Lie algebra projectors and the kinematics of collective motions

1981 ◽  
Vol 14 (1) ◽  
pp. 97-109 ◽  
Author(s):  
P Gulshani
2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.


2018 ◽  
Vol 13 (3) ◽  
pp. 59-63 ◽  
Author(s):  
D.T. Siraeva

Equations of hydrodynamic type with the equation of state in the form of pressure separated into a sum of density and entropy functions are considered. Such a system of equations admits a twelve-dimensional Lie algebra. In the case of the equation of state of the general form, the equations of gas dynamics admit an eleven-dimensional Lie algebra. For both Lie algebras the optimal systems of non-similar subalgebras are constructed. In this paper two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras of the twelve-dimensional Lie algebra. The reduction of the constructed submodels to invariant submodels of eleven-dimensional and twelve-dimensional Lie algebras is proved.


Impact ◽  
2019 ◽  
Vol 2019 (10) ◽  
pp. 84-86
Author(s):  
Keisuke Fujii

The coordination and movement of people in large crowds, during sports games or when socialising, seems readily explicable. Sometimes this occurs according to specific rules or instructions such as in a sport or game, at other times the motivations for movement may be more focused around an individual's needs or fears. Over the last decade, the computational ability to identify and track a given individual in video footage has increased. The conventional methods of how data is gathered and interpreted in biology rely on fitting statistical results to particular models or hypotheses. However, data from tracking movements in social groups or team sports are so complex as they cannot easily analyse the vast amounts of information and highly varied patterns. The author is an expert in human behaviour and machine learning who is based at the Graduate School of Informatics at Nagoya University. His challenge is to bridge the gap between rule-based theoretical modelling and data-driven modelling. He is employing machine learning techniques to attempt to solve this problem, as a visiting scientist in RIKEN Center for Advanced Intelligence Project.


Author(s):  
Ercüment H. Ortaçgil
Keyword(s):  

The discussions up to Chapter 4 have been concerned with the Lie group. In this chapter, the Lie algebra is constructed by defining the operators ∇ and ∇̃.


1992 ◽  
Vol 07 (23) ◽  
pp. 2077-2085 ◽  
Author(s):  
A. D. POPOV

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.


Sign in / Sign up

Export Citation Format

Share Document