Constructing one-parameter families of elliptic curves with moderate rank

We give several new constructions for moderate rank elliptic curves over Q(T). In particular we construct infinitely many rational elliptic surfaces (not in Weierstrass form) of rank 6 over Q using polynomials of degree two in T. While our method generates linearly independent points, we are able to show the rank is exactly 6 without having to verify the points are independent. The method generalizes; however, the higher rank surfaces are not rational, and we need to check that the constructed points are linearly independent.     

Constructing orthogonal pandiagonal Latin squares and panmagic squares from modular n‐queens solutions

In this article, we show how to construct pairs of orthogonal pandiagonal Latin squares and panmagic squares from certain types of modular n‐queens solutions. We prove that when these modular n‐queens solutions are symmetric, the panmagic squares thus constructed will be associative, where for an n × n associative magic square A = (a_ij), for all i and j it holds that a_ij + an?i?1,n?j?1 = c for a fixed c. We further show how to construct orthogonal Latin squares whose modular difference diagonals are Latin from any modular n‐queens solution. As well, we analyze constructing orthogonal pandiagonal Latin squares from particular classes of non‐linear modular n‐queens solutions. These pandiagonal Latin squares are not row cyclic, giving a partial solution to a problem of Hedayat. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 221–234, 2007     

Surface reconstructions of InGaAs alloys

The surface reconstructions of In_xGa_1−xAs alloys grown by molecular beam epitaxy on the (0 0 1) surfaces of GaAs and InAs have been studied by reflection high-energy electron diffraction and scanning tunnelling microscopy. A surface phase diagram is presented for the nominally strain-free alloy as a function of substrate temperature and alloy composition, and structural models for the commonly observed 3× reconstructions are discussed. Two new, electronically stable structural models are described that account for the transition of the In_xGa_1−xAs surface alloy from a c(4 × 4) to an asymmetric 3× reconstruction and that are fully consistent with all current experimental evidence.     

A vanishing theorem for supersymmetric quantum field theory and finite size effects in multiphase cluster expansions

We apply cluster expansion methods to to theN=2 Wess-Zumino models in finite volume, in two space-time dimensions. We show that in the region of convergence of the cluster expansion, a vanishing theorem holds for the supercharge of the theory; that is, the dimension of the kernel of the Hamiltonian is equal to the index of the supercharge.Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 90-07206Supported in part by National Science Foundation Mathematical Sciences Postodoctoral Research Fellowship DmS 88-07291     

Stochastic Visual Interactive Simulation Models

Many writers and practitioners have mentioned the difficulties that result from randomness in visual interactive simulation or animated simulation modelling. This paper discusses the use of VIS to model transient system behaviour, and proposes some approaches to stochastic VIS modelling which may be helpful in overcoming the difficulties.     

Octahedral metallo-mesogens of chromium, molybdenum and tungsten with 1,4,7-trisubstituted 1,4,7-triazacyclononane and three carbonyl groups as ligands

Liquid crystalline complexes with chromium, molybdenum and with tungsten as metallic centres are reported. 1,4,7-Trisubstituted 1,4,7-triazacyclononane and three carbonyl groups are coordinated in an octahedral geometry. The observed mesophases are characterized as disordered rectangular columnar of a pyramidic type.     

Some Invariance Principles for Random Vectors in the Generalized Domain of Attraction of the Multivariate Normal Law

For independent identically distributed random vectors belonging to the generalized Domain of Attraction of the multivariate normal law, we define two partial sum processes analogous to that of Donsker's Theorem. We prove that each converges in distribution to a Brownian Motion in the space of continuous functions. One process uses nonrandom operator normalization, and the other is a studentization of the first, using normalization by the empirical covariance operator.