Topological Test Spaces

A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with incommensurable random quantities. In the case of quantum mechanics, the relevant test space, the set of orthonormal bases of a Hilbert space, carries significant topological structure. This paper inaugurates a general study of topological test spaces. Among other things, we show that any topological test space with a compact space of outcomes is of finite rank. We also generalize results of Meyer and Clifton-Kent by showing that, under very weak assumptions, any second-countable topological test space contains a dense semi-classical test space.Comment: 12 pp., LaTeX 2e. To appear in Int. J. Theor. Phy

Essential nonlinearities in hearing

Our hearing organ, the cochlea, evidently poises itself at a Hopf bifurcation to maximize tuning and amplification. We show that in this condition several effects are expected to be generic: compression of the dynamic range, infinitely shrap tuning at zero input, and generation of combination tones. These effects are "essentially" nonlinear in that they become more marked the smaller the forcing: there is no audible sound soft enough not to evoke them. All the well-documented nonlinear aspects of hearing therefore appear to be consequences of the same underlying mechanism.Comment: 4 pages, 3 figure

QCD sum rules for the pseudoscalar decay constants - To constrain the strange quark mass

We study the higher order corrections of quark masses to the Gell-Mann$-$Oakes$-$Renner (GOR) relation by constructing QCD sum rules exclusively for pseudoscalar mesons from the axial-vector correlation function, $i \int d^4x~ e^{ip\cdot x}$. To project out the pseudoscalar meson contributions, we apply $-p^\mu p^\nu/p^2$ to this correlation function and construct sum rules for the decay constants of pseudoscalar mesons, $f_\pi, f_k$ and $f_{\eta_8}$. The OPE is proportional to quark masses due to PCAC. To leading order in quark mass, each sum rule reproduces the corresponding GOR relation. For kaon and $\eta_8$, the deviation from the GOR relation due to higher orders in quark mass is found to be substantial. But the deviation gives better agreements with the phenomenology. Our sum rule provides a sensitive relation between $f_K$ and $m_s$, which stringently constrain the value for $m_s$. To reproduce the experimental value for $f_K$, $m_s$ is found to be 186 MeV at 1 GeV scale. The $f_{\eta_8}$ sum rule also supports this finding.Comment: 14 pages including 3 figures. slightly revised. Accepted for publication in Physical Review

Simultaneous resonant x-ray diffraction measurement of polarization inversion and lattice strain in polycrystalline ferroelectrics

International audienceStructure-property relationships in ferroelectrics extend over several length scales from the individual unit cell to the macroscopic device, and with dynamics spanning a broad temporal domain. Characterizing the multi-scale structural origin of electric field-induced polarization reversal and strain in ferroelectrics is an ongoing challenge that so far has obscured its fundamental behaviour. By utilizing small intensity differences between Friedel pairs due to resonant scattering, we demonstrate a time-resolved X-ray diffraction technique for directly and simultaneously measuring both lattice strain and, for the first time, polarization reversal during in-situ electrical perturbation. This technique is demonstrated for BaTiO3-BiZn0.5Ti0.5O3 (BT-BZT) polycrystalline ferroelectrics, a prototypical lead-free piezoelectric with an ambiguous switching mechanism. This combines the benefits of spectroscopic and diffraction-based measurements into a single and robust technique with time resolution down to the ns scale, opening a new door to in-situ structure-property characterization that probes the full extent of the ferroelectric behaviou

Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point $z$ if either the scaled $L^{p,q}_{x,t}$-norm of the velocity with $3/p+2/q\leq 2$, $1\leq q\leq \infty$, or the $L^{p,q}_{x,t}$-norm of the vorticity with $3/p+2/q\leq 3$, $1 \leq q < \infty$, or the $L^{p,q}_{x,t}$-norm of the gradient of the vorticity with $3/p+2/q\leq 4$, $1 \leq q$, $1 \leq p$, is sufficiently small near $z$

A Blow-Up Criterion for Classical Solutions to the Compressible Navier-