Advantages of hypercube network and torus topology are used to derive an embedded architecture for product network known as torus embedded hypercube scalable interconnection network. This paper analyzes torus embedded hypercube network pertinent to parallel architecture. The network metrics are used to show how good embedded network can be designed for parallel computation. Network parameter an...

In this paper, we study the application of the function field sieve algorithm for computing discrete logarithms over finite fields of the form Fqn when q is a medium-sized prime power. This approach is an alternative to a recent paper of Granger and Vercauteren for computing discrete logarithms in tori, using efficient torus representations. We show that when q is not too large, a very efficien...

Twisted torus knots are with some full twists added along number of adjacent strands. There infinitely many known examples twisted which actually knots. We give eight more infinite families such a single negative twist.

Three recent articles in Nature: Physics, on plasma physics issues relevant to the ITER fusion power experiment*[see inset], have Australian connections. Although Australia does not yet have any formal involvement with what is claimed to be the world‟s largest truly international scientific experiment, this connection is not surprising in view of the long and distinguished history of Australian...

This paper studies the extension of the Hofer metric and general Finsler metrics on the Hamiltonian symplectomorphism group Ham(M,ω) to the identity component Symp0(M,ω) of the symplectomorphism group. In particular, we prove that the Hofer metric on Ham(M,ω) does not extend to a bi-invariant metric on Symp0(M,ω) for many symplectic manifolds. We also show that for the torus T2n with the standa...