Given an abstract group G, an N dimensional orthogonal matrix representation G of G, and an “initial vector” x ∈ R , Slepian defined the group code generated by the representation G to be the set of vectors Gx. If G is a group of permutation matrices, the set Gx is called a “permutation code”. For permutation codes a ’stack algorithm’ decoder exists that, in the presence of low noise, produces ...

In a longitudinal study, infants' habituation and mothers' encouragement of attention were assessed at 5 months, and toddlers' language comprehension, language production, and pretense play and mothers' encouragement of attention were assessed at 13 months. Structural equation modeling was used to examine the unique contributions of infant habituation and maternal stimulation to toddlers' cogni...

The probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. Several authors have investigated this notion with methods of the representation theory and with combinatorial techniques. Here we illustrate that a wider context may be considered and show some structural restrictions on the group.

We call a Clayey graph Γ = Cay(G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aunt(Γ). in this paper, we give a classification of all non-normal Clayey graphs of finite abelian group with valency 6. 

We give a unitary irreducible representation of the proper Poincar\'e group that leads to an operational version classical relativistic dynamics massive spinless particle. Unlike quantum mechanics, in this theory there is no uncertainty principle between position and momentum. It will be shown contains Koopman-von Neumann formalism as particular case, explicit connection with Hamiltonian mechan...