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.

International Grassland Congress Outlook: An historical review and future expectations

Features of the history of the International Grassland Congress are mentioned. Aspects of a number of failed themes in grassland science are described with respect to molecular biology, intensive systems of ruminant production, carbohydrate use in plant growth, plant succession and range condition, and stocking method. Future expectations are focused on meeting a balance of objectives, maintaining reductionist science, taking new initiatives in plant improvement and in the development of animal production systems, and reducing barriers to international trade. The adoption of grassland science depends upon the growth of new learning, especially through cyclical interaction between scientists and farmers.

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).

Expression and role of roundabout-1 in embryonic Xenopus forebrain

The receptor Roundabout-1 (Robo1) and its ligand Slit are known to influence axon guidance and central nervous system (CNS) patterning in both vertebrate and nonvertebrate systems. Although Robo-Slit interactions mediate axon guidance in the Drosophila CNS, their role in establishing the early axon scaffold in the embryonic vertebrate brain remains unclear. We report here the identification and expression of a Xenopus Robo1 orthologue that is highly homologous to mammalian Robo1. By using overexpression studies and immunohistochemical and in situ hybridization techniques, we have investigated the role of Robo1 in the development of a subset of neurons and axon tracts in the Xenopus forebrain. Robo1 is expressed in forebrain nuclei and in neuroepithelial cells underlying the main axon tracts. Misexpression of Robo1 led to aberrant development of axon tracts as well as the ectopic differentiation of forebrain neurons. These results implicate Robo1 in both neuronal differentiation and axon guidance in embryonic vertebrate forebrain. (C) 2002 Wiley-Liss, Inc.

Transformation and transposon mutagenesis of Leifsonia xyli subsp. Xyli, causal organism of Ratoon Stunting Discease of sugarcane

Conditions have been developed for genetic transformation and insertional mutagenesis in Leifsonia xyli subsp. xyli (Lxx), the causal organism of ratoon stunting disease (RSD), one of the most damaging and intractable diseases of sugarcane internationally. Transformation frequencies ranged from 1 to 10 colony forming units (CFU)/mug of plasmid DNA using Clavibacter/Escherichia coli shuttle vectors pCG188, pDM302, and pDM306 and ranged from 50 to 500 CFU/mug using cosmid cloning vectors pLAFR3 and pLAFR5-km. The transformation/transposition frequency was 0 to 70 CFU/mug of DNA, using suicide vectors pUCD623 and pSLTP2021 containing transposable elements Tn4431 and Tn5, respectively. It was necessary to grow Lxx in media containing 0.1% glycine for electroporation and to amplify large plasmids in a dam(-)/dcm(-) E. coli strain and purify the DNA by anion exchange. To keep selection pressure at an optimum, the transformants were grown on nitrocellulose filters (0.2-mum pore size) on media containing the appropriate antibiotics. Transposon Tn4431 containing a promoterless lux operon from Vibrio fischeri and a tetracycline-resistance gene was introduced on the suicide vector pUCD623. All but 1% of the putative transposon mutants produce light, indicating transposition into functional Lxx genes. Southern blot analysis of these transformants indicates predominantly single transposon insertions at unique sites. The cosmid cloning vector pLAFR5-km was stably maintained in Lxx. The development of a transformation and transposon mutagenesis system opens the way for molecular analysis of pathogenicity determinants in Lxx.

Reproductive biology of the eastern shovelnose ray, Aptychotrema rostrata (Shaw & Nodder, 1794), from Moreton Bay, Queensland, Australia

The eastern shovelnose ray, Aptychotrema rostrata (Rhinobatidae), is an endemic batoid common to the east coast of Australia. The reproductive cycle was studied in Moreton Bay, south-eastern Queensland, over a 14-month period. Aptychotrema rostrata is an aplacental yolksac viviparous species with an annual, seasonal reproductive cycle in Moreton Bay. Females mature at 54-66 cm total length, and males at 60-68 cm total length. Gravid females were observed during September-November and parturition occurred in November-December. Vitellogenesis does not proceed in parallel with gestation. Ovulation and copulation probably occur during July-September, resulting in a gestational period of 3-5 months. Uterine fecundity ranges from 4 to 18, with a significant positive relationship between uterine fecundity and maternal body length. In mature males, a peak in the proportion of mature spermatocysts in the testes was observed in July, whereas gonadosomatic index peaked in April.