Determination of static space requirements for finishing bulls based on image analysis

In Europe, conventional housing systems for finishing bulls (Bos taurus) tend to consist of group pens with a high stocking density. Up until now there have been no regulations in place defining bulls' space requirements, even although insufficient space allowance is considered to impair animal welfare. Our study aimed to measure the surface area that finishing bulls occupy in standing and lying positions. We observed 46 bulls on a German fattening farm. The animals from one pen were assigned to one of three weight classes (W1: < 450 kg; W2: 450–649 kg; W3: ≥ 650 kg), and two pens of each weight class were examined. For image recordings, a camera trap was installed above the pens. To analyse the covered surface, the recorded images (n = 242) were edited. Furthermore, the observed lying postures were differentiated in terms of lying position and stretched-out legs. On average, the areas covered by the bulls increased with class of bodyweight. A finishing bull covered up to 1.21 m2 in a standing position and up to 1.57 m2 in a lying position, the most space being needed in an outstretched position. The calculated values provide information only about the surface a finishing bull covered in different positions in the pen. In practice, additional dynamic and social space must be taken into account for recommendations on space requirements, in order to ensure adequate inter-individual distances, social interaction and characteristic behaviours to improve animal welfare.

Wormhole solutions in modified f(R,φ,X) gravity

This work aims to investigate the wormhole solutions in the background of [Formula: see text] theory of gravity, where [Formula: see text] is Ricci scalar, [Formula: see text] is scalar potential, and [Formula: see text] is the kinetic term. We consider spherically symmetric static space–time for exploring the wormhole geometry with anisotropic fluid. For our current analysis, we consider a particular equation of state parameter to study the behavior of traceless fluid and examine the physical behavior of energy density and pressure components. Furthermore, we also choose a particular shape function and explore the energy conditions. It can be noticed that energy conditions are violated for both shape functions. The violation of energy conditions indicates the existence of exotic matter and wormhole. Therefore, it can be concluded that our results are stable and realistic. The interesting feature of this work is to show two- and three-dimensional plotting for the analysis of wormhole geometry.

Planimetric Determination of the Static Space of Cull Sows as the First Step towards a Recommendation of Loading Densities for Cull Sows during Road Transportation in the European Union

The available floor space is an important welfare factor for cull sows during transportation. Sows of modern genetics reach a size and weight far exceeding those of fattening pigs. In most countries, there are no binding, consistent regulations for the maximum loading densities, especially for sows during road transportation. As a first step towards such recommendations, the physical floor space requirement (static space) of 100 sows of a current breed, while standing and lying down, were determined using contrast-based planimetry. An average sow covered about 0.42–0.47 m2 (standing postures) up to 0.53–0.63 m2 (lying postures). The largest measured area was 0.72 m2 for a sow lying in the belly-chest position. We detected a significant dependency of the covered floor area and the live weight, which supports the common practice to derive space requirements and recommendations based on live weight. Also, our results suggest that especially heavy sows, under currently usual loading densities, are at risk of having insufficient floor space requirements during transport. The results cannot be used to define the space required by a sow to carry out movements or sustain the individual need for distance (social/dynamic space) but provide data on the static space covered by sows of current breeds.

The Science and Religion behind Western Classical Architecture—Illustrated by the Examples of the Pantheon and Notre Dame Cathedral

Architecture is the language of the earth, and light is the language of the sky. When the architecture opens a hole, the flowing light tilts down, and a dialogue between man and God unfolds, the science and religion behind it also tells a story. Great architects can not only build in static space, but also capture the dynamic light to become a part of the building. This paper takes the Pantheon and Notre Dame as examples to explore the scientific connotation and humanistic spirit behind them.

