Some open problems in the nonlinear classification of Banach spaces

1983 ◽  
pp. 91-95
Author(s):  
S. Heinrich ◽  
P. Mankiewicz
Keyword(s):  
Banach Spaces ◽  
Open Problems ◽  
Nonlinear Classification

Classification of Cloud Systems Cyber-security Threats and Solutions Directives

2017 ◽  
Vol 2 (3) ◽  
pp. 1
Author(s):  
Hanane Bennasar ◽  
Mohammad Essaaidi ◽  
Ahmed Bendahmane ◽  
Jalel Benothmane
Keyword(s):  
Cloud Computing ◽  
Cyber Security ◽  
Data Security ◽  
Denial Of Service ◽  
Security Threats ◽  
Huge Number ◽  
Open Problems ◽  
Long Period ◽  
Near Future

Cloud computing cyber security is a subject that has been in top flight for a long period and even in near future. However, cloud computing permit to stock up a huge number of data in the cloud stockage, and allow the user to pay per utilization from anywhere via any terminal equipment. Among the major issues related to Cloud Computing security, we can mention data security, denial of service attacks, confidentiality, availability, and data integrity. This paper is dedicated to a taxonomic classification study of cloud computing cyber-security. With the main objective to identify the main challenges and issues in this field, the different approaches and solutions proposed to address them and the open problems that need to be addressed.

scholarly journals A characterisation of Hilbert spaces via orthogonality and proximinality

2005 ◽  
Vol 71 (1) ◽  
pp. 107-111
Author(s):  
Fathi B. Saidi
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Real Banach Space ◽  
Nonzero Element ◽  
Dimensional Subspace ◽  
Two Dimensional ◽  
Orthogonal Direction ◽  
Open Problems

In this paper we adopt the notion of orthogonality in Banach spaces introduced by the author in [6]. There, the author showed that in any two-dimensional subspace F of E, every nonzero element admits at most one orthogonal direction. The problem of existence of such orthogonal direction was not addressed before. Our main purpose in this paper is the investigation of this problem in the case where E is a real Banach space. As a result we obtain a characterisation of Hilbert spaces stating that, if in every two-dimensional subspace F of E every nonzero element admits an orthogonal direction, then E is isometric to a Hilbert space. We conclude by presenting some open problems.

scholarly journals Nonlinear Classification of Multispectral Imagery Using Representation-Based Classifiers

2017 ◽  
Vol 9 (7) ◽  
pp. 662 ◽  
Author(s):  
Yan Xu ◽  
Qian Du ◽  
Wei Li ◽  
Chen Chen ◽  
Nicolas Younan
Keyword(s):  
Multispectral Imagery ◽  
Nonlinear Classification

Classification of Activated Sludge Settleability Using Linear and Nonlinear Classification Functions

2008 ◽  
Vol 41 (2) ◽  
pp. 14600-14605
Author(s):  
Geert Gins ◽  
Jef Vanlaer ◽  
Ilse Y. Smets ◽  
Jan F. Van Impe
Keyword(s):  
Activated Sludge ◽  
Nonlinear Classification ◽  
Linear And Nonlinear ◽  
Sludge Settleability

scholarly journals Applications of ultrapowers to the uniform and Lipschitz classification of Banach spaces

1982 ◽  
Vol 73 (3) ◽  
pp. 225-251 ◽  
Author(s):  
S. Heinrich ◽  
P. Mankiewicz
Keyword(s):  
Banach Spaces

scholarly journals Computability-theoretic complexity of effective Banach spaces

2022 ◽  
Author(s):  
◽  
Long Qian
Keyword(s):  
Banach Space ◽  
Lower Bound ◽  
Banach Spaces ◽  
Lower Bounds ◽  
Approximation Property ◽  
Upper Bounds ◽  
Space Theory ◽  
Approximation Properties ◽  
Open Problems

<p><b>We investigate the geometry of effective Banach spaces, namely a sequenceof approximation properties that lies in between a Banach space having a basis and the approximation property.</b></p> <p>We establish some upper bounds on suchproperties, as well as proving some arithmetical lower bounds. Unfortunately,the upper bounds obtained in some cases are far away from the lower bound.</p> <p>However, we will show that much tighter bounds will require genuinely newconstructions, and resolve long-standing open problems in Banach space theory.</p> <p>We also investigate the effectivisations of certain classical theorems in Banachspaces.</p>

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