Daughter crystals in orientation relationship with a parent crystal are called variants. They can be created by a structural phase transition (Landau or reconstructive), by twinning or by precipitation. Internal and external classes of transformations defined from the point groups of the parent and daughter phases and from a transformation matrix allow the orientations of the distinct variants ...

This paper is devoted to the evaluation of the generating series of the connection coefficients of the double cosets of the hyperoctahedral group. Hanlon, Stanley, Stembridge (1992) showed that this series, indexed by a partition ν, gives the spectral distribution of some random matrices that are of interest in random matrix theory. We provide an explicit evaluation of this series when ν = (n) ...

Consider the group of integers Z under addition. Let H be the subgroup of even integers. Notice that if you take the elements of H and add one, then you get all the odd elements of Z. In fact if you take the elements of H and add any odd integer, then you get all the odd elements. On the other hand, every element of Z is either odd or even, and certainly not both (by convention zero is even and...

In this paper, we discuss an improvement of an algorithm to search for primes p and coset-partitions of (Z/pZ) that yield Ramsey algebras over Z/pZ. We also prove an upper bound on the modulus p in terms of the number of cosets. We have, as a corollary, that there is no prime p for which there exists a partition of (Z/pZ) into 13 cosets that yields a 13-color Ramsey algebra. Thus A263308(13) = 0.

This paper presents an efficient approach to the classification of the affine equivalence classes of cosets of the first order ReedMuller code with respect to cryptographic properties such as correlationimmunity, resiliency and propagation characteristics. First, we apply the method to completely classify all the 48 classes into which the general affine group AGL(2, 5) partitions the cosets of ...

In other words, a coset is what we get when we take a subgroup and shift it (either on the left or on the right). The best way to think about cosets is that they are shifted subgroups, or translated subgroups. Note g lies in both gH and Hg, since g = ge = eg. Typically gH 6= Hg. When G is abelian, though, left and right cosets of a subgroup by a common element are the same thing. When an abelia...

I review some marginal deformations of SU(2) and SL(2, R) Wess–Zumino–Witten models , which are relevant for the investigation of the moduli space of NS5/F1 brane configurations. Particular emphasis is given to the asymmetric deformations, triggered by electric or magnetic fluxes. These exhibit critical values, where the target spaces become exact geometric cosets such as S 2 ≡ SU(2)/U(1) or Ad...

The duality symmetry group of the cosets SU(n, 1) SU(n)⊗ U(1) , which describe the moduli space of a two-dimensional subspace of an orbifold model with (n − 1) complex Wilson lines moduli, is discussed. The full duality group and its explicit action on the moduli fields are derived. ∗ e-mail: [email protected]. 1 The derivation of a field theoretic low-energy effective action from string ...

Several interesting features of coset models " without fixed points " are easily understood via Chern-Simons theory. In this paper we derive explicit formulae for the handle-squashing operator in these cosets. These operators are fixed, linear combinations of the irreducible representations of the coset. As a simple application of these curious formulae, we compute the traces of all genus-one o...

Recently Golay complementary sets were shown to exist in the subsets of second-order cosets of a q-ary generalization of the first-order Reed–Muller (RM) code. We show that mutually orthogonal Golay complementary sets can also be directly constructed from second-order cosets of a q-ary generalization of the first-order RM code. This identification can be used to construct zero correlation zone ...