scholarly journals POLYNOMIAL ENDOMORPHISMS PRESERVING OUTER RANK IN TWO VARIABLES

2012 ◽  
Vol 86 (2) ◽  
pp. 186-192
Author(s):  
YONG JIN ◽  
XIANKUN DU
Keyword(s):  
Fixed Point ◽  
Polynomial Ring ◽  
Nonzero Constant ◽  
Polynomial Endomorphisms

AbstractAn endomorphism φ of a polynomial ring is said to preserve outer rank if φ sends each polynomial to one with the same outer rank. For the polynomial ring in two variables over a field of characteristic 0 we prove that an endomorphism φ preserving outer rank is an automorphism if one of the following conditions holds: (1) the Jacobian of φ is a nonzero constant; (2) the image of φ contains a coordinate; (3) φ has a ‘fixed point’.

scholarly journals Endomorphisms Preserving Coordinates of Polynomial Algebras

2013 ◽  
Vol 20 (03) ◽  
pp. 523-526
Author(s):  
Yu-Chang Li ◽  
Jie-Tai Yu
Keyword(s):  
Finite Number ◽  
Polynomial Ring ◽  
Characteristic Zero ◽  
Infinite Field ◽  
Polynomial Algebras ◽  
Nonzero Constant

It is proved that the Jacobian of a k-endomorphism of k[x1,…,xn] over a field k of characteristic zero, taking every tame coordinate to a coordinate, must be a nonzero constant in k. It is also proved that the Jacobian of an R-endomorphism of A=:R[x1,…,xn] (where R is a polynomial ring in a finite number of variables over an infinite field k), taking every R-linear coordinate of A to an R-coordinate of A, is a nonzero constant in k.

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.

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion
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