scholarly journals PLANE MAPS WITH DENOMINATOR. PART III: NONSIMPLE FOCAL POINTS AND RELATED BIFURCATIONS

2005 ◽  
Vol 15 (02) ◽  
pp. 451-496 ◽  
Author(s):  
GIAN-ITALO BISCHI ◽  
LAURA GARDINI ◽  
CHRISTIAN MIRA
Keyword(s):  
Focal Point ◽  
Dynamic Properties ◽  
Focal Points ◽  
One Dimensional ◽  
Global Dynamic ◽  
Critical Sets ◽  
One To One ◽  
The One ◽  
Noninvertible Maps ◽  
Qualitative Changes

This paper continues the study of the global dynamic properties specific to maps of the plane characterized by the presence of a denominator that vanishes in a one-dimensional submanifold. After two previous papers by the same authors, where the definitions of new kinds of singularities, called focal points and prefocal sets, are given, as well as the particular structures of the basins and the global bifurcations related to the presence of such singularities, this third paper is devoted to the analysis of nonsimple focal points, and the bifurcations associated with them. We prove the existence of a one-to-one relation between the points of a prefocal curve and arcs through the focal point having all the same tangent but different curvatures. In the case of nonsimple focal points, such a relation replaces the one-to-one correspondence between the slopes of arcs through a focal point and the points along the associated prefocal curve that have been proved and extensively discussed in the previous papers. Moreover, when dealing with noninvertible maps, other kinds of relations can be obtained in the presence of nonsimple focal points or prefocal curves, and some of them are associated with qualitative changes of the critical sets, i.e. with the structure of the Riemann foliation of the plane.

KNOT POINTS IN TWO-DIMENSIONAL MAPS AND RELATED PROPERTIES

2009 ◽  
Vol 19 (02) ◽  
pp. 545-555 ◽  
Author(s):  
F. TRAMONTANA ◽  
L. GARDINI ◽  
D. FOURNIER-PRUNARET ◽  
P. CHARGE
Keyword(s):  
Focal Point ◽  
Singular Line ◽  
Two Dimensional ◽  
Focal Points ◽  
Singular Set ◽  
One Dimensional ◽  
Attracting Set ◽  
Straight Line ◽  
Special Character ◽  
Stable And Unstable Sets

We consider the class of two-dimensional maps of the plane for which there exists a whole one-dimensional singular set (for example, a straight line) that is mapped into one point, called a "knot point" of the map. The special character of this kind of point has been already observed in maps of this class with at least one of the inverses having a vanishing denominator. In that framework, a knot is the so-called focal point of the inverse map (it is the same point). In this paper, we show that knots may also exist in other families of maps, not related to an inverse having values going to infinity. Some particular properties related to focal points persist, such as the existence of a "point to slope" correspondence between the points of the singular line and the slopes in the knot, lobes issuing from the knot point and loops in infinitely many points of an attracting set or in invariant stable and unstable sets.

A FDM Solving Method of Large-Strain Consolidation of Multi-Layers Super Soft-Soil

2011 ◽  
Vol 71-78 ◽  
pp. 1880-1884
Author(s):  
Hai Jia Wen ◽  
Jia Lan Zhang
Keyword(s):  
Numerical Method ◽  
Large Strain ◽  
Soft Soil ◽  
Focal Points ◽  
One Dimensional ◽  
Practical Engineering ◽  
K Function ◽  
Soil Foundation ◽  
Soft Soil Foundation ◽  
The One

The aim is to present a numerical method to solve the large-strain consolidation of super soft-soil. The theory of large-strain consolidation (LSC) is acted as the better method for analysis on the consolidation problem of super soft-soil foundation. The focal points are, based on practical engineering, the one-dimensional LSC equations being derived, the consolidation coefficients being inquired and so on. Based on these, one-dimensional nonlinear LSC equation is solved by the FDM, the e~p and e~k function that are according with the practical engineering is introduced into the solving progress, and the multi-layers super soft-soil is also considered in the progress successfully etc. Finally, a case showed the satisfied analysis result by LSCFDM. And some realizations about LSC analysis on super soft-soil are concluded.

scholarly journals Publisher's Note: Static and dynamic properties of low-temperature order in the one-dimensional semiconductor (NbSe4)3I [Phys. Rev. B 94 , 104113 (2016)]

