scholarly journals Bifurcations along the Boundary Curves of Red Fixed Components in the Parameter Space for Uniparametric, Jarratt-Type Simple-Root Finders

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 51 ◽  
Author(s):  
Min-Young Lee ◽  
Young Ik Kim
Keyword(s):  
Parameter Space ◽  
Bifurcation Point ◽  
Simple Root ◽  
Plane Curve ◽  
Computational Experiments ◽  
Elementary Approach ◽  
Parametric Space ◽  
Geometric Figures ◽  
Extensive Analysis ◽  
Boundary Curves

Bifurcations have been studied with an extensive analysis of boundary curves of red, fixed components in the parametric space for a uniparametric family of simple-root finders under the Möbius conjugacy map applied to a quadratic polynomial. An elementary approach from the perspective of a plane curve theory properly describes the geometric figures resembling a circle or cardioid to characterize the underlying boundary curves that are parametrically expressed. Moreover, exact bifurcation points for satellite components on the boundaries have been found, according to the fact that the tangent line at a bifurcation point simultaneously touches the red fixed component and the satellite component. Computational experiments implemented with examples well reflect the significance of the theoretical backgrounds pursued in this paper.

scholarly journals Parameter space dimension reduction of an adaptive interpolator during multidimensional signal differential compression

2019 ◽  
pp. 23-30
Author(s):  
A I Maksimov ◽  
M V Gashnikov
Keyword(s):  
Dimension Reduction ◽  
Parameter Space ◽  
Compression Ratio ◽  
Space Dimension ◽  
Computational Experiments ◽  
Parameter Range ◽  
Compression Method ◽  
Multidimensional Signals ◽  
Multidimensional Signal ◽  
Adaptive Interpolator

We propose a new adaptive multidimensional signal interpolator for differential compression tasks. To increase the efficiency of interpolation, we optimize its parameters space by the minimum absolute interpolation error criterion. To reduce the complexity of interpolation optimization, we reduce the dimension of its parameter range. The correspondence between signal samples in a local neighbourhood is parameterized. Besides, we compare several methods for such parameterization. The developed adaptive interpolator is embedded in the differential compression method. Computational experiments on real multidimensional signals confirm that the use of the proposed interpolator can increase the compression ratio.

scholarly journals Multi-parameter uncertainty analysis of a bifurcation point

2006 ◽  
Vol 13 (5) ◽  
pp. 531-540 ◽  
Author(s):  
B. Knopf ◽  
M. Flechsig ◽  
K. Zickfeld
Keyword(s):  
Uncertainty Analysis ◽  
Parameter Space ◽  
Summer Monsoon ◽  
Bifurcation Point ◽  
Parameter Uncertainty ◽  
Climate Models ◽  
Novel Approach ◽  
Wide Range ◽  
Parameter Uncertainty Analysis ◽  
Parameter Values

Abstract. Parameter uncertainty analysis of climate models has become a standard approach for model validation and testing their sensitivity. Here we present a novel approach that allows one to estimate the robustness of a bifurcation point in a multi-parameter space. In this study we investigate a box model of the Indian summer monsoon that exhibits a saddle-node bifurcation against those parameters that govern the heat balance of the system. The bifurcation brings about a change from a wet summer monsoon regime to a regime that is characterised by low precipitation. To analyse the robustness of the bifurcation point itself and its location in parameter space, we perform a multi-parameter uncertainty analysis by applying qualitative, Monte Carlo and deterministic methods that are provided by a multi-run simulation environment. Our results show that the occurrence of the bifurcation point is robust over a wide range of parameter values. The position of the bifurcation, however, is found to be sensitive on these specific parameter choices.

scholarly journals On geometric variation theory

1999 ◽  
Vol 156 ◽  
pp. 159-169
Author(s):  
Yoshihiro Shikata
Keyword(s):  
Parameter Space ◽  
Variation Theory ◽  
Closed Geodesics ◽  
Geometric Figures ◽  
Topological Change ◽  
Current Flows ◽  
Geometric Variation ◽  
Minimal Networks

We construct here a framework for a geometric variation of 1 dimensional geometric figures regarding them as sets of ordered points. In this framework, we can make full use of cut and paste technique to find a way to go down to the geometric smallest figure, including the topological change of the parameter space. Therefore we can discuss practical problems like switching of current flows and the minimal networks not only multiple closed geodesics.

