Let G be a finite group with given subgroups H and K. π an irreducible complex representation of such that its space H-invariant vectors as well the K-invariant are both one dimensional. vH (resp. vK) denote K-invariant) vector unit norm in G-invariant inner product 〈,〉π on π. Our interest is computing square absolute value 〈vH,vK〉π. This correlation constant c(π;H,K) defined by Gross [3]. In t...

An orthogonality space is a set equipped with symmetric and irreflexive binary relation. We consider spaces the additional property that any collection of mutually orthogonal elements gives rise to structure Boolean algebra. Together maps preserve substructures, we are led category NOS normal spaces. Moreover, an finite rank called linear if for two distinct e f there third one g such exactly p...

We present in this communication a new method to localize a face in an image. The originality of work presented consists on the use of vectors of geometrical moments like entries to a Forward BackPropagation neural network which provide at its output layer a vector of co-ordinates in (R,θ) representing pixels surrounding the face contained in the treated image. Very known for their orthogonalit...

For the double complex structure of grading-restricted vertex algebra cohomology defined in \cite{Huang}, we introduce a multiplication elements spaces. We show that orthogonality and bi-grading conditions applied on spaces, provide relation among mappings actions co-boundary operators. Thus, endow spaces with bi-graded differential algebra. then simples classes for algebra, their independence ...

A novel approach in quantifying code orthogonality factor for UTRA-FDD systems is extended in this paper to include the impact of down-link beamforming. The effects of fixed beam forming on code orthogonality is analysed through the aid of real channel data taken from urban cellular environments. The results show a significant overall improvement in code orthogonality with beam forming, especia...

In this note we establish connections between the orthogonality of conjugates of a finite or infinite quasigroup and some strictly transitive subsets of the complete multiplication group of this quasigroup. These connections are used for the investigation of orthogonality of distinct pairs of conjugates for quasigroups (loops) from some classes. For finite quasigroups the quasi-identities corre...