New ideas for Higher-Order Array Processing are introduced. The paper focuses on fourth-order cumulant statistics. They are expressed in an index-free formalism (that is believed to be of general interest) allowing the exploitation of all their symmetry properties. We show that, when dealing with 4-index quantities, symmetries are related to rank properties. The rich symmetry structure yields a...

Tetra-yttrium(III) tris-ulfide disilicate, Y(4)S(3)(Si(2)O(7)), crystallizes in the Sm(4)S(3)(Si(2)O(7)) structure type. The structure consists of isolated (Si(2)O(7))(6-) units (2mm. symmetry) and two crystallo-graphically independent Y(3+) cations bridged by one S and one O atom. The first Y atom (site symmetry .m.) is coordinated by three O atoms and three S atoms in a trigonal-prismatic arr...

For the classification of SPT phases, defining an index is a central problem. In famous paper (Pollmann et al. Phys Rev B 81:064439, 2010), Pollmann, Tuner, Berg, and Oshikawa introduced $${{\mathbb {Z}}}_2$$ -indices for injective matrix products states which have either {Z}}}_2\times {{\mathbb dihedral group (of $$\pi $$ -rotations about x, y, z-axes) symmetry, time-reversal or reflection sym...

We study a mechanism of symmetry transition upon compactification of 5-dimensional field theory on S/Z2. The transition happens unless all components in a multiplet of a symmetry group have a common Z2 parity on S /Z2. This mechanism is applied to a breakdown of SU(5) gauge symmetry in grand unified theory and phenomenological implications are discussed. ∗e-mail: [email protected]

a r t i c l e i n f o Keywords: Surface structure Structure sensitivity STM Single crystal High Miller index A set of six spherically curved Cu single crystals referred to as Surface Structure Spread Single Crystals (S 4 Cs) has been prepared in such a way that their exposed surfaces collectively span all possible crystallographic surface orientations that can be cleaved from the face centered ...

In this note we discuss some symmetry groups as nice examples of group extensions. We begin by a short general discussion of symmetry groups. An isometry of R is a distancepreserving bijection of R. For examples of isometries, translations by a vector, rotations about a point, and reflections about a hyperplane are all isometries. Let Isom(R) be the set of all isometries of R. This is a group u...

Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices respectively. We show that the probability density function for the corresponding spacings between consecutive eigenvalues can be written exactly in the Wigner surmise type form a(s)e −b(s) for a simply related to a Painlevé transcendent and b its anti-derivative....

In this paper we present various $4d$ $\mathcal{N}=1$ dualities involving theories obtained by gluing two $E[USp(2N)]$ blocks via the gauging of a common $USp(2N)$ symmetry with addition $2L$ fundamental matter chiral fields. For $L=0$ in particular theory has quantum deformed moduli space breaking and its index takes form delta-function. We interpret it as Identity wall which identifies surviv...