Addendum: New Proof of Finite-Dimensional Selection Theorem

1998 ◽  
pp. 126-145
Author(s):  
Dušan Repovš ◽  
Pavel Vladimirovič Semenov
Keyword(s):  
Selection Theorem ◽  
Finite Dimensional

scholarly journals A convex-valued selection theorem with a non-separable Banach space

2018 ◽  
Vol 7 (2) ◽  
pp. 197-209
Author(s):  
Pascal Gourdel ◽  
Nadia Mâagli
Keyword(s):  
Banach Space ◽  
Metric Space ◽  
Separable Banach Space ◽  
Lower Semicontinuous ◽  
Constructive Proof ◽  
Selection Theorem ◽  
Finite Dimensional ◽  
Nonempty Convex

AbstractIn the spirit of Michael’s selection theorem [6, Theorem 3.1”’], we consider a nonempty convex-valued lower semicontinuous correspondence {\varphi:X\to 2^{Y}}. We prove that if φ has either closed or finite-dimensional images, then there admits a continuous single-valued selection, where X is a metric space and Y is a Banach space. We provide a geometric and constructive proof of our main result based on the concept of peeling introduced in this paper.

A total finite-dimensional selection theorem

1998 ◽  
Vol 39 (5) ◽  
pp. 835-843
Author(s):  
S. M. Ageev ◽  
D. Repovs
Keyword(s):  
Selection Theorem ◽  
Finite Dimensional

scholarly journals A generalization of Michael finite dimensional selection theorem

2011 ◽  
Vol 34 (3) ◽  
pp. 464-473
Author(s):  
Adel A. George Michael
Keyword(s):  
Selection Theorem ◽  
Finite Dimensional

Finite-Dimensional Selection Theorem

1998 ◽  
pp. 84-114
Author(s):  
Dušan Repovš ◽  
Pavel Vladimirovič Semenov
Keyword(s):  
Selection Theorem ◽  
Finite Dimensional

Non-Linear Dynamics of Cardiovascular Variability Signals

1994 ◽  
Vol 33 (01) ◽  
pp. 81-84 ◽  
Author(s):  
S. Cerutti ◽  
S. Guzzetti ◽  
R. Parola ◽  
M.G. Signorini
Keyword(s):  
Dimensional Space ◽  
Severe Heart Failure ◽  
Parametric Models ◽  
Deterministic Systems ◽  
Finite Dimensional ◽  
Return Maps ◽  
Pathological Conditions ◽  
Non Linear ◽  
Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

Thermal-fluid control via finite-dimensional approximation

1996 ◽  
Author(s):  
Ajit Shenoy ◽  
Eugene Cliff ◽  
Matthias Heinkenschloss
Keyword(s):  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
Fluid Control
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