This paper describes a new algorithm for determining all discrete contact symmetries of any differential equation whose Lie contact symmetries are known. The method is constructive and is easy to use. It is based upon the observation that the adjoint action of any contact symmetry is an automorphism of the Lie algebra of generators of Lie contact symmetries. Consequently, all contact symmetries...

RKMK methods and Crouch-Grossman methods are two classes of Lie group methods. The former is using flows and commutators of a Lie algebra of vector fields as a part of the method definition. The latter uses only compositions of flows of such vector fields, but the number of flows which needs to be computed is much higher than in the RKMK methods. We present a new type of methods which avoids th...

Let us suppose G is right-multiply prime. Is it possible to extend hulls? We show that every semi-Gaussian subalgebra is measurable. It is not yet known whether Y 6= ∞, although [31] does address the issue of invertibility. Here, admissibility is clearly a concern.

This Letter focuses on studying non-Noether symmetries and conserved quantities of the nonconservative dynamical system. Based on the relationships among motion, nonconservative forces and Lagrangian, we present conservation laws on non-Noether symmetries for nonconservative dynamical systems. A criterion is obtained on which non-Noether symmetry leads to Noether symmetry in nonconservative sys...

A new definition of conditional invariance for boundary value problems involving a wide range of boundary conditions (including initial value problems as a special case) is proposed. It is shown that other definitions worked out in order to find Lie symmetries of boundary value problems with standard boundary conditions, followed as particular cases from our definition. Simple examples of direc...

the purpose of this paper is to analyze in detail a special nonlinear partial differentialequation (npde) of the second order which is important in physical, chemical and technicalapplications. the present npde describes nonlinear diffusion and is of interest in several partsof physics, chemistry and engineering problems alike. since nature is not linear intrinsicallythe nonlinear case is there...

0. Introduction. Quantum invariants of framed links whose components are colored by modules of a simple Lie algebra g are Laurent polynomials in v1/D (with integer coefficients), where v is the quantum parameter and D an integer depending on g. We show that quantum invariants, with a suitable normalization, are Laurent polynomials in v2. We also establish two symmetry properties of quantum link...