A fast diffusion equation is investigated with symmetry point of view. The set of exact non-Lie solutions constructed by M.L. Gandarias [Phys. Lett. A, 2001,V.286, 153-160] are supplemented with the similar ones. The non-classical symmetries of the corresponding potential equation are completely classified with respect to the Lie symmetry group of this equation. As a result, we obtain new wide ...

Rotational power spectrum analysis of scanning transmission electron micrographs of negatively stained herpesvirus capsids has given direct evidence for the 6-fold symmetry of the herpesvirus hexon capsomere. Individual hexons have been analyzed in situ without interference from other parts of the capsid because only one level of the capsid was in focus in the micrograph. This study found hexon...

The presence of a (Lie-point) symmetry for a differential equation leads naturally to the useful notions of symmetric sets of solutions, i.e. of sets which are mapped into themselves by the symmetry, and of orbits of solutions. We introduce the definition of partial symmetry, and show that the above notions may be preserved, although the symmetry is not exact. We consider the quite exceptional ...

Abstract: The method of linear determining equations is constructed to study conditional Lie–Bäcklund symmetry and the differential constraint of a two-component second-order evolution system, which generalize the determining equations used in the search for classical Lie symmetry. As an application of the approach, the two-component reaction-diffusion system with power diffusivities is conside...

We classify from Lie symmetry standpoint the hyperbolic heat equation with temperature-dependent medium properties. We prove that the hyperbolic heat equation may admit a two-, three-, fouror infinitedimensional symmetry Lie algebra depending on the functional form of density, thermal conductivity, and specific heat. The last possibility corresponds to exactly linearizable hyperbolic heat equat...

A transformation is derived which takes the Lorenz integrable system into the well-known Euler equations of a torque-free rigid body about a fixed point, i.e. the famous motionà la Poinsot. The proof is based on Lie group analysis applied to two third-order ordinary differential equations admitting the same two-dimensional Lie symmetry algebra. Lie's classification of two-dimensional symmetry a...

A transformation is derived which takes Lorenz integrable system into the well-known Euler equations of a free-torque rigid body with a fixed point, i.e. the famous motionà la Poinsot. The proof is based on Lie group analysis applied to two third order ordinary differential equations admitting the same two-dimensional Lie symmetry algebra. Lie's classification of two-dimensional symmetry algebr...

This paper presents a symmetry analysis based on Lie groups of a system of ordinary differential equations (ODEs) modelling the p53mdm2 regulatory pathway. This pathway is being investigated across several research groups as a biological system from which to extract dynamical and algebraic characteristics relevant to the emerging concept of Interaction Computing. After providing a conceptual mo...

Tetra-n-butylammonium bromide forms the title semi-clathrate hydrate crystal, C16H36N+.Br-.38H2O, under atmospheric pressure. The cation and anion lie at sites with mm symmetry and seven water molecules lie at sites with m symmetry in space group Pmma. Br- anions construct a cage structure with the water molecules. Tetra-n-butylammonium cations are disordered and are located at the centre of fo...