The theory of finite groups is of central importance in mathematics, and finds wide applications in all the physical sciences and elsewhere. In essence it is the deep study of symmetry in all its innumerable manifestations, and so has applications in all situations where symmetry occurs. The building blocks of finite groups are the ‘simple’ groups, analogous to the prime numbers in number theor...

A phenomenological explanation of the magnetoelectric behavior of Co3TeO6 is developed. We explain the second harmonic generation data and the magnetic field induced spontaneous electric polarization in the magnetically ordered phase below 20 K. Disciplines Physical Sciences and Mathematics | Physics Comments Harris, A. B. (2012). Symmetry Analysis of Multiferroic Co3TeO6. Physical Review B, 85...

Rotation symmetry is less constraining than space-time symmetry. The free electron propagator is a projection operator that we show can be constructed from rotation symmetric projection operators. Rotation-based identifications of time, space, energy, momentum, polarization matrices, and the positron hypothesis are determined by the constraints that turn rotation symmetric projection operators ...

Takens Dynamical Systems and Turbulence, Lecture Notes in Mathematics, edited by D. A. Rand and L. S. Young Springer-Verlag, New York, 1981 , Vol. 898, pp. 366–381 has shown that a dynamical system may be reconstructed from scalar data taken along some trajectory of the system. A reconstruction is considered successful if it produces a system diffeomorphic to the original. However, if the origi...

We present new rectangular mixed finite elements for linear elasticity. The approach is based on a modification of the Hellinger-Reissner functional in which the symmetry of the stress field is enforced weakly through the introduction of a Lagrange multiplier. The elements are analogues of the lowest order elements described in Arnold, Falk and Winther [ Mixed finite element methods for linear ...

The theory of finite groups is of central importance in mathematics, and finds wide applications in all the physical sciences and elsewhere. In essence it is the deep study of symmetry in all its innumerable manifestations, and so has applications in all situations where symmetry occurs. The building blocks of finite groups are the ‘simple’ groups, analogous to the prime numbers in number theor...

The problem of invariant output tracking is considered: given a control system admitting a symmetry group G, design a feedback such that the closed-loop system tracks a desired output reference and is invariant under the action of G. Invariant output errors are defined as a set of scalar invariants of G; they are calculated with the Cartan moving frame method. It is shown that standard tracking...

Rotating rings of tetrahedra are well known from recreational mathematics. Rings of N tetrahedra with N even are analyzed by symmetry-adapted versions of classical counting rules of mechanism analysis. For N ≥ 6 a single state of selfstress is found, together with N − 5 symmetry-distinct mechanisms, which include the eponymous rotating mechanism. For N = 4 in a generic configuration, a single m...

With any even Hecke symmetry R (that is a Hecke type solution of the Yang-Baxter equation) we associate a quasitensor category. We formulate a condition on R implying that the constructed category is rigid and its commutativity isomorphisms RU,V are natural in the sense of [T]. We show that this condition leads to rescaling the initial Hecke symmetry. We suggest a new way of introducing traces ...