2016 ◽  
Vol 94 (17) ◽  
Author(s):  
D. Dominko ◽  
S. Vdović ◽  
H. Skenderović ◽  
D. Starešinić ◽  
K. Biljaković ◽  
...  
Keyword(s):  
Low Temperature ◽  
Dynamic Properties ◽  
One Dimensional ◽  
The One

scholarly journals Static and dynamic properties of low-temperature order in the one-dimensional semiconductor(NbSe4)3I

2016 ◽  
Vol 94 (10) ◽  
Author(s):  
D. Dominko ◽  
S. Vdović ◽  
H. Skenderović ◽  
D. Starešinić ◽  
K. Biljaković ◽  
...  
Keyword(s):  
Low Temperature ◽  
Dynamic Properties ◽  
One Dimensional ◽  
The One

scholarly journals Dynamic properties of the one-dimensional Bose-Hubbard model

2011 ◽  
Vol 93 (3) ◽  
pp. 30002 ◽  
Author(s):  
S. Ejima ◽  
H. Fehske ◽  
F. Gebhard
Keyword(s):  
Hubbard Model ◽  
Dynamic Properties ◽  
One Dimensional ◽  
The One

Plane Maps with Denominator. Part II: Noninvertible Maps with Simple Focal Points

2003 ◽  
Vol 13 (08) ◽  
pp. 2253-2277 ◽  
Author(s):  
Gian-Italo Bischi ◽  
Laura Gardini ◽  
Christian Mira
Keyword(s):  
Focal Point ◽  
Single Point ◽  
Focal Points ◽  
Previous Part ◽  
Noninvertible Maps ◽  
Set Of Points

This paper is the second part of an earlier work devoted to the properties specific to maps of the plane characterized by the presence of a vanishing denominator, which gives rise to the generation of new types of singularities, called set of nondefinition, focal points and prefocal curves. A prefocal curve is a set of points which are mapped (or "focalized") into a single point, called focal point, by the inverse map when it is invertible, or by at least one of the inverses when it is noninvertible. In the case of noninvertible maps, the previous text dealt with the simplest geometrical situation, which is nongeneric. To be more precise this situation occurs when several focal points are associated with a given prefocal curve. The present paper defines the generic case for which only one focal point is associated with a given prefocal curve. This is due to the fact that only one inverse of the map has the property of focalization, but with properties different from those of invertible maps. Then the noninvertible maps of the previous Part I appear as resulting from a bifurcation leading to the merging of two prefocal curves, without merging of two focal points.

Numerical simulation study of the charge density wave dynamic properties in the one-dimensional systems

2013 ◽  
Vol 36 (1) ◽  
pp. 60-63
Author(s):  
A. Arbaoui ◽  
N. Habiballah ◽  
M. Qjani ◽  
K. Sbiaai ◽  
A. Hajjaji ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Charge Density ◽  
Simulation Study ◽  
Charge Density Wave ◽  
Dynamic Properties ◽  
Density Wave ◽  
One Dimensional ◽  
Wave Dynamic ◽  
The One

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Influence of Rim Run-Out on the Nonuniformity of Tire-Wheel Assemblies

1994 ◽  
Vol 22 (2) ◽  
pp. 99-120 ◽  
Author(s):  
T. B. Rhyne ◽  
R. Gall ◽  
L. Y. Chang
Keyword(s):  
Finite Element ◽  
Radial Force ◽  
Membrane Model ◽  
Model Experiments ◽  
Force Variation ◽  
One To One ◽  
The One

Abstract An analytical membrane model is used to study how wheel imperfections are converted into radial force variation of the tire-wheel assembly. This model indicates that the radial run-out of the rim generates run-out of the tire-wheel assembly at slightly less than the one to one ratio that was expected. Lateral run-out of the rim is found to generate radial run-out of the tire-wheel assembly at a ratio that is dependent on the tire design and the wheel width. Finite element studies of a production tire validate and quantify the results of the membrane model. Experiments using a specially constructed precision wheel demonstrate the behavior predicted by the models. Finally, a population of production tires and wheels show that the lateral run-out of the rims contribute a significant portion to the assembly radial force variation. These findings might be used to improve match-mounting results by taking lateral rim run-out into account.

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