Cubic Polynomial Maps with Periodic Critical Orbit, Part I

2009 ◽  
pp. 333-411 ◽  
Author(s):  
John Milnor
Keyword(s):  
Critical Orbit ◽  
Polynomial Maps ◽  
Cubic Polynomial

scholarly journals Weak Néron models for cubic polynomial maps over a non-Archimedean field

2012 ◽  
Vol 153 (4) ◽  
pp. 415-428 ◽  
Author(s):  
Jean-Yves Briend ◽  
Liang-Chung Hsia
Keyword(s):  
Polynomial Maps ◽  
Cubic Polynomial ◽  
Neron Models ◽  
Néron Models

Ont he monodromy representation of polynomial maps in n variables

2002 ◽  
Vol 39 (3-4) ◽  
pp. 361-367
Author(s):  
A. Némethi ◽  
I. Sigray
Keyword(s):  
Cohomology Group ◽  
Jacobian Conjecture ◽  
Natural Basis ◽  
Generic Fiber ◽  
Monodromy Representation ◽  
Polynomial Maps ◽  
Polynomial Map

For a   non-constant polynomial map f: Cn?Cn-1 we consider the monodromy representation on the cohomology group of its generic fiber. The main result of the paper determines its dimension and provides a natural basis for it. This generalizes the corresponding results of [2] or [10], where the case n=2 is solved. As  applications,  we verify the Jacobian conjecture for (f,g) when the generic fiber of f is either rational or elliptic. These are generalizations of the corresponding results of [5], [7], [8], [11] and [12], where the case  n=2 is treated.

Path Planning of Mobile Robot Using Improved Artificial Bee Colony Algorithm

2020 ◽  
Vol 38 (9A) ◽  
pp. 1384-1395
Author(s):  
Rakaa T. Kamil ◽  
Mohamed J. Mohamed ◽  
Bashra K. Oleiwi
Keyword(s):  
Mobile Robot ◽  
Comparative Research ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Dynamic Control ◽  
Computational Time ◽  
Bee Colony ◽  
Shortest Distance ◽  
Minimum Number ◽  
Cubic Polynomial

A modified version of the artificial Bee Colony Algorithm (ABC) was suggested namely Adaptive Dimension Limit- Artificial Bee Colony Algorithm (ADL-ABC). To determine the optimum global path for mobile robot that satisfies the chosen criteria for shortest distance and collision–free with circular shaped static obstacles on robot environment. The cubic polynomial connects the start point to the end point through three via points used, so the generated paths are smooth and achievable by the robot. Two case studies (or scenarios) are presented in this task and comparative research (or study) is adopted between two algorithm’s results in order to evaluate the performance of the suggested algorithm. The results of the simulation showed that modified parameter (dynamic control limit) is avoiding static number of limit which excludes unnecessary Iteration, so it can find solution with minimum number of iterations and less computational time. From tables of result if there is an equal distance along the path such as in case A (14.490, 14.459) unit, there will be a reduction in time approximately to halve at percentage 5%.

Cubic polynomial patches through geodesics

2008 ◽  
Vol 40 (1) ◽  
pp. 56-61 ◽  
Author(s):  
Marco Paluszny
Keyword(s):  
Cubic Polynomial

scholarly journals Development of a semi-parametric PAR (Photosynthetically Active Radiation) partitioning model for the United States, version 1.0

2014 ◽  
Vol 7 (5) ◽  
pp. 2477-2484 ◽  
Author(s):  
J. C. Kathilankal ◽  
T. L. O'Halloran ◽  
A. Schmidt ◽  
C. V. Hanson ◽  
B. E. Law
Keyword(s):  
United States ◽  
Elevation Angle ◽  
Model Performance ◽  
Diffuse Radiation ◽  
The United States ◽  
Polynomial Model ◽  
Coefficient Of Determination ◽  
Data Set ◽  
Cubic Polynomial ◽  
Solar Elevation Angle

Abstract. A semi-parametric PAR diffuse radiation model was developed using commonly measured climatic variables from 108 site-years of data from 17 AmeriFlux sites. The model has a logistic form and improves upon previous efforts using a larger data set and physically viable climate variables as predictors, including relative humidity, clearness index, surface albedo and solar elevation angle. Model performance was evaluated by comparison with a simple cubic polynomial model developed for the PAR spectral range. The logistic model outperformed the polynomial model with an improved coefficient of determination and slope relative to measured data (logistic: R2 = 0.76; slope = 0.76; cubic: R2 = 0.73; slope = 0.72), making this the most robust PAR-partitioning model for the United States currently available.

scholarly journals Algebraic independence of multipliers of periodic orbits in the space of polynomial maps of one variable

2014 ◽  
Vol 36 (4) ◽  
pp. 1156-1166 ◽  
Author(s):  
IGORS GORBOVICKIS
Keyword(s):  
Periodic Orbits ◽  
Moduli Space ◽  
Algebraic Independence ◽  
Complex Polynomials ◽  
Generic Point ◽  
Algebraic Functions ◽  
Polynomial Maps ◽  
Affine Subspaces

We consider the space of complex polynomials of degree $n\geq 3$ with $n-1$ distinct marked periodic orbits of given periods. We prove that this space is irreducible and the multipliers of the marked periodic orbits, considered as algebraic functions on that space, are algebraically independent over $\mathbb{C}$. Equivalently, this means that at its generic point the moduli space of degree-$n$ polynomial maps can be locally parameterized by the multipliers of $n-1$ arbitrary distinct periodic orbits. We also prove a similar result for a certain class of affine subspaces of the space of complex polynomials of degree $n$.

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