OPTIMAL FIXED-POINT CONTINUOUS LINEAR SMOOTHING

1966 ◽  
Author(s):  
James S. Meditch
Keyword(s):  
Fixed Point ◽  
Continuous Linear ◽  
Linear Smoothing

On Optimal Fixed Point Linear Smoothing

1967 ◽  
Vol 6 (2) ◽  
pp. 189-199 ◽  
Author(s):  
J. S. MEDITCH
Keyword(s):  
Fixed Point ◽  
Linear Smoothing

Sensitivity analysis of fixed point linear smoothing algorithms

1968 ◽  
Vol 8 (4) ◽  
pp. 321-337 ◽  
Author(s):  
ROBERT E. GRIFFIN ◽  
ANDREW P. SAGE
Keyword(s):  
Sensitivity Analysis ◽  
Fixed Point ◽  
Linear Smoothing

scholarly journals Points of narrowness and uniformly narrow operators

2017 ◽  
Vol 9 (1) ◽  
pp. 37-47 ◽  
Author(s):  
A.I. Gumenchuk ◽  
I.V. Krasikova ◽  
M.M. Popov
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Measure Space ◽  
Linear Operators ◽  
Continuous Linear ◽  
Standard Tool ◽  
Orthogonally Additive ◽  
Orthogonally Additive Operators ◽  
Continuous Linear Operators

It is known that the sum of every two narrow operators on $L_1$ is narrow, however the same is false for $L_p$ with $1 < p < \infty$. The present paper continues numerous investigations of the kind. Firstly, we study narrowness of a linear and orthogonally additive operators on Kothe function spaces and Riesz spaces at a fixed point. Theorem 1 asserts that, for every Kothe Banach space $E$ on a finite atomless measure space there exist continuous linear operators $S,T: E \to E$ which are narrow at some fixed point but the sum $S+T$ is not narrow at the same point. Secondly, we introduce and study uniformly narrow pairs of operators $S,T: E \to X$, that is, for every $e \in E$ and every $\varepsilon > 0$ there exists a decomposition $e = e' + e''$ to disjoint elements such that $\|S(e') - S(e'')\| < \varepsilon$ and $\|T(e') - T(e'')\| < \varepsilon$. The standard tool in the literature to prove the narrowness of the sum of two narrow operators $S+T$ is to show that the pair $S,T$ is uniformly narrow. We study the question of whether every pair of narrow operators with narrow sum is uniformly narrow. Having no counterexample, we prove several theorems showing that the answer is affirmative for some partial cases.

Mental equilibrium: Identifying fixed-point attractors in the stream of thought

2003 ◽  
Author(s):  
Robin R. Vallacher ◽  
Andrzej Nowak ◽  
Matthew Rockloff
Keyword(s):  
Fixed Point

Bifurcation in a Simple Model of the Cardiovascular System

2000 ◽  
Vol 39 (02) ◽  
pp. 118-121 ◽  
Author(s):  
S. Akselrod ◽  
S. Eyal
Keyword(s):  
Nonlinear Dynamics ◽  
Blood Pressure ◽  
Heart Rate ◽  
Fixed Point ◽  
Cardiovascular System ◽  
Modified Model ◽  
Mayer Waves ◽  
Sustained Oscillations ◽  
Human Cardiovascular System ◽  
Physiological Values

Abstract:A simple nonlinear beat-to-beat model of the human cardiovascular system has been studied. The model, introduced by DeBoer et al. was a simplified linearized version. We present a modified model which allows to investigate the nonlinear dynamics of the cardiovascular system. We found that an increase in the -sympathetic gain, via a Hopf bifurcation, leads to sustained oscillations both in heart rate and blood pressure variables at about 0.1 Hz (Mayer waves). Similar oscillations were observed when increasing the -sympathetic gain or decreasing the vagal gain. Further changes of the gains, even beyond reasonable physiological values, did not reveal another bifurcation. The dynamics observed were thus either fixed point or limit cycle. Introducing respiration into the model showed entrainment between the respiration frequency and the Mayer waves.

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