In the following, isomorphism of an arbitrary finite group of symmetry, non-crystallographic symmetry (quaternion groups, Pauli matrices groups, and other abstract subgroups), in addition to the permutation group, are considered. Application of finite groups of permutations to the packing space determines space tilings by policubes (polyominoes) and forms a structure. Such an approach establish...

A method of finding relative periodic orbits for differential equations with continuous symmetries is described and its utility demonstrated by computing relative periodic solutions for the one-dimensional complex Ginzburg-Landau equation (CGLE) with periodic boundary conditions. A relative periodic solution is a solution that is periodic in time, up to a transformation by an element of the equ...

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...

Maximum mixing in atmospheric neutrino oscillation, as well as vanishing of the MNS matrix element Ue3, are consequences of a 2-3 symmetry, under which the neutrino mass matrix is invariant under the interchange of second and third generation neutrinos. These predictions of the 2-3 symmetry are consistent with the results of Super-Kamiokande, K2K, and CHOOZ experiments. If the symmetry is exact...

Small deformations of a viscoelastic body are considered through the linear Maxwell and Kelvin-Voigt models in the quasi-static equilibrium. A robust mixed finite element method, enforcing the symmetry of the stress tensor weakly, is proposed for these equations on simplicial tessellations in two and three dimensions. A priori error estimates are derived and numerical experiments presented. The...

Mappings from a master element to the physical mesh element, in conjunction with local metrics such as those appearing in the Target-matrix paradigm, are used to measure quality at points within an element. The approach is applied to both linear and quadratic triangular elements; this enables, for example, one to measure quality within a quadratic finite element. Quality within an element may a...

The isomerization properties of an azocarbazole macrocycle in solution were investigated utilizing NMR spectroscopy with in situ irradiation in combination with DFT calculations. It was demonstrated that the position of azo units in a rigid macrocyclic system influences the photoisomerization pathway even if the initial all-E isomer is highly symmetric. Furthermore, the effect of ring strain on...

We introduce a new mixed method for linear elasticity. The novelty is a simplicial element for the approximate stress. For every positive integer k, the row-wise divergence of the element space spans the set of polynomials of total degree k. The degrees of freedom are suited to achieve continuity of the normal stresses. What makes the element distinctive is that its dimension is the smallest re...