On the Continuity of the Nemytskij Operator between the Spaces 𝐿𝑝1(𝑋) and 𝐿𝑝2(𝑋)

2006 β—½  
Vol 13 (2) β—½  
pp. 261-265
Author(s):  
Marek Galewski
Keyword(s):  
Sufficient Condition β—½  
Nemytskij Operator

Abstract We provide a generalized sufficient condition for the continuity of the Nemytskij operator between 𝐿𝑝1(𝑋) and 𝐿𝑝2(𝑋). An example is given.

The Current Situation in Chemical Stabilization of Biological Materials

1972 β—½  
Vol 30 β—½  
pp. 132-133
Author(s):  
John H. Luft
Keyword(s):  
Electron Microscopy β—½  
Electron Microscope β—½  
Osmium Tetroxide β—½  
Molecular Level β—½  
Cross Linking β—½  
Chemical Stabilization β—½  
Specimen Preparation β—½  
Sufficient Condition β—½  
Radio Telescopes

With information processing devices such as radio telescopes, microscopes or hi-fi systems, the quality of the output often is limited by distortion or noise introduced at the input stage of the device. This analogy can be extended usefully to specimen preparation for the electron microscope; fixation, which initiates the processing sequence, is the single most important step and, unfortunately, is the least well understood. Although there is an abundance of fixation mixtures recommended in the light microscopy literature, osmium tetroxide and glutaraldehyde are favored for electron microscopy. These fixatives react vigorously with proteins at the molecular level. There is clear evidence for the cross-linking of proteins both by osmium tetroxide and glutaraldehyde and cross-linking may be a necessary if not sufficient condition to define fixatives as a class.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 β—½  
Vol 17 (3) β—½  
pp. 257-266 β—½  
Author(s):  
Mark H. Taylor β—½  
F. Todd DeZoort β—½  
Edward Munn β—½  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest β—½  
Auditor Independence β—½  
Public Confidence β—½  
Sufficient Condition β—½  
Necessary And Sufficient Condition β—½  
Accounting Profession β—½  
The Public β—½  
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 β—½  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis β—½  
Political Authority β—½  
The State β—½  
Sufficient Condition β—½  
Necessary And Sufficient Condition β—½  
State Institutions β—½  
State Of Nature β—½  
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 β€œacquired 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 Power graphs and exchange property for resolving sets

Open Mathematics β—½  
2019 β—½  
Vol 17 (1) β—½  
pp. 1303-1309 β—½  
Author(s):  
Ghulam Abbas β—½  
Usman Ali β—½  
Mobeen Munir β—½  
Syed Ahtsham Ul Haq Bokhary β—½  
Shin Min Kang
Keyword(s):  
Present Article β—½  
Linear Algebra β—½  
Finite Groups β—½  
Robot Navigation β—½  
Simple Graph β—½  
Exchange Property β—½  
Metric Dimension β—½  
Sufficient Condition β—½  
Resolving Set β—½  
Dihedral Groups

Abstract Classical applications of resolving sets and metric dimension can be observed in robot navigation, networking and pharmacy. In the present article, a formula for computing the metric dimension of a simple graph wihtout singleton twins is given. A sufficient condition for the graph to have the exchange property for resolving sets is found. Consequently, every minimal resolving set in the graph forms a basis for a matriod in the context of independence defined by Boutin [Determining sets, resolving set and the exchange property, Graphs Combin., 2009, 25, 789-806]. Also, a new way to define a matroid on finite ground is deduced. It is proved that the matroid is strongly base orderable and hence satisfies the conjecture of White [An unique exchange property for bases, Linear Algebra Appl., 1980, 31, 81-91]. As an application, it is shown that the power graphs of some finite groups can define a matroid. Moreover, we also compute the metric dimension of the power graphs of dihedral groups.

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