Let Γ be an abelian group and B be a subset of Γ. The addition Cayley graph G′ = Cay(Γ, B) is the graph having the vertex set V (G′) = Γ and the edge set E(G′) = {ab : a + b ∈ B}, where a, b ∈ Γ. For a positive integer n > 1, the unitary addition Cayley graph Gn is the graph whose vertex set is Zn, the integers modulo n and if Un denotes set of all units of the ring Zn, then two vertices a, b a...

We show that for two partially ordered semigroups S and T with common local units, there exists a unitary Morita context with surjective maps if and only if the categories of closed right Sand T posets are equivalent.

The entanglement transfer from electrons localized in a pair of quantum dots to free photons is governed by optical selection rules, enforced by conservation of angular momentum. We point out that the transfer can not by achieved by means of unitary evolution unless the angular momentum of the two initial qubit states differs by 2 units of ¯ h. In particular, for spin-entangled electrons the di...

The entanglement transfer from electrons localized in a pair of quantum dots to circularly polarized photons is governed by optical selection rules, enforced by conservation of angular momentum. We point out that the transfer can not be achieved by means of unitary evolution unless the angular momentum of the two initial qubit states differs by 2 units of ¯ h. In particular, for spin-entangled ...

in this work, using eigenvalues and eigenvectors of unitary cayley graphs over finite local rings and elementary linear algebra, we characterize which local rings allowing pst occurring in its unitary cayley graph. moreover, we have some developments when $r$ is a product of local rings.

‎We study $R$-groups for $p$-adic inner forms of quasi-split special unitary groups‎. ‎We prove Arthur's conjecture‎, ‎the isomorphism between the Knapp-Stein $R$-group and the Langlands-Arthur $R$-group‎, ‎for quasi-split special unitary groups and their inner forms‎. ‎Furthermore‎, ‎we investigate the invariance of the Knapp-Stein $R$-group within $L$-packets and between inner forms‎. ‎This w...

A signed graph (or sigraph in short) is an ordered pair S = (Su, σ), where Su is a graph G = (V,E) and σ : E → {+,−} is a function from the edge set E of Su into the set {+,−}. For a positive integer n > 1, the unitary Cayley graph Xn is the graph whose vertex set is Zn, the integers modulo n and if Un denotes set of all units of the ring Zn, then two vertices a, b are adjacent if and only if a...

This letter proposes a new practical multiuser MIMO (MU-MIMO) scheme, which is an evolution of the well-known Per User Unitary beamforming Rate Control (PU2RC) proposed for 3GPP-LTE and IEEE802.16m standards. The proposed scheme includes an efficient user scheduling algorithm which alleviates the major weakness of the conventional PU2RC. Numerical results show that the proposed scheme provides ...

Christakos, Constantinos N. On the detection and measurement (Christakos 1994; also see the appendix in Christakos et al. of synchrony in large neural populations by coherence analysis. 1991). This approach uses as a tool the coherence function J. Neurophysiol. 78: 3453–3459, 1997. This study considers the between unitary and population-aggregate activity (UTA copossibility of using coherence a...