scholarly journals Convergence of Generalized Collatz Problem in k-Adic Field

2021 ◽  
Vol 23 (1) ◽  
pp. 33-47
Author(s):  
Yushu Zhu ◽  
◽  
Sensen Chen ◽  
Qing-You Sun
Keyword(s):  
Fixed Point ◽  
Number Field ◽  
Algebraic Systems ◽  
Periodic Sequences ◽  
Period Problem ◽  
Series Transformation ◽  
Collatz Problem

In this article, we define a new series transformation called transformation and probe into its fixed point and periodicity. We extend the number field of the transform period problem to a wider field. Different constraints are imposed on then different periodic columns are formed after finite transformations. We obtain that their periodic sequences are and respectively after derivation. As an application, it can provide a reference for C problems in more complex algebraic systems.

scholarly journals Remarks on endomorphisms and rational points

2011 ◽  
Vol 147 (6) ◽  
pp. 1819-1842 ◽  
Author(s):  
E. Amerik ◽  
F. Bogomolov ◽  
M. Rovinsky
Keyword(s):  
Fixed Point ◽  
Number Field ◽  
Algebraic Variety ◽  
Rational Points ◽  
Potential Density ◽  
Cubic Fourfold

AbstractLet X be an algebraic variety and let f:X−−→X be a rational self-map with a fixed point q, where everything is defined over a number field K. We make some general remarks concerning the possibility of using the behaviour of f near q to produce many rational points on X. As an application, we give a simplified proof of the potential density of rational points on the variety of lines of a cubic fourfold, originally proved by Claire Voisin and the first author in 2007.

scholarly journals Existence of Positive Solutions for a Class of Nonlinear Algebraic Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Yongqiang Du ◽  
Guang Zhang ◽  
Wenying Feng
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Nonlinear Term ◽  
Zero Point ◽  
Coefficient Matrix ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Algebraic Systems ◽  
Infinite Point ◽  
Nonlinear Algebraic Systems ◽  
Existence Of Positive Solutions

Based on Guo-Krasnoselskii’s fixed point theorem, the existence of positive solutions for a class of nonlinear algebraic systems of the formx=GFxis studied firstly, whereGis a positiven×nsquare matrix,x=col⁡(x1,x2,…,xn), andF(x)=col⁡(f(x1),f(x2),…,f(xn)), where,F(x)is not required to be satisfied sublinear or superlinear at zero point and infinite point. In addition, a new cone is constructed inRn. Secondly, the obtained results can be extended to some more general nonlinear algebraic systems, where the coefficient matrixGand the nonlinear term are depended on the variablex. Corresponding examples are given to illustrate these results.

scholarly journals Critically separable rational maps in families

2012 ◽  
Vol 148 (6) ◽  
pp. 1880-1896 ◽  
Author(s):  
Clayton Petsche
Keyword(s):  
Fixed Point ◽  
Elliptic Curves ◽  
Number Field ◽  
Rational Maps ◽  
Finiteness Theorem ◽  
Good Reduction ◽  
Rational Map ◽  
Arithmetic Complexity ◽  
Special Case

AbstractGiven a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps in these families, we prove a finiteness theorem which is analogous to Shafarevich’s theorem for elliptic curves. We also define the minimal critical discriminant, a global object which can be viewed as a measure of arithmetic complexity of a rational map. We formulate a conjectural bound on the minimal critical discriminant, which is analogous to Szpiro’s conjecture for elliptic curves, and we prove that a special case of our conjecture implies Szpiro’s conjecture in the semistable case.

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

K-STRATUM LIMIT AND K-STRATUM INTEGRAL ON THE GENERALIZED NUMBER FIELD

1982 ◽  
Vol 2 (4) ◽  
pp. 375-388
Author(s):  
Jiwu Wang ◽  
Tai Kang
Keyword(s):  
Number Field

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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