Effects of Integrating Mathematical Concepts into a Nutrition Unit in the Animal Science Curriculum

Achievement test scores in mathematics have been a concern among educators for many years. Teaching contextualized mathematics has been found to be effective and includes providing a direct application to real-life scenarios rather than teaching linear equations and algebraic principles in isolation. This study measured the effects of integrating mathematical skills in one instructional unit in an animal science curriculum. Students from eight schools participated in the research study. Students completed a pretest measuring their existing mathematical skills and self-efficacy in math. All students were taught a unit of instruction about animal nutrition and feeding. The control group received a typical nutrition unit and the treatment group received the same unit of instruction with the addition of mathematical skill integration. Following the unit of instruction, students completed a posttest survey, which included a mathematics attitudinal scale, posttreatment self-efficacy scale, and posttreatment mathematics skills questions. No statistically significant difference was found in mathematics self-efficacy or mathematics skills between the control group and treatment. However, results indicated a strong positive relationship between students’ mathematics self-efficacy and their mathematics skills. Further, highest level of mathematics courses completed and overall grade point average were statistically significant factors in predicting mathematics self-efficacy

A Note on the Instability of Lorentzian Taub-NUT-Space

I show that there are no SU(2)-invariant (time-dependent) tensorial perturbations of Lorentzian Taub-NUT space. It follows that the spacetime is unstable at the linear level against generic perturbations. I speculate that this fact is responsible for so far unsuccessful attempts to define a sensible thermodynamics for NUT-charged spacetimes.Comment: 13 pages, no figure

Non-existence of Skyrmion-Skyrmion and Skyrmion-anti-Skyrmion static equilibria

We consider classical static Skyrmion-anti-Skyrmion and Skyrmion-Skyrmion configurations, symmetric with respect to a reflection plane, or symmetric up to a $G$-parity transformation respectively. We show that the stress tensor component completely normal to the reflection plane, and hence its integral over the plane, is negative definite or positive definite respectively. Classical Skyrmions always repel classical Skyrmions and classical Skyrmions always attract classical anti-Skyrmions and thus no static equilibrium, whether stable or unstable, is possible in either case. No other symmetry assumption is made and so our results also apply to multi-Skyrmion configurations. Our results are consistent with existing analyses of Skyrmion forces at large separation, and with numerical results on Skymion-anti-Skyrmion configurations in the literature which admit a different reflection symmetry. They also hold for the massive Skyrme model. We also point out that reflection symmetric self-gravitating Skyrmions or black holes with Skyrmion hair cannot rest in symmetric equilibrium with self-gravitating anti-Skyrmions.Comment: v2 Typos corrected, refs added. v3 Journal versio

Semi-classical stability of AdS NUT instantons

The semi-classical stability of several AdS NUT instantons is studied. Throughout, the notion of stability is that of stability at the one-loop level of Euclidean Quantum Gravity. Instabilities manifest themselves as negative eigenmodes of a modified Lichnerowicz Laplacian acting on the transverse traceless perturbations. An instability is found for one branch of the AdS-Taub-Bolt family of metrics and it is argued that the other branch is stable. It is also argued that the AdS-Taub-NUT family of metrics are stable. A component of the continuous spectrum of the modified Lichnerowicz operator on all three families of metrics is found.Comment: 18 pages, 3 figures; references adde

The Sensitivity of Harassment to Orbit: Mass Loss from Early-Type Dwarfs in Galaxy Clusters

