Species Preference Influences on Cattle Grazing Behaviour

Lotus corniculatus offers specific nutritional benefits to animals, but exploiting these advantages in grazing systems depends on the proportion of lotus in the feed offered and the animals\u27 preference, hence desire to select for it. To determine preference for lotus, heifers were offered free-choice in contrasting, spatially separated but adjacent monocultures of ryegrass-lotus or red clover-lotus. Following a one-week period to adjust to the species offered and their arrangement, 10 young heifers were observed at 10-minute intervals during daylight hours, and the species they were on and whether or not they were grazing was recorded. This procedure was conducted in summer (February) and autumn (May). Partial preference was determined from the proportion of time spent grazing each species. Preference for lotus was higher when the alternative species was ryegrass, than when it was red clover, in both summer (75:25 vs 53:47) and autumn (67:33 vs 54:46), although this preference for lotus in the ryegrass-lotus contrast reduced in autumn compared with that exhibited in summer. Total grazing time, which was similar for each contrast, was lower in autumn (6 hrs) than in summer (9 hrs). For the ryegrass-lotus contrast, the reduced grazing time in autumn resulted from reduced time grazing lotus, whereas on the red clover-lotus contrast they reduced grazing time equally on both species

Partial Preference of Grazing Cattle for Contrasting Legume Swards

Yearling heifers in groups of 3 grazed 405 m2 plots made up of alternating 2.4m wide strips of white clover/birdsfoot trefoil (WC+BT) or red clover (RC) in the proportions of 80:20, 67:33, 33:67 and 20:80 for periods of 3 days over four replicates in time, balanced for effects of previous treatment. Observation of the distribution of grazing activity and biting rate were made over 3 hour periods each evening. Biting rates were consistently higher on (WC+BT) than RC (52.3 vs 46.3 ± 0.59 bites.min-1 P(0.0001). Animals initially showed partial preference for the minor sward component in each treatment but regression of the proportion of grazing activity on proportion of total area for (WC+BT) approached unity with time, indicating the development of essentially neutral behaviour as herbage on minority strips was depleted

Gap Probabilities for Edge Intervals in Finite Gaussian and Jacobi Unitary Matrix Ensembles

The probabilities for gaps in the eigenvalue spectrum of the finite dimension $N \times N$ random matrix Hermite and Jacobi unitary ensembles on some single and disconnected double intervals are found. These are cases where a reflection symmetry exists and the probability factors into two other related probabilities, defined on single intervals. Our investigation uses the system of partial differential equations arising from the Fredholm determinant expression for the gap probability and the differential-recurrence equations satisfied by Hermite and Jacobi orthogonal polynomials. In our study we find second and third order nonlinear ordinary differential equations defining the probabilities in the general $N$ case. For N=1 and N=2 the probabilities and thus the solution of the equations are given explicitly. An asymptotic expansion for large gap size is obtained from the equation in the Hermite case, and also studied is the scaling at the edge of the Hermite spectrum as $N \to \infty$, and the Jacobi to Hermite limit; these last two studies make correspondence to other cases reported here or known previously. Moreover, the differential equation arising in the Hermite ensemble is solved in terms of an explicit rational function of a {Painlev\'e-V} transcendent and its derivative, and an analogous solution is provided in the two Jacobi cases but this time involving a {Painlev\'e-VI} transcendent.Comment: 32 pages, Latex2

On the gravitational field of static and stationary axial symmetric bodies with multi-polar structure

We give a physical interpretation to the multi-polar Erez-Rozen-Quevedo solution of the Einstein Equations in terms of bars. We find that each multi-pole correspond to the Newtonian potential of a bar with linear density proportional to a Legendre Polynomial. We use this fact to find an integral representation of the $\gamma$ function. These integral representations are used in the context of the inverse scattering method to find solutions associated to one or more rotating bodies each one with their own multi-polar structure.Comment: To be published in Classical and Quantum Gravit

Third order superintegrable systems separating in polar coordinates

A complete classification is presented of quantum and classical superintegrable systems in $E_2$ that allow the separation of variables in polar coordinates and admit an additional integral of motion of order three in the momentum. New quantum superintegrable systems are discovered for which the potential is expressed in terms of the sixth Painlev\'e transcendent or in terms of the Weierstrass elliptic function

Persistence of Perennial Ryegrass, Tall Fescue and Cocksfoot Following Sequential Annual Sowings: Influence of Species, Cultivar and Pasture Age on Inter-Annual Variability in Yield and Botanical Composition

The persistence of sown, temperate pasture species is an important determinant of perennial pasture-grass productivity. Defining the traits that affect persistence is essential for improving pasture longevity through plant breeding and for identifying criteria that should be included in cultivar ranking indices such as the DairyNZ, Forage Value Index. Compared with a conventional longitudinal study, in which pasture from a single sowing is monitored over time, repeated annual sowings allow the effects on persistence of sowing year and the ensuing interactions between environment and age of pasture to be identified. A repeated sowings experiment was commenced at two sites: under sheep grazing in Canterbury, New Zealand and under cattle grazing in Waikato, New Zealand. At each site, eight cultivars of perennial ryegrass representing different ploidy, flowering date, and decade of cultivar release, and one cultivar each of tall fescue and cocksfoot were sown in a randomised complete block design with four replicates, in autumn each year. The longitudinal cohort (i.e., the measurements conducted over time following each annual sowing) is the experimental unit for effects of sowing year and age. This paper reports interim data from the longest available longitudinal cohort, sown in autumn 2016 at Waikato on pasture yield and botanical composition measured in spring and autumn for six successive years following sowing. Repeated measures analysis of the six years of pasture data was used to identify trends over time and inter-annual variability in the effects of cultivar and site

Chaos and Rotating Black Holes with Halos

The occurrence of chaos for test particles moving around a slowly rotating black hole with a dipolar halo is studied using Poincar\'e sections. We find a novel effect, particles with angular momentum opposite to the black hole rotation have larger chaotic regions in phase space than particles initially moving in the same direction.Comment: 9 pages, 4 Postscript figures. Phys. Rev. D, in pres

Hamiltonians separable in cartesian coordinates and third-order integrals of motion

We present in this article all Hamiltonian systems in E(2) that are separable in cartesian coordinates and that admit a third-order integral, both in quantum and in classical mechanics. Many of these superintegrable systems are new, and it is seen that there exists a relation between quantum superintegrable potentials, invariant solutions of the Korteweg-De Vries equation and the Painlev\'e transcendents.Comment: 19 pages, Will be published in J. Math. Phy