Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation

This Note investigates the properties of the traveling waves solutions of the nonlocal Fisher equation. The existence of such solutions has been proved recently in Berestycki et al. (2009) [3] but their asymptotic behavior was still unclear. We use here a new numerical approximation of these traveling waves which shows that some traveling waves connect the two homogeneous steady states 0 and 1, which is a striking fact since 0 is dynamically unstable and 1 is unstable in the sense of Turing.     

Students’ self-regulation of emotions in mathematics: an analysis of meta-emotional knowledge and skills

Over the past decade, the concept of self-regulated learning has broadened to include motivational, volitional, and emotional components next to (meta-)cognitive ones. In this article, we present a meta-emotion perspective as an essential component of a conceptual framework on self-regulation that fully acknowledges the role of emotions. Against this background, a study is presented that attempts to contribute to the clarification of the relevance and the functioning of students’ meta-emotional knowledge and emotional regulation skills in school-related mathematical activities. It investigates the coping strategies that 393 students of the second (age 14) and fourth (age 16) year of secondary school report to use to regulate their emotions in three different mathematical school settings (i.e., a mathematics test, a difficult mathematics homework, and a difficult mathematics lesson). More specifically, it aims (1) to document the nature and frequency of the reported coping strategies, and (2) to explore—for the three different mathematical school settings—relationships between these reported coping strategies and personal characteristics (i.e., students’ familiarity with the particular school settings, their track in secondary education, their achievement level, their age, and gender). The results indicate that students report to know and to make use of several coping strategies in school-related mathematical activities, and reveal that the use of these strategies is related to specific person-related characteristics. In conclusion, we elaborate on how schools and teachers can stimulate students to acquire appropriate strategies and skills to self-regulate their emotions.     

Symplectic microgeometry II: generating functions

We adapt the notion of generating functions for lagrangian submanifolds to symplectic microgeometry. We show that a symplectic micromorphism always admits a global generating function. As an application, we describe hamiltonian flows as special symplectic micromorphisms whose local generating functions are the solutions of Hamilton-Jacobi equations. We obtain a purely categorical formulation of the temporal evolution in classical mechanics.     

Grüss-type bounds for covariances and the notion of quadrant dependence in expectation

We show that Grüss-type probabilistic inequalities for covariances can be considerably sharpened when the underlying random variables are quadrant dependent in expectation (QDE). The herein established covariance bounds not only sharpen the classical Grüss inequality but also improve upon recently derived Grüss-type bounds under the assumption of quadrant dependency (QD), which is stronger than QDE. We illustrate our general results with examples based on specially devised bivariate distributions that are QDE but not QD. Such results play important roles in decision making under uncertainty, and particularly in areas such as economics, finance, and insurance.     

A Generalized Grothendieck Inequality and Nonlocal Correlations that Require High Entanglement

Suppose that Alice and Bob make local two-outcome measurements on a shared entangled quantum state. We show that, for all positive integers d, there exist correlations that can only be reproduced if the local Hilbert-space dimension is at least d. This establishes that the amount of entanglement required to maximally violate a Bell inequality must depend on the number of measurement settings, not just the number of measurement outcomes. We prove this result by establishing a lower bound on a new generalization of Grothendieck’s constant.     

Synthesis and Sm/Sm doping effects on photoluminescence properties of Sr4Al14O25

Complete and partial samarium reduction was achieved under strong reducing atmosphere by solid-state and combustion synthesis of Sr_3.96Sm_0.04Al₁₄O₂₅. Dependence of different fluxing agents on the formation of various strontium aluminates was examined. The samples were investigated by X-ray powder diffraction, temperature dependent luminescence decay and photoluminescence measurements. Excitation with UV radiation resulted in sharp and well resolved emission lines of samarium ions. Distinct temperature behavior for Sm²⁺ and Sm³⁺ were detected in the range of 100-500 K. Estimated emission thermal quenching values (TQ_1/2) for divalent samarium were approximately 270 K while for trivalent state around 660 K. Measured luminescence decay values of Sm²⁺ are substantially lower than for Sm³⁺,≈1.7 and ≈2.7 ms, respectively. The spectral feature of Sm²⁺ emission spectrum indicates that dopant occupies low symmetry site in Sr₄Al₁₄O₂₅ compound.     

Observation of transverse polarization asymmetries of charged pion pairs in e+e- annihilation near √s = 10.58 GeV

The interference fragmentation function translates the fragmentation of a quark with a transverse projection of the spin into an azimuthal asymmetry of two final-state hadrons. In e(+)e(-) annihilation the product of two interference fragmentation functions is measured. We report nonzero asymmetries for pairs of charge-ordered π(+)π(-) pairs, which indicate a significant interference fragmentation function in this channel. The results are obtained from a 672 fb(-1) data sample that contains 711 × 10(6) π(+)π(-) pairs and was collected at and near the Υ(4S) resonance, with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider.     

Quantum dynamics of a driven correlated system coupled to phonons

Nonequilibrium interplay between charge, spin, and lattice degrees of freedom on a square lattice is studied for a single charge carrier doped in the t-J-Holstein model. In the presence of a static electric field we calculate the quasistationary state. With increasing electron-phonon (e-ph) coupling the carrier mobility decreases; however, we find increased steady state current due to e-ph coupling in the regime of negative differential resistance. We explore the distribution of absorbed energy between the spin and the phonon subsystem. For model parameters as relevant for cuprates, the majority of the gained energy flows into the spin subsystem.