A generalisation of the Hopf Construction and harmonic morphisms into \s^2

In this paper we construct a new family of harmonic morphisms \varphi:V^5\to\s^2, where $V^5$ is a 5-dimensional open manifold contained in an ellipsoidal hypersurface of \c^4=\r^8. These harmonic morphisms admit a continuous extension to the completion ${V^{\ast}}^5$, which turns out to be an explicit real algebraic variety. We work in the context of a generalization of the Hopf construction and equivariant theory.Comment: 10 page

Smarter task assignment or greater effort: the impact of incentives on team performance

We use an experiment to study the impact of team-based incentives, exploiting rich data from personnel records and management information systems. Using a triple difference design, we show that the incentive scheme had an impact on team performance, even with quite large teams. We examine whether this effect was due to increased effort from workers or strategic task reallocation. We find that the provision of financial incentives did raise individual performance but that managers also disproportionately reallocated efficient workers to the incentivised tasks. We show that this reallocation was the more important contributor to the overall outcome

The effect of online education on pre-service teachers’ knowledge of peer tutoring

The purpose of this study was to find the effectiveness of online education compared to text-based education when teaching pre-service educators about peer tutoring in physical education. As students with disabilities are being more regularly included in general education classes, it is important that pre-service teachers have ample and quality opportunities to learn about important topics and strategies within education, such as peer tutoring. This study compared knowledge scores between the experimental group (online education) and the control group (text-based education). The online education group received the knowledge through podcasts that were created using Mayer’s principles for multimedia learning. No significant differences were found between the two groups between the two groups on their knowledge of peer tutoring. Future research should explore using a larger population with a more diverse sample. Considerations for future research should also include length of intervention and the use of a knowledge retention test

On the second variation of the biharmonic Clifford torus in S-4

The flat torus T = S-1 (1/2) x S-1 (1/2) admits a proper biharmonic isometric immersion into the unit 4-dimensional sphere S-4 given by Phi = i o phi, where phi : T -> S-3 (1/root 2) is the minimal Clifford torus and i : S-3 (1 root 2) -> S-4 is the biharmonic small hypersphere. The first goal of this paper is to compute the biharmonic index and nullity of the proper biharmonic immersion Phi. After, we shall study in the detail the kernel of the generalised Jacobi operator I-2 Phi. We shall prove that it contains a direction which admits a natural variation with vanishing first, second and third derivatives, and such that the fourth derivative is negative. In the second part of the paper, we shall analyse the specific contribution of phi to the biharmonic index and nullity of Phi. In this context, we shall study a more general composition (Phi) over tilde = i o (phi) over tilde, where (phi) over tilde : M-m -> Sn-1 (1/root 2), m >= 1, n >= 3, is a minimal immersion and i : Sn-1 (1/root 2) -> S-n is the biharmonic small hypersphere. First, we shall determine a general sufficient condition which ensures that the second variation of (Phi) over tilde is nonnegatively defined on C((phi) over tilde -1TSn-1(1/root 2)). Then, we complete this type of analysis on our Clifford torus and, as a complementary result, we obtain the p-harmonic index and nullity of phi. In the final section, we compare our general results with those which can be deduced from the study of the equivariant second variation

On the Stability of the Equator Map for Higher Order Energy Functionals

Let Bn ⊂ ℝn and Sn ⊂ Rn+1 denote the Euclidean n-dimensional unit ball and sphere, respectively. The extrinsic k-energy functional is defined on the Sobolev space Wk,2 (Bn, Sn) as follows: Ekext(u) = ∫Bn |Δs u|2 dx when k = 2s, and Ekext(u) = ∫Bn|∇ Δs u|2 dx when k = 2s + 1. These energy functionals are a natural higher order version of the classical extrinsic bienergy, also called Hessian energy. The equator map u∗: Bn → Sn, defined by u∗(x) = (x/|x|,0), is a critical point of Ekext(u) provided that n ≥ 2k + 1. The main aim of this paper is to establish necessary and sufficient conditions on k and n under which u∗: Bn → Sn is minimizing or unstable for the extrinsic k-energy

The October 2000 flooding in Valle d'Aosta (Italy): Event description and land planning measures for the risk mitigation

On October 13-16th, 2000 heavy rainfalls in the Northwestern Italian Alps caused huge flooding and landslides with significant damages to houses and infrastructures and several life losses. In this paper a description of the main events that affected Valle d’Aosta’s region and the subsequent land planning measures adopted for the risk mitigation are presented. After a first meteorological and hydrological framing, based on the data of the regional monitoring system (that pointed out rainfalls up to 236 mm in 24 h also in high‐altitude zones, because of the rise of the isotherm 0°C around 3000 m above sea level), the main effects of the event (extensive flooding, landslides, soil slips and debris flows) in the regional catchment of the Dora Baltea river are described. Through aerial and direct surveys those effects have been transferred into a thematic cartography within two months from the event, in order to have detailed elements for the technical, administrative and political land planning decisions, and, on this basis, a new regional directive containing detailed measures for the hydro‐geological risk mitigation and land safety has been adopted. © 2003 by Taylor nad Francis Group, LLC