SO(p, q) = {g ∈ SLp+q(R) : g>Qg = Q} (where Q = ( 1p 0 0 −1q ) )  SU(2) −→ SO(3) SL2(R) −→ SO(2, 1) SU(2)× SU(2) −→ SO(4) SL2(C) −→ SO(3, 1) SL2(R)× SL2(R) −→ SO(2, 2) Sp∗(2, 0) −→ SO(5) Sp∗(1, 1) −→ SO(4, 1) Sp2(R) −→ SO(3, 2) SU(4) −→ SO(6) SL2(H) −→ SO(5, 1) SU(2, 2) −→ SO(4, 2) SL4(R) −→ SO(3, 3) Thus, these are small examples...

A $Gamma$-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a $Gamma$-so-ring. In this paper we introduce the notions of subdirect product and $(phi,rho)$-product of $Gamma$-so-rings and study $(phi,rho)$-represen...

Developments in computer and communication technologies over the past ten years aptly support the use of the term global village to describe the present worldwide provision and distribution of information. These technologies are increasingly being employed in Africa, but their presence is not widespread and evenly distributed. Librarians in Africa are establishing the basic tools and organizati...

Metastases are tumors that develop at a distance from their primary origin and are responsible for the death of 90% of cancer patients. For over a century the notion of seed (migrating cells) and soil (the locus where those cells anchor) provided an accurate account of which were the protagonists in their genesis. Despite aggressive efforts to unravel the dynamics involving migrating cells and ...

Starting from the classical r-matrix of the non-standard (or Jordanian) quantum deformation of the sl(2,R) algebra, new triangular quantum deformations for the real Lie algebras so(2, 2), so(3, 1) and iso(2, 1) are simultaneously constructed by using a graded contraction scheme; these are realized as deformations of conformal algebras of (1 + 1)-dimensional spacetimes. Timetype and space-type q...