Surfaces of ℙ3 containing one conic and one line

2019 ◽  
Vol 29 (01) ◽  
pp. 9-21
Author(s):  
André L. Meireles Araújo ◽  
José Alberto Maia ◽  
Fernando Xavier
Keyword(s):  
Parameter Space ◽  
Plane Curve ◽  
Complete Intersections ◽  
General Surface ◽  
Smooth Compactification

We know from a result due to Noether–Lefschetz that a very general surface of degree at least 4 in [Formula: see text] contains only curves which are complete intersections with other surfaces. The main goal of this paper is to construct an explicit and smooth compactification of a parameter space for surfaces in [Formula: see text] of degree [Formula: see text] for all sufficiently large [Formula: see text], containing one conic and one line. The construction also applies to surfaces in [Formula: see text] containing one plane curve and one line. As an application, we compute the degree of the locus of surfaces of degree [Formula: see text] containing one conic and one line.

Meet fractal curves with 1C:MathKit

2020 ◽  
pp. 38-48
Author(s):  
O. M. Korchazhkina
Keyword(s):  
Methodological Approach ◽  
Fractal Curve ◽  
Iterative Processes ◽  
Geometric Figures ◽  
Modern Natural ◽  
Geometric Objects ◽  
Ict Tools ◽  
Subject Areas ◽  
The Subject ◽  
And Mathematics

The article presents a methodological approach to studying iterative processes in the school course of geometry, by the example of constructing a Koch snowflake fractal curve and calculating a few characteristics of it. The interactive creative environment 1C:MathKit is chosen to visualize the method discussed. By performing repetitive constructions and algebraic calculations using ICT tools, students acquire a steady skill of work with geometric objects of various levels of complexity, comprehend the possibilities of mathematical interpretation of iterative processes in practice, and learn how to understand the dialectical unity between finite and infinite parameters of flat geometric figures. When students are getting familiar with such contradictory concepts and categories, that replenishes their experience of worldview comprehension of the subject areas they study through the concept of “big ideas”. The latter allows them to take a fresh look at the processes in the world around. The article is a matter of interest to schoolteachers of computer science and mathematics, as well as university scholars who teach the course “Concepts of modern natural sciences”.

Playful activities in the learning of geometric notions in children of initial, Callao

2019 ◽  
Vol 1 (1) ◽  
pp. 22
Author(s):  
Carla Marilia Ayala Valladares ◽  
Juana Maria Cruz Montero ◽  
Angel Saldarriaga Melgar
Keyword(s):  
Experimental Design ◽  
Favorable Effect ◽  
Measuring Instruments ◽  
Geometric Shapes ◽  
Geometric Figures ◽  
Quasi Experimental ◽  
Probabilistic Sample

The main purpose of the research was to determine the effects of the program of ludic activities for the learning of geometry in children of five years in all their dimensions orientation and location, geometric shapes and measurement, through its components: location in space, identify locations and positions of objects, identify and characterize geometric figures and communicate the qualities of these, likewise identify, classify magnitudes and use various measuring instruments. The type of research was applied, with a quasi-experimental design, the population was constituted by 103 children, and a non-probabilistic sample was used for convenience with a sample of 51 children, divided into two control and experimental groups. The geometry instrument was used to collect information. The favorable effect of the program of playful activities in the learning of geometric notions in children of initial - Callao, 2018 was determined.

MEASUREMENT AND COMPUTATIONAL EXPERIMENTS WITHIN NEWBORN'S BRAIN COOLING PROCESS

2018 ◽  
Author(s):  
Dominika Bandoła ◽  
Andrzej J. Nowak ◽  
Ziemowit Ostrowski ◽  
Marek Rojczyk ◽  
Wojciech Walas
Keyword(s):  
Computational Experiments ◽  
Brain Cooling ◽  
Cooling Process
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