We conduct a comprehensive numerical study of the orbital dependence of harassment on early-type dwarfs consisting of 168 different orbits within a realistic, Virgo-like cluster, varying in eccentricity and pericentre distance. We find harassment is only effective at stripping stars or truncating their stellar disks for orbits that enter deep into the cluster core. Comparing to the orbital distribution in cosmological simulations, we find that the majority of the orbits (more than three quarters) result in no stellar mass loss. We also study the effects on the radial profiles of the globular cluster systems of early-type dwarfs. We find these are significantly altered only if harassment is very strong. This suggests that perhaps most early-type dwarfs in clusters such as Virgo have not suffered any tidal stripping of stars or globular clusters due to harassment, as these components are safely embedded deep within their dark matter halo. We demonstrate that this result is actually consistent with an earlier study of harassment of dwarf galaxies, despite the apparent contradiction. Those few dwarf models that do suffer stellar stripping are found out to the virial radius of the cluster at redshift=0, which mixes them in with less strongly harassed galaxies. However when placed on phase-space diagrams, strongly harassed galaxies are found offset to lower velocities compared to weakly harassed galaxies. This remains true in a cosmological simulation, even when halos have a wide range of masses and concentrations. Thus phase-space diagrams may be a useful tool for determining the relative likelihood that galaxies have been strongly or weakly harassed.Comment: 17 pages, 13 figures, Accepted to MNRAS 8th September 201

Electrodynamics of Abrikosov vortices: the Field Theoretical Formulation

Electrodynamic phenomena related to vortices in superconductors have been studied since their prediction by Abrikosov, and seem to hold no fundamental mysteries. However, most of the effects are treated separately, with no guiding principle. We demonstrate that the relativistic vortex worldsheet in spacetime is the object that naturally conveys all electric and magnetic information, for which we obtain simple and concise equations. Breaking Lorentz invariance leads to down-to-earth Abrikosov vortices, and special limits of these equations include for instance dynamic Meissner screening and the AC Josephson relation. On a deeper level, we explore the electrodynamics of two-form sources in the absence of electric monopoles, in which the electromagnetic field strength itself acquires the characteristics of a gauge field. This novel framework leaves room for unexpected surprises.Comment: LaTeX, 23 pages, 5 figure

The Simplicial Ricci Tensor

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The 4-dimensional Ric is the Einstein tensor for such spacetimes. More recently the Ric was used by Hamilton to define a non-linear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher-dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area -- an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimension.Comment: 19 pages, 2 figure

Optical Metrics and Projective Equivalence

Trajectories of light rays in a static spacetime are described by unparametrised geodesics of the Riemannian optical metric associated with the Lorentzian spacetime metric. We investigate the uniqueness of this structure and demonstrate that two different observers, moving relative to one another, who both see the universe as static may determine the geometry of the light rays differently. More specifically, we classify Lorentzian metrics admitting more than one hyper--surface orthogonal time--like Killing vector and analyze the projective equivalence of the resulting optical metrics. These metrics are shown to be projectively equivalent up to diffeomorphism if the static Killing vectors generate a group $SL(2, \R)$, but not projectively equivalent in general. We also consider the cosmological $C$--metrics in Einstein--Maxwell theory and demonstrate that optical metrics corresponding to different values of the cosmological constant are projectively equivalent.Comment: 18 pages, two figures, final version, to appear in Physical Review

Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry

We consider a triality between the Zermelo navigation problem, the geodesic flow on a Finslerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field. From the latter viewpoint, the data of the Zermelo problem are encoded in a (conformally) Painleve-Gullstrand form of the spacetime metric, whereas the data of the Randers problem are encoded in a stationary generalisation of the usual optical metric. We discuss how the spacetime viewpoint gives a simple and physical perspective on various issues, including how Finsler geometries with constant flag curvature always map to conformally flat spacetimes and that the Finsler condition maps to either a causality condition or it breaks down at an ergo-surface in the spacetime picture. The gauge equivalence in this network of relations is considered as well as the connection to analogue models and the viewpoint of magnetic flows. We provide a variety of examples.Comment: 37 pages, 6 figure

Social preferences, accountability, and wage bargaining

We assess the extent of preferences for employment in a collective wage bargaining situation with heterogeneous workers. We vary the size of the union and introduce a treatment mechanism transforming the voting game into an individual allocation task. Our results show that highly productive workers do not take employment of low productive workers into account when making wage proposals, regardless of whether insiders determine the wage or all workers. The level of pro-social preferences is small in the voting game, while it increases as the game is transformed into an individual allocation task. We interpret this as an accountability effect