We investigate non-commutative differential calculus on the supersymmetric version of quantum space in which quatum supergroups are realized. Multiparametric quantum deformation of the general linear supergroup, GLq(m|n), is studied and the explicit form for the R̂-matrix is presented. We apply these results to the quantum phase-space construction of OSpq(2n|2m) and calculate their R̂-matrices. ∗...

It is proved that up to isomorphism there is only one (2,2)-dimensional supertorus associated to a nontrivial representation of its underlying 2-torus, and that it has nontrivial odd brackets. This supertorus is obtained by finding out first a canonical form for its Lie superalgebra, and then using Lie’s technique to represent it faithfully as supervector fields on a supermanifold. Those superv...

Phyllite and quartzite, probably Precambrian, trend meridionally and dip steeply in the New River Gorge above the junction with the Salisbury River in southern Tasmania. Further upstream an association of silty dolomite and conglomerate is less deformed and may be younger. Siliceous conglomerate boulders occur in the New River below the gorge. Late Ordovician carbonates of the Gordon Group are ...

Supersymmetry was first applied to high energy physics. In the early eighties, it found a second and very fruitful field of applications in stochastic quantum physics. This relates to Random Matrix Theory, the topic I focus on in this contribution. I review several aspects of more mathematical interest, in particular, supersymmetric extensions of the Itzykson– Zuber and the Berezin–Karpelevich ...

Present work is based on the concept of integral safety management of system of systems and it gives the proposal of set of measures into the simultaneously modern concept of communities called “smart cities”. The target is to ensure the safe smart city, i.e. the human community that will ensure the security and the development of their citizens under the conditions of normal, abnormal and crit...

The complete set of formulas describing the new quantum deformation of the OSP (1; 2) supergroup is provided. A general ansatz is solved for the deformation of the Borel subalgebra of its dual quantum deformation of osp(1; 2). ∗Talk given at the 7-th Colloquium ”Quantum Groups and Integrable Systems”, Prague 1998. 1

Let M0 = G0/H be a (pseudo)-Riemannian homogeneous spin manifold, with reductive decomposition g0 = h + m and let S(M0) be the spin bundle defined by the spin representation Ãd : H → GLR(S) of the stabilizer H . This article studies the superizations of M0, i.e. its extensions to a homogeneous supermanifold M = G/H whose sheaf of superfunctions is isomorphic to Λ(S(M0)). Here G is the Lie super...

Drinfeld twist is applied to the Lie algebra gl(2) so that a two-parametric deformation of it is obtained, which is identical to the Jordanian deformation of the gl(2) obtained by Aneva et al. The same twist element is applied to deform the Lie superalgebra sl(1/2), since the gl(2) is embedded into the sl(1/2). By making use of the FRT-formalism, we construct a deformation of the Lie supergroup...

In this paper, we give the quantum analogue of the dual matrices for the quantum supergroup GLq(1|1) and discuss these properties of the quantum dual supermatrices.

Smart phones are innovations that currently provide immense benefits and convenience to users in society. However, not all members of society are accepting and using smart phones; more specifically, for this research study silver-surfers or older adults (50+) are a demographic group displaying such an attitude. Currently, there is minimal knowledge of the reasons for older adults adopting and u...