In this paper we construct a large class of modules for toroidal Lie superalgebras. Toroidal Lie superalgebras are universal central extensions of g⊗A where g is a basic classical Lie superalgebra and A is Laurent polynomial ring in several variables. The case where g is a simple finite dimensional Lie algebra is included.

We derive formulas for (i) the number of distinct toroidal n × n binary arrays, allowing rotation of rows and/or columns as well as matrix transposition, and (ii) the number of distinct toroidal n × n binary arrays, allowing rotation and/or reflection of rows and/or columns as well as matrix transposition.

We show that a k x n diagonal mesh is isomorphic to a 9 x 9 -9 x 9 twisted toroidal mesh, i.e., a network similar to a standard 9 x 9 toroidal mesh, but with opposite handed twists of 9 in the two directions, which results in a loss of (9)2 nodes

A formula for the number of toroidal m × n binary arrays, allowing rotation of the rows and/or the columns but not reflection, is known. Here we find a formula for the number of toroidal m × n binary arrays, allowing rotation and/or reflection of the rows and/or the columns.

This paper studies deterministic movement over toroidal grids, integrating local information, bounded memory and choice at individual nodes. The research is motivated by recent work on deterministic random walks, and applications in multi-agent systems. Several results regarding passing tokens through toroidal grids are discussed, as well as some open questions.

In this paper, we shall prove that a projective-planar (resp., toroidal) triangulation G has K6 as a minor if and only if G has no quadrangulation isomorphic to K4 (resp., K5) as a subgraph. As a application of the theorems, we can prove that Hadwiger’s conjecture is true for projective-planar and toroidal triangulations.

Characteristics of toroidal rotation pro�les in tokamak plasmas are studied under the in�uence of fast-ion losses due to a toroidal �eld (TF) ripple by using a one-dimensional multi-�uid transport code, TASK/TX. When a neutral beam (NB) is injected into a plasma, a part of fast ions is lost due to the effect of the TF ripple. The radial current then �ows inward in the bulk plasma to keep quasi-...