General relativistic hydrodynamics on a moving-mesh I: static space–times

ABSTRACT We present the moving-mesh general relativistic hydrodynamics solver for static space–times as implemented in the code, MANGA. Our implementation builds on the architectures of MANGA and the numerical relativity python package NRPy+. We review the general algorithm to solve these equations and, in particular, detail the time-stepping; Riemann solution across moving faces; conversion between primitive and conservative variables; validation and correction of hydrodynamic variables; and mapping of the metric to a Voronoi moving-mesh grid. We present test results for the numerical integration of an unmagnetized Tolman–Oppenheimer–Volkoff star for 24 dynamical times. We demonstrate that at a resolution of 106 mesh generating points, the star is stable and its central density drifts downwards by 2 per cent over this time-scale. At a lower resolution, the central density drift increases in a manner consistent with the adopted second-order spatial reconstruction scheme. These results agree well with the exact solutions, and we find the error behaviour to be similar to Eulerian codes with second-order spatial reconstruction. We also demonstrate that the new code recovers the fundamental mode frequency for the same TOV star but with its initial pressure depleted by 10 per cent.

Schrödinger wave functional of a quantum scalar field in static space-times from precanonical quantization

The functional Schrödinger representation of a scalar field on an [Formula: see text]-dimensional static space-time background is argued to be a singular limiting case of the hypercomplex quantum theory of the same system obtained by the precanonical quantization based on the space-time symmetric De Donder–Weyl Hamiltonian theory. The functional Schrödinger representation emerges from the precanonical quantization when the ultraviolet parameter [Formula: see text] introduced by precanonical quantization is replaced by [Formula: see text], where [Formula: see text] is the time-like tangent space Dirac matrix and [Formula: see text] is an invariant spatial [Formula: see text]-dimensional Dirac’s delta function whose regularized value at [Formula: see text] is identified with the cutoff of the volume of the momentum space. In this limiting case, the Schrödinger wave functional is expressed as the trace of the product integral of Clifford-algebra-valued precanonical wave functions restricted to a certain field configuration and the canonical functional derivative Schrödinger equation is derived from the manifestly covariant Dirac-like precanonical Schrödinger equation which is independent of a choice of a codimension-one foliation.

Sequential warped products: Curvature and conformal vector fields

In this note, we introduce a new type of warped products called as sequential warped products to cover a wider variety of exact solutions to Einstein?s field equation. First, we study the geometry of sequential warped products and obtain covariant derivatives, curvature tensor, Ricci curvature and scalar curvature formulas. Then some important consequences of these formulas are also stated. We provide characterizations of geodesics and two different types of conformal vector fields, namely, Killing vector fields and concircular vector fields on sequential warped product manifolds. Finally, we consider the geometry of two classes of sequential warped product space-time models which are sequential generalized Robertson-Walker space-times and sequential standard static space-times.

Biometric measurement of static space required by weaned piglets kept in groups of eight during 6 weeks

Adequate space allocation is deemed to be an important criterion for animal welfare in modern pig farming. However, it is not a simple matter to determine how much space a group of pigs needs, and precise, animal-based data about the floor area needed by the body dimensions of group-housed pigs in different weight categories are currently lacking. So as to collect biometric data on the static space of weaned pigs kept in groups and to evaluate current spatial requirements, an automatic measurement of the floor area covered by the pigs’ bodies within groups was performed. Consequently, the resulting free space in a pen, available for (non-) locomotor behaviours, was calculated. In three batches, two groups of eight piglets each were formed after weaning. Using three-dimensional cameras that recorded a piglets’ pen from top view and a software for image analysis, the exact static space of a group considering different body positions was measured and specified in square centimetres. Measurements were taken weekly for a total period of 6 weeks per batch. The area covered by the bodies of a group of eight piglets increased almost linearly with increasing average bodyweight (R 2 = 0.99, n = 1645 images). The highest mean static space was measured in Week 6 (1.54 m2, average bodyweight: 25.2 kg) when 100% of piglets were lying with less than 50% huddling. When 100% of piglets within a group were lying, more than 50% huddling reduced the mean static space to 1.4 m2 (P &lt; 0.05). When all pigs of a group were lying, significantly more space was covered than in situations when all pigs of a group were standing (1.54 m2 vs 1.36 m2, P &lt; 0.05). Exclusively in Week 1, when piglets were lying with more than 50% huddling, the space covered by the group was slightly reduced compared with the situation when 100% of piglets were standing. By the automatic method, realistic results on the static space of piglets kept in groups were achieved. Space requirements of the largest animals in the most space-demanding body positions should be the basis for space recommendations for nursery pigs.