scholarly journals On a Law of Combination of Operators bearing on the Theory of Continuous Transformation Groups

1896 ◽  
Vol s1-28 (1) ◽  
pp. 381-390 ◽  
Author(s):  
J. E. Campbell
Keyword(s):  
Transformation Groups ◽  
Continuous Transformation

scholarly journals Transformation groups on real plane and their differential invariants

2006 ◽  
Vol 2006 ◽  
pp. 1-17 ◽  
Author(s):  
Maryna O. Nesterenko
Keyword(s):  
Lie Algebras ◽  
Differential Invariants ◽  
Transformation Groups ◽  
Real Plane ◽  
Continuous Transformation ◽  
The Real ◽  
Finite Dimensional ◽  
Complete Sets ◽  
Finite Dimensional Lie Algebras ◽  
Invariant Differentiation

Complete sets of bases of differential invariants, operators of invariant differentiation, and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of finite-dimensional Lie algebras on the real plane are revisited.

Pattern Recognition in Kittens: Performance on Lie Patterns

Perception ◽  
1983 ◽  
Vol 12 (4) ◽  
pp. 393-410 ◽  
Author(s):  
Peter C Dodwell ◽  
Frances E Wilkinson ◽  
Michael W von Grünau
Keyword(s):  
Experimental Study ◽  
Pattern Recognition ◽  
Pattern Analysis ◽  
Transformation Group ◽  
Transformation Groups ◽  
Continuous Transformation ◽  
Anatomy And Physiology ◽  
Visual Behaviour ◽  
Lie Transformation ◽  
Pattern Information

Despite a vast accumulation of knowledge about the anatomy and physiology of the cat's visual system in recent years, and about its early development, there has been very little experimental study of the development of visual behaviour in this species. This is especially true of the kitten's ability to recognize patterns. Two experiments are reported that aim to remedy some part of this deficiency, and that also serves to examine a particular hypothesis about the basis of pattern analysis in the young organism. This is Hoffman's hypothesis that the orbits of elementary Lie transformation groups (a species of continuous transformation group) represent the basis for coding pattern information.

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