Casimirs and Lax operators from the structure of Lie algebras

This paper uses the structure of the Lie algebras to identify the Casimir invariant functions and Lax operators for matrix Lie groups. A novel mapping is found from the cotangent space to the dual Lie algebra which enables Lax operators to be found. The coordinate equations of motion are given in terms of the structure constants and the Hamiltonian.

Restricted dispersal reduces the strength of spatial density dependence in a tropical bird population

Spatial processes could play an important role in density-dependent population regulation because the disproportionate use of poor quality habitats as population size increases is widespread in animal populations-the so-called buffer effect. While the buffer effect patterns and their demographic consequences have been described in a number of wild populations, much less is known about how dispersal affects distribution patterns and ultimately density dependence. Here, we investigated the role of dispersal in spatial density dependence using an extraordinarily detailed dataset from a reintroduced Mauritius kestrel (Falco punctatus) population with a territorial (despotic) breeding system. We show that recruitment rates varied significantly between territories, and that territory occupancy was related to its recruitment rate, both of which are consistent with the buffer effect theory. However, we also show that restricted dispersal affects the patterns of territory occupancy with the territories close to release sites being occupied sooner and for longer as the population has grown than the territories further away. As a result of these dispersal patterns, the strength of spatial density dependence is significantly reduced. We conclude that restricted dispersal can modify spatial density dependence in the wild, which has implications for the way population dynamics are likely to be impacted by environmental change.

Effects of restricted water availability and increased temperature on the grain filling, drying and quality of winter wheat

Experiments in controlled environments examined the effects of the timing and severity of drought, and increased temperature, on grain development of Hereward winter wheat. Environmental effects on grain specific weight, protein content, Hagberg Falling Number, SDS-sedimentation volume, and sulphur content were also studied. Drought and increased temperature applied before the end of grain filling shortened the grain filling period and reduced grain yield, mean grain weight and specific weight. Grain filling was most severely affected by drought between days 1-14 after anthesis. Protein content was increased by stresses before the end of grain growth, because nitrogen harvest index was less severely affected than was dry matter harvest index. Hagberg Falling Number was increased to the greatest extent by stresses applied 15-28 days after anthesis. Treatment effects on grain sulphur content were similar to those on protein content, such that N:S ratio was not significantly affected by drought nor temperature stresses. The effects of restricted water on grain yield and quality were linearly related to soil moisture between 44 and about 73% field capacity (FC) from days 15-28. Drought stress (but not temperature stress) before the end of grain filling decreased SDS-sedimentation volume relative to drought applied later. (C) 2003 Elsevier Science Ltd. All rights reserved.

Effect of restricted suckling of calves on the productivity of crossbred dairy cattle

An experiment on restricted suckling of crossbred dairy cows was conducted at the Livestock Research Centre, Tanga in north-east Tanzania. The objective of the experiment was to evaluate the comparative productivity of Bos taurus x Bos indicus cows of medium and high levels of Bos taurus inheritance, whose calves were either bucket-reared or suckled residual milk. Lactation milk yield, length and persistency were 1563 L, 289 days, and 1.0, respectively, for the bucket-reared and 1592 L, 289 days and 1.4, respectively, for the suckling group. Days to observed oestrus, first insemination and conception for cows whose calves were bucket-reared were 47, 74 and 115 days, respectively, and 57, 81 and 126 days, respectively, for the suckling cows. The calf weights were similar at 1 year of age. The productivity of the cows, measured as the annual milk offtake, was not significantly higher for those that suckled their calves than for those whose calves were bucket-reared.

Restricted expression of NADPH oxidase/peroxidase gene (Duox) in zone VII of the ascidian endostyle

The ascidian Ciona intestinalis, a marine invertebrate chordate, is an emerging model system for developmental and evolutionary studies. The endostyle, one of the characteristic organs of ascidians, is a pharyngeal structure with iodine-concentrating and peroxidase activities and is therefore considered to be homologous to the follicular thyroid of higher vertebrates. We have previously reported that a limited part of the endostyle (zone VII) is marked by the expression of orthologs of the thyroid peroxidase (TPO) and thyroid transcription factor-2 (TTF-2/FoxE) genes. In this study, we have identified the Ciona homolog of NADPH oxidase/peroxidase (Duox), which provides hydrogen peroxide (H2O2) for iodine metabolism by TPO in the vertebrate thyroid. Expression patterns assessed by in situ hybridization have revealed that Ciona Duox (Ci-Duox) is predominantly expressed in the dorsal part of zone VII of the endostyle. Furthermore, two-color fluorescent in situ hybridization with Ci-Duox and Ciona TPO (CiTPO) has revealed that the ventral boundary of the Ci-Duox domain of expression is more dorsal than that of CiTPO. We have also characterized several genes, such as Ci-Fgf8/17/18, 5HT7, and Ci-NK4, which are predominantly expressed in the ventral part of zone VII, in a region complementary to the Ci-Duox expression domain. These observations suggest that, at the molecular level, zone VII has a complex organization that might have some impact on the specification of cell types and functions in this thyroid-equivalent element of the ascidian endostyle.

Synthesis of oxepane ring containing monocyclic, conformationally restricted bicyclic and spirocyclic nucleosides from d-glucose: a cycloaddition approach

Carbohydrate-derived substrates having (i) C-5 nitrone and C-3-O-allyl, (ii) C-4 vinyl and a C-3-O-tethered nitrone, and (iii) C-5 nitrone and C-4-allyloxymethyl generated tetracyclic isoxazolidinooxepane/-pyrart ring systems upon intramolecular nitrone cycloaddition reactions. Deprotection of the 1,2acetonides of these derivatives followed by introduction of uracil base via Vorbruggen reaction condition and cleavage of the isooxazolidine rings as well as of benzyl groups by transfer hydrogenolysis yielded an oxepane ring containing blicyclic and spirocyclic nucleosides. The corresponding oxepane based nucleoside analogues were prepared by cleavage of isoxazolidine and furanose rings, coupling of the generated amino functiontalities with 5-amino-4,6-dichloropyrimidine, cyclization to purine rings, and finally aminolysis.

Effects of restricted water availability and increased temperature on the grain filling, drying and quality of winter wheat

Experiments in controlled environments examined the effects of the timing and severity of drought, and increased temperature, on grain development of Hereward winter wheat. Environmental effects on grain specific weight, protein content, Hagberg Falling Number, SDS-sedimentation volume, and sulphur content were also studied. Drought and increased temperature applied before the end of grain filling shortened the grain filling period and reduced grain yield, mean grain weight and specific weight. Grain filling was most severely affected by drought between days 1-14 after anthesis. Protein content was increased by stresses before the end of grain growth, because nitrogen harvest index was less severely affected than was dry matter harvest index. Hagberg Falling Number was increased to the greatest extent by stresses applied 15-28 days after anthesis. Treatment effects on grain sulphur content were similar to those on protein content, such that N:S ratio was not significantly affected by drought nor temperature stresses. The effects of restricted water on grain yield and quality were linearly related to soil moisture between 44 and about 73% field capacity (FC) from days 15-28. Drought stress (but not temperature stress) before the end of grain filling decreased SDS-sedimentation volume relative to drought applied later. (C) 2003 Elsevier Science Ltd. All rights reserved.

The geometry of optimal control solutions on some six dimensional lie groups

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E-3, the spheres S-3 and the hyperboloids H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions are illustrated.