Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd [Phys. Rev. A 65, 040301(R) (2002)] provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems are qudits, that is, have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.

Nutritional strategies for the prevention of hypocalcaemia at calving for dairy cows in pasture-based systems

This review considers the current literature on the macro-mineral nutrition of the soon-to-calve, or transition, dairy cow. Calcium is the main focus, since milk fever (clinical hypocalcaemia) appears to be the most common mineral-related problem faced by the transition cow Australia-wide. The importance of minimising calcium intake and optimising the balance of the key dietary electrolytes, sodium, potassium, sulfate, and chloride, in the weeks before calving is highlighted. Excess dietary potassium can, in some situations, induce milk fever, perhaps even more effectively than excess calcium. Excess sodium remains under suspicion. In contrast, excess dietary chlorine and, to a lesser extent, sulfur can improve the ability of the cow to maintain calcium homeostasis. Diets that promote either a hypomagnesaemia or hyperphosphataemia have also the potential to precipitate milk fever at calving. Current prevention strategies focus on the use of forages with moderate to low levels of calcium, potassium, and sodium, and also rely on or utilise addition of chloride and sulfate in the form of 'anionic' feeds. Anionic salts are one example of an anionic feed. However, legitimate questions remain as to the effectiveness of anionic salts in pasture-feeding systems. The causes and prevention of milk fever are considered from the perspective of the variety of Australian feedbases. Impediments to the use of anionic feeds in Australia feeding systems are outlined. The potential for improving maternal reserves of calcium around calving to reduce the risk of milk fever is also discussed.

Phase variable restriction-modification systems in Moraxella catarrhalis

A repetitive DNA motif was used as a marker to identify novel genes in the mucosal pathogen Moraxella catarrhalis. There is a high prevalence of such repetitive motifs in virulence genes that display phase variable expression. Two repeat containing loci were identified using a digoxigenin-labelled 5'-(CAAC)(6)-3' oligonucleotide probe. The repeats are located in the methylase components of two distinct type III restriction-modification (R-M) systems. We suggest that the phase variable nature of these R-M systems indicates that they have an important role in the biology of M. catarrhalis. (C) 2002 Published by Elsevier Science B.V. on behalf of the Federation of European Microbiological Societies.

Partial automation of database processing of simulation outputs from L-systems models of plant morphogenesis

Models of plant architecture allow us to explore how genotype environment interactions effect the development of plant phenotypes. Such models generate masses of data organised in complex hierarchies. This paper presents a generic system for creating and automatically populating a relational database from data generated by the widely used L-system approach to modelling plant morphogenesis. Techniques from compiler technology are applied to generate attributes (new fields) in the database, to simplify query development for the recursively-structured branching relationship. Use of biological terminology in an interactive query builder contributes towards making the system biologist-friendly. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

Perp-systems and partial geometries

A perp-system R(r) is a maximal set of r-dimensional subspaces of PG(N,q) equipped with a polarity rho, such that the tangent space of an element of R(r) does not intersect any element of R(r). We prove that a perp-system yields partial geometries, strongly regular graphs, two-weight codes, maximal arcs and k-ovoids. We also give some examples, one of them yielding a new pg(8,20,2).

A uniform white-noise model for fixed-point roundoff errors in digital systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.