In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry method for third-order differential equations.In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry m...

We consider properties of ows, the relationships between them, and whether numerical integrators can be made to preserve these properties. This is done in the context of automorphisms and antiautomorphisms of a certain group generated by maps associated to vector elds. This new framework uniies several known constructions. The main application is to explore the relationship between spatial symm...

A brief account of symmetry in its Greek origins is presented and its role in the analysis of data indexed by permutations is discussed, with examples of ranked preference data and short biological sequences.

We review the construction of continuous wavelet transforms adapted to a given symmetry. Then we discuss in detail successively spatial wavelets, wavelets on the sphere and space-time wavelets. 1. HOW TO DEFINE AN ADAPTED WAVELET TRANSFORM? As it is well-known [1], wavelet analysis comes in two versions: the continuous one, used mostly for signal or image analysis, and the discrete one, origina...

As it is well known, symmetry plays a crucial role in the theoretical physics. On other hand, the Noether symmetry is a useful procedure to select models motivated at a fundamental level, and to discover the exact solution to the given lagrangian. In this work, Noether symmetry in f(T) theory on a spatially homogeneous and anisotropic Bianchi type I universe is considered. We discuss the Lagran...