On Cayley-Aronhold realizations of $\mathrm{sl}\left( {n + 1,\;K} \right)$

Right gw-Majorization on M_{n,m}

Triangular Cayley maps of Kn, n, n

Session: 1K

A dual-transducer system was used to test concepts for on-line guidance and lesion monitoring during ultrasound therapy. The system used a spherical-cap therapy transducer (4 MHz; 40-mm dia.; 90-mm focus) with a central, collinear transducer (7.5 MHz; 10-mm dia.) for A-mode examination. A digital system provided 3 operational modes, tested in in-vitro liver. Mode 1 senses in-situ therapy-beam h...

On the Characteristic Polynomial of n-Cayley Digraphs

A digraph Γ is called n-Cayley digraph over a group G, if there exists a semiregular subgroup RG of Aut(Γ) isomorphic to G with n orbits. In this paper, we represent the adjacency matrix of Γ as a diagonal block matrix in terms of irreducible representations of G and determine its characteristic polynomial. As corollaries of this result we find: the spectrum of semi-Cayley graphs over abelian g...

On Restricted Unitary Cayley Graphs and Symplectic Transformations Modulo n

We present some observations on a restricted variant of unitary Cayley graphs modulo n, and implications for a decomposition of elements of symplectic operators over the integers modulo n. We define quadratic unitary Cayley graphs Gn, whose vertex set is the ring Zn, and where residues a, b modulo n are adjacent if and only if their difference is a quadratic residue. By bounding the diameter of...