theory ◽  
Degree Of Freedom ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Topological Graph ◽  
Topological Graph Theory ◽  
Hybrid Mechanism ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Case Number

Based on the analysis of current developing state of graph theory, define the description of spacial moving capability of common couples and translation base and rotation base of mechanism, based on the new description method in topological graph theory. DOF(degree of freedom) of hybrid mechanism analysised with example based on the definition of dimensionity of branch spacial moving capability and mechanism spacial moving capability, necessary and sufficient condition of nonsingularity of mechanism presented, as well as the necessary and sufficient condition of singularity of mechanism deduced , in-phase and assimilation condition and in-phase and dissimilarity condition and asynchronism condition of limitation of input base of branch adopted, case number of position singularity and pose singularity and position and pose singularity obtained then, still the way of founding the combination and case number of common serial mechanism and parallel mechanism and hybrid mechanism mentioned.

Model-based Assessment of Data Availability in Health Information Systems

2008 ◽  
Vol 47 (05) ◽  
pp. 417-424 ◽  
Author(s):  
A. Strübing ◽  
A. Winter
Keyword(s):  
Information Systems ◽  
Health Information ◽  
Information Management ◽  
Health Information Systems ◽  
Data Availability ◽  
Sufficient Condition ◽  
Formal Definition ◽  
Application Systems ◽  
Communication Links ◽  
Definition Of

Summary Objectives: To introduce a formal definition of data availability as a contribution to trustworthiness of health information systems and to automatically detect respective weaknesses and propose solutions. Method: Specifying an ontology, based on enterprise functions and application systems of (health) information systems and closely linked to the Three-Layer Graph-Based Meta Model (3LGM2). Deriving appropriate measures and algorithms. Results: A formal definition for data availability is introduced and elucidated by an example. This concept is used e.g. to disclose missing communication links and to suggest solutions. Conclusions: Data availability is a necessary but not sufficient condition for trustworthiness of health information systems. If information management has a thorough description of the information system at its disposal, e.g. by using 3LGM2, the calculation of data availability does not need further efforts.

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