scholarly journals Bounded Domains of Generalized Riesz Methods with the Hahn Property

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Maria Zeltser
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Infinite Matrix ◽  
Bounded Domains ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Hausdorff Matrix ◽  
Additional Assumptions

In 2002 Bennett et al. started the investigation to which extent sequence spaces are determined by the sequences of 0s and 1s that they contain. In this relation they defined three types of Hahn properties for sequence spaces: the Hahn property, separable Hahn property, and matrix Hahn property. In general all these three properties are pairwise distinct. If a sequence spaceEis solid and(0,1ℕ∩E)β=Eβ=ℓ1then the two last properties coincide. We will show that even on these additional assumptions the separable Hahn property and the Hahn property still do not coincide. However if we assumeEto be the bounded summability domain of a regular Riesz matrixRpor a regular nonnegative Hausdorff matrixHp, then this assumption alone guarantees thatEhas the Hahn property. For any (infinite) matrixAthe Hahn property of its bounded summability domain is related to the strongly nonatomic property of the densitydAdefined byA. We will find a simple necessary and sufficient condition for the densitydAdefined by the generalized Riesz matrixRp,mto be strongly nonatomic. This condition appears also to be sufficient for the bounded summability domain ofRp,mto have the Hahn property.

scholarly journals Regular matrix transformation on triple sequence spaces

2017 ◽  
Vol 35 (1) ◽  
pp. 85 ◽  
Author(s):  
Shyamal Debnath ◽  
Bimal Chandra Das
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Matrix Transformation ◽  
Sufficient Condition ◽  
Regular Matrix ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The main aim of this paper is to introduce the necessary and sufficient condition for a particular type of transformation of the form A: (a......)  be regular from a triple sequence space to another triple sequence space. 

scholarly journals Symmetry and concentration behavior of ground state in axially symmetric domains

2004 ◽  
Vol 2004 (12) ◽  
pp. 1019-1030
Author(s):  
Tsung-Fang Wu
Keyword(s):  
Ground State ◽  
Semilinear Elliptic Equation ◽  
Bounded Domains ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Axially Symmetric ◽  
Ground State Solutions ◽  
Semilinear Elliptic ◽  
Necessary And Sufficient ◽  
Concentration Behavior

We letΩ(r)be the axially symmetric bounded domains which satisfy some suitable conditions, then the ground-state solutions of the semilinear elliptic equation inΩ(r)are nonaxially symmetric and concentrative on one side. Furthermore, we prove the necessary and sufficient condition for the symmetry of ground-state solutions.

scholarly journals Characterizations of majorization on summable sequences

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2193-2202
Author(s):  
Kosuru Raju ◽  
Subhajit Saha
Keyword(s):  
Sequence Space ◽  
Dimensional Space ◽  
Sufficient Condition ◽  
Infinite Dimensional Space ◽  
Necessary And Sufficient Condition ◽  
Infinite Dimensional ◽  
Summable Sequence ◽  
Necessary And Sufficient

In this paper, we prove a necessary and sufficient condition for majorization on the summable sequence space. For this we redefine the notion of majorization on an infinite dimensional space and therein investigate properties of the majorization. We also prove the infinite dimensional Schur-Horn type and Hardy-Littlewood-P?lya type theorems.

scholarly journals Normal solvability of general linear elliptic problems

2005 ◽  
Vol 2005 (7) ◽  
pp. 733-756 ◽  
Author(s):  
A. Volpert ◽  
V. Volpert
Keyword(s):  
Elliptic Problems ◽  
Unbounded Domains ◽  
General Linear ◽  
Bounded Domains ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Ellipticity Condition ◽  
Normal Solvability ◽  
General Elliptic ◽  
Necessary And Sufficient

The paper is devoted to general elliptic problems in the Douglis-Nirenberg sense. We obtain a necessary and sufficient condition of normal solvability in the case of unbounded domains. Along with the ellipticity condition, proper ellipticity and Lopatinsky condition that determine normal solvability of elliptic problems in bounded domains, one more condition formulated in terms of limiting problems should be imposed in the case of unbounded domains.

The orbit set and the orthogonal quotient

2016 ◽  
Vol 15 (06) ◽  
pp. 1650101
Author(s):  
Ravi A. Rao ◽  
Selby Jose
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Additional Assumptions

We study the injectivity of the map (of pointed sets) [Formula: see text], which we had constructed in [12]. We obtain a necessary and sufficient condition for the kernel to be non-trivial under some additional assumptions on [Formula: see text].

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.

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