Point Classification of Second Order ODEs: Tresse Classification Revisited and Beyond

2009 ◽  
pp. 199-221 ◽  
Author(s):  
Boris Kruglikov
Keyword(s):  
Second Order

SATANIC AND THELEMIC CIRCLES ON KNOTS

2013 ◽  
Vol 22 (05) ◽  
pp. 1350017 ◽  
Author(s):  
G. FLOWERS
Keyword(s):  
Geometric Interpretation ◽  
Second Order ◽  
Geometric Properties ◽  
Vassiliev Invariants ◽  
Vassiliev Invariant ◽  
Knot Diagrams

While Vassiliev invariants have proved to be a useful tool in the classification of knots, they are frequently defined through knot diagrams, and fail to illuminate any significant geometric properties the knots themselves may possess. Here, we provide a geometric interpretation of the second-order Vassiliev invariant by examining five-point cocircularities of knots, extending some of the results obtained in [R. Budney, J. Conant, K. P. Scannell and D. Sinha, New perspectives on self-linking, Adv. Math. 191(1) (2005) 78–113]. Additionally, an analysis on the behavior of other cocircularities on knots is given.

Lie group classification of second-order ordinary difference equations

2000 ◽  
Vol 41 (1) ◽  
pp. 480-504 ◽  
Author(s):  
Vladimir Dorodnitsyn ◽  
Roman Kozlov ◽  
Pavel Winternitz
Keyword(s):  
Lie Group ◽  
Difference Equations ◽  
Group Classification ◽  
Second Order ◽  
Lie Group Classification

On the classification of rational second-order Bézier curves

2008 ◽  
Vol 41 (2) ◽  
pp. 176-181
Author(s):  
M. I. Grigor’ev ◽  
V. N. Malozemov ◽  
A. N. Sergeev
Keyword(s):  
Second Order ◽  
Bezier Curves ◽  
Bézier Curves

scholarly journals PROPOSAL OF THE SPATIAL DEPENDENCE EVALUATION FROM THE POWER SEMIVARIOGRAM MODEL

2017 ◽  
Vol 23 (3) ◽  
pp. 461-475 ◽  
Author(s):  
Ismael Canabarro Barbosa ◽  
Edemar Appel Neto ◽  
Enio Júnior Seidel ◽  
Marcelo Silva de Oliveira
Keyword(s):  
Spatial Correlation ◽  
Spatial Dependence ◽  
Second Order ◽  
Power Model ◽  
Semivariogram Model ◽  
Model Based ◽  
Symmetrical Distribution ◽  
Model Adjustment ◽  
Equivalent Factor

Abstract: In Geostatistics, the use of measurement to describe the spatial dependence of the attribute is of great importance, but only some models (which have second-order stationarity) are considered with such measurement. Thus, this paper aims to propose measurements to assess the degree of spatial dependence in power model adjustment phenomena. From a premise that considers the equivalent sill as the estimated semivariance value that matches the point where the adjusted power model curves intersect, it is possible to build two indexes to evaluate such dependence. The first one, SPD * , is obtained from the relation between the equivalent contribution (α) and the equivalent sill (C * = C 0 + α), and varies from 0 to 100% (based on the calculation of spatial dependence areas). The second one, SDI * , beyond the previous relation, considers the equivalent factor of model (FM * ), which depends on the exponent β that describes the force of spatial dependence in the power model (based on spatial correlation areas). The SDI * ,for β close to 2, assumes its larger scale, varying from 0 to 66.67%. Both indexes have symmetrical distribution, and allow the classification of spatial dependence in weak, moderate and strong.

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