The relation between the properties of a specific crystallographic site and the properties of the full crystal is discussed by using spherical tensors. The concept of spherical tensors is introduced and the way it transforms under the symmetry operations of the site and from site to site is described in detail. The law of spherical tensor coupling is given and illustrated with the example of th...

In this paper we propose the possible use of a new type of salient points we call CASS (Centers of Approximate Spherical Symmetry) that are extracted from the Multiscale Area Projection transform described in [GL12]. In particular, we show that it is possible to build graphs joining these points following maximal values of the MAPT (Radial Symmetry Graphs) and that these graphs can be used to e...

Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential equations. For the equations so obtained, first integrals are deduced which consequently give rise to explicit solutions. Potential symmetries, which are realized as...

The embedding of a given point set with non-crystallographic symmetry into higher-dimensional space is reviewed, with special emphasis on the Minkowski embedding known from number theory. This is a natural choice that does not require an a priori construction of a lattice in relation to a given symmetry group. Instead, some elementary properties of the point set in physical space are used, and ...

We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of difference equations are introduced as invariants of the action of the symmetry group. Linear equations are modules over the skew group algebra, solutions are morphisms relating a given equation to other equ...

Following an earlier work we derive a gauge-independent canonical structure for a fully relativistic multicomponent plasma theory. The Klimontovich form of the distribution function is used to derive the basic Poisson bracket relations for the canonical variables/~, B, and E. The Poisson bracket relations provide an explicit canonical realization of the Lie algebra of the Poincar6 group and the...

Symmetry simplifications are introduced in configuration interaction (CI) by reducing the number of symmetry-allowed space types if there is degeneracy in some of the molecular orbitals by constructing the unique space types. A new symmetry group which we call the configuration symmetry group is defined and is shown to be expressible as a generalized wreath product group. Generating functions a...