This paper extends the concept of the PLR-group from the neo-Riemannian theory, which acts on the set of major and minor triads, to a PS-group, which acts on the set of major and minor seventh chords. Like the PLR-group, the PS-group is isomorphic to D12, the dihedral group of order 24, and only compositions of two operations are needed to generate all group elements. Unlike the actions from PL...

We study a construction of the Mathieu group M12 using a game reminiscent of Loyd’s “15-puzzle”. The elements of M12 are realized as permutations on 12 of the 13 points of the finite projective plane of order 3. There is a natural extension to a “pseudogroup” M13 acting on all 13 points, which exhibits a limited form of sextuple transitivity. Another corollary of the construction is a metric, a...

Group mobility has become more evidently a phenomenon that will occur to MANET applications. This paper presents an extension to one of the current MANET WG standards, namely, OLSR for such scenarios. The extension LANMAR+OLSR seeks to provide OLSR the functionality of Landmark Routing, a scalable routing protocol designed for large-scale MANETs exhibiting group mobility. This paper describes t...

In this paper we show that over any field K of characteristic different from 2, the Maslov index gives rise to a 2-cocycle on the stable symplectic group with values in the Witt group. We also show that this cocycle admits a natural reduction to I2(K) and that the induced natural homomorphism from K2Sp(K)→ I2(K) is indeed the homomorphism given by the symplectic symbol {x, y} mapping to the Pfi...

In this paper, we describe a first step towards a collaborative extension of the well-known 3D-Slicer; this platform is nowadays used as a standalone tool for both surgical planning and medical intervention. We show how this tool can be easily modified to make it collaborative so that it may constitute an integrated environment for expertise exchange as well as a useful tool for academic purposes.

We show that the universal odd Chern form, defined on the stable unitary group U , extends to the loop group LU as an equivariantly closed differential form. This provides an odd analogue to the Bismut-Chern form that appears in supersymmetric field theories. We also describe the associated transgression form, the so-called Bismut-Chern-Simons form, and explicate some properties it inherits as ...

The structure of a cotangent bundle is investigated for quantum linear groups GLq(n) and SLq(n). Using a q-version of the Cayley-Hamilton theorem we construct an extension of the algebra of differential operators on SLq(n) (otherwise called the Heisenberg double) by spectral values of the matrix of right invariant vector fields. We consider two applications for the spectral extension. First, we...

We give an example of a subgroup of SL2 C which is a strictly ascending HNN extension of a non-abelian finitely generated free group F . In particular, we exhibit a free group F in SL2 C of rank 6 which is conjugate to a proper subgroup of itself. This answers positively a question of Drutu and Sapir (2005). The main ingredient in our construction is a specific finite volume (non-compact) hyper...

This paper presents a robust, scalable extension to the recently proposed multicast Group Key Management Protocol (GKMP) ([1], [2]), in terms of security administration. The GKMP has two major security related problems, (a) lack of any mechanism to remove a compromised group administrator, (b) lack of scalability. We are able to remove a compromised single panel member from generating the group...

the full automorphism group of $u_6(2)$ is a group of the form $u_6(2){:}s_3$. the group $u_6(2){:}s_3$ has a maximal subgroup $2^9{:}(l_3(4){:}s_3)$ of order 61931520. in the present paper, we determine the fischer-clifford matrices (which are not known yet) and hence compute the character table of the split extension $2^9{:}(l_3(4){:}s_3)$.