The Jordan normal form of higher order Osserman algebraic curvature tensors

We construct new examples of algebraic curvature tensors so that the Jordan normal form of the higher order Jacobi operator is constant on the Grassmannian of subspaces of type $(r,s)$ in a vector space of signature $(p,q)$. We then use these examples to establish some results concerning higher order Osserman and higher order Jordan Osserman algebraic curvature tensors

Operator Formalism on General Algebraic Curves

The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems is developed. The physical states are expressed by means of creation and annihilation operators as in the complex plane and the correlation functions are evaluated starting from simple normal ordering rules. The Hilbert space of the theory exhibits an interesting internal structure, being splitted into $n$ ($n$ is the number of branches of the curve) independent Hilbert spaces. Exploiting the operator formalism a large collection of explicit formulas of string theory is derived.Comment: 34 pages of plain TeX + harvmac, With respect to the first version some new references have been added and a statement in the Introduction has been change

Giant intra-abdominal hydatid cysts with multivisceral locations

The disseminated intra-peritoneal hydatid disease is a very rare finding. A case of disseminated intra abdominal hydatid disease is presented along with a review of literature and various therapeutic modalitie

Effect of Hexagonal Boron Nitride on Energy Band Gap of Graphene Antidot Structures

The zero band gap (Eg) graphene becomes narrow Eg semiconductor when graphene is patterned with periodic array of hexagonal shaped antidots, the resultant is the hexagonal Graphene Antidot Lattice (hGAL). Based on the number of atomic chains between antidots, hGALs can be even and odd. The even hGALs (ehGAL) are narrow Eg semiconductors and odd hGALs (ohGAL) are semi-metals. The Eg opening up by hGALs is not sufficient to operate a realistic switching transistor. Also hGAL transistors realized on Si/SiO2 substrate are suffering with low carrier mobility and ON-OFF current ratio. In order to achieve a sizable Eg with good mobility, AB Bernal stacked hGALs on hexagonal Boron Nitride (hBN), ABA Bernal stacked hBN / hGAL / hBN sandwiched structures and AB misaligned hGAL /hBN structures are reported here for the first time. Using the first principles method the electronic structure calculations are performed. A sizable Eg of about 1.04 eV (940+100 meV) is opened when smallest neck width medium radius ehGAL supported on hBN and about 1.1 eV (940 + 200 meV) is opened when the same is sandwiched between hBN layers. A band gap on the order of 71 meV is opened for Bernal stacked ohGAL / hBN and nearly 142 meV opened for hBN / ohGAL /hBN structures for smallest radius and width of nine atomic chains between antidots. Unlike a misaligned graphene on hBN, the misaligned ohGAL/hBN structure shows increased Eg. This study could open up new ways of band gap engineering for graphene based nanostructures. Keywords: Graphene, graphene antidots, hexagonal boron nitride, band structure, band gap engineeringComment: 14 pages, 5 figures, Innovative Systems Design and Engineering,Vol 3, No 12 (2012