A Scale Invariant Clustering using Minimum Volume Ellipsoids

2006 ◽  
Author(s):  
Mahesh Kumar ◽  
James B. Orlin
Keyword(s):  
Minimum Volume ◽  
Scale Invariant

Scale-invariant clustering with minimum volume ellipsoids

2008 ◽  
Vol 35 (4) ◽  
pp. 1017-1029 ◽  
Author(s):  
Mahesh Kumar ◽  
James B. Orlin
Keyword(s):  
Minimum Volume ◽  
Scale Invariant

Scale-Invariant Theory of Optical Properties of Fractal Clusters

1990 ◽  
Author(s):  
Vadim A. Markel ◽  
Leonid S. Muratov ◽  
Mark I. Stockman ◽  
Thomas F. George
Keyword(s):  
Optical Properties ◽  
Invariant Theory ◽  
Scale Invariant ◽  
Fractal Clusters

Best Matching: Technical Details

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Point Particle ◽  
Euclidean Group ◽  
Scale Invariant ◽  
Similarity Group ◽  
N Body Problem ◽  
Technical Details ◽  
Matching Procedure ◽  
Principal Fibre ◽  
Principal Fibre Bundle ◽  
Gauge Connection

The best matching procedure described in Chapter 4 is equivalent to the introduction of a principal fibre bundle in configuration space. Essentially one introduces a one-dimensional gauge connection on the time axis, which is a representation of the Euclidean group of rotations and translations (or, possibly, the similarity group which includes dilatations). To accommodate temporal relationalism, the variational principle needs to be invariant under reparametrizations. The simplest way to realize this in point–particle mechanics is to use Jacobi’s reformulation of Mapertuis’ principle. The chapter concludes with the relational reformulation of the Newtonian N-body problem (and its scale-invariant variant).

Singularities

2018 ◽  
Author(s):  
S. G. Rajeev
Keyword(s):  
Stokes Equations ◽  
Negative Answer ◽  
Three Dimensions ◽  
Picard Iteration ◽  
Navier Stokes ◽  
Scale Invariant ◽  
Navier Stokes Equations ◽  
L2 Norm ◽  
Two Dimensional Flow ◽  
Physical Consequences

The initial value problem of the incompressible Navier–Stokes equations is explained. Leray’s classic study of it (using Picard iteration) is simplified and described in the language of physics. The ideas of Lebesgue and Sobolev norms are explained. The L2 norm being the energy, cannot increase. This gives sufficient control to establish existence, regularity and uniqueness in two-dimensional flow. The L3 norm is not guaranteed to decrease, so this strategy fails in three dimensions. Leray’s proof of regularity for a finite time is outlined. His attempts to construct a scale-invariant singular solution, and modern work showing this is impossible, are then explained. The physical consequences of a negative answer to the regularity of Navier–Stokes solutions are explained. This chapter is meant as an introduction, for physicists, to a difficult field of analysis.

scholarly journals Herriott Cell Design With Minimum Volume and Multiple Reflection Rings for Infrared Gas Sensing

2019 ◽  
Vol 31 (7) ◽  
pp. 541-544
Author(s):  
Ming Dong ◽  
Chuantao Zheng ◽  
Yu Zhang ◽  
Yiding Wang ◽  
Frank K. Tittel
Keyword(s):  
Gas Sensing ◽  
Multiple Reflection ◽  
Cell Design ◽  
Minimum Volume ◽  
Herriott Cell

scholarly journals Scaling of entanglement in 2 + 1-dimensional scale-invariant field theories

2015 ◽  
Vol 2015 (2) ◽  
pp. P02010 ◽  
Author(s):  
Xiao Chen ◽  
Gil Young Cho ◽  
Thomas Faulkner ◽  
Eduardo Fradkin
Keyword(s):  
Field Theories ◽  
Scale Invariant
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