A Trinomial Analogue of Bailey's Lemma and N=2 Superconformal Invariance

We propose and prove a trinomial version of the celebrated Bailey's lemma. As an application we obtain new fermionic representations for characters of some unitary as well as nonunitary models of N = 2 superconformal field theory (SCFT). We also establish interesting relations between N = 1 and N = 2 models of SCFT with central charges $(3/2)( 1 -{2(2 - 4\nu)^2}/{2(4\nu)})$ and $3(1 - 2/{4\nu})$. A number of new mock theta function identities are derived.Comment: Reference and note adde

Teachers and Careers: The role of school teachers in delivering career and employability learning

Teach Firs

A double bounded key identity for Goellnitz's (big) partition theorem

Given integers i,j,k,L,M, we establish a new double bounded q-series identity from which the three parameter (i,j,k) key identity of Alladi-Andrews-Gordon for Goellnitz's (big) theorem follows if L, M tend to infinity. When L = M, the identity yields a strong refinement of Goellnitz's theorem with a bound on the parts given by L. This is the first time a bounded version of Goellnitz's (big) theorem has been proved. This leads to new bounded versions of Jacobi's triple product identity for theta functions and other fundamental identities.Comment: 17 pages, to appear in Proceedings of Gainesville 1999 Conference on Symbolic Computation

Distributed feedback lasers

A ridge waveguide distributed feedback laser was developed in InGaAsP. These devices have demonstrated CW output powers over 7 mW with threshold currents as low as 60 mA at 25 C. Measurements of the frequency response of these devices show a 3 dB bandwidth of about 2 GHz, which may be limited by the mount. The best devices have a single mode spectra over the entire temperature range tested with a side mode suppression of about 20 dB in both CW and pulsed modes. The design of this device, including detailed modeling of the ridge guide structure, effective index calculations, and a discussion of the grating configuration are presented. Also, the fabrication of the devices is presented in some detail, especially the fabrication of and subsequent growth over the grating. In addition, a high frequency fiber pigtailed package was designed and tested, which is a suitable prototype for a commercial package

New Finite Rogers-Ramanujan Identities

We present two general finite extensions for each of the two Rogers-Ramanujan identities. Of these one can be derived directly from Watson's transformation formula by specialization or through Bailey's method, the second similar formula can be proved either by using the first formula and the q-Gosper algorithm, or through the so-called Bailey lattice.Comment: 19 pages. to appear in Ramanujan

Generating functions for canonical systems of fermions

The method proposed by Pratt to derive recursion relations for systems of degenerate fermions [Phys. Rev. Lett. 84, 4255 (2000), arXiv:nucl-th/9905055] relies on diagrammatic techniques. This efficient formalism assumes no explicit two-body interactions, makes possible the inclusion of conservation laws and requires low computational time. In this brief report, we show that such recursion relations can be obtained from generating functions, without any restriction as concerns the number of conservation laws (e.g. total energy or angular momentum).Comment: submitted to Physical Review