We present a mathematical framework and algorithm for characterizing and extracting partial intrinsic symmetries of surfaces, which is a fundamental building block for many modern geometry processing algorithms. Our goal is to compute all “significant” symmetry information of the shape, which we define as r-symmetries, i.e., we report all isometric self-maps within subsets of the shape that con...

Equivalence in physics is discussed on the basis of experimental data accompanied by experimental errors. It is pointed out that the introduction of the equivalence being consistent with the mathematical definition is possible only in theories constructed on non-standard number spaces by taking the experimental errors as infinitesimal numbers. Following the idea for the equivalence, a new descr...

The second-order ordinary differential equations can have one, two, three or eight independent symmetries. Sophus Lie showed that the equations with eight symmetries and only these equations can be linearized by a change of variables. Moreover he demonstrated that these equations are at most cubic in the first derivative and gave a convenient invariant description of all linearizable equations....

In the framework of Galilei classical and mechanics (i.e. , generally relativistic classical mechanics on a spacetime with absolute time) developed by Jadczyk and Modugno, we analyse systematically the relations between symmetries of the geometric objects. We show that the (holonomic) infinitesimal symmetries of the cosymplectic structure and of its potentials are also symmetries of spacelike m...

We investigate the duality between local (complex analytic) projec- tive structures on surfaces and two dimensional neighborhoods of rational curves having self-intersection +1. study analytic classification, existence normal forms, pencil/fibration decomposition, infinitesimal symmetries. deduce some transcendental result about Painlev'e equations.

A presentation of the problem of calculating the vector coupling coefficients for SU3 ⊃ SU2⊗U1 is made, in the spirit of traditional treatments of SU2 coupling. The coefficients are defined as the overlap matrix element between product states and a coupled state with good SU3 quantum numbers. A technique for resolution of the outer degeneracy problem, based upon actions of the infinitesimal gen...

We apply the theory of infinitesimal transformations for study a family 1+1 fifth-order partial differential equations which have been proposed before description multiple kink solutions. In this analysis we perform complete classification Lie symmetries and one-dimensional optimal system. The results are applied derivation similarity solutions in particular find travel-wave scaling show that k...

The sets of the integrable lattice equations, which generalize the Toda lattice, are considered. The hierarchies of the first integrals and infinitesimal symmetries are found. The properties of the multi-soliton solutions are discussed. PACS: 05.45.Yv; 02.30.Ik; 05.50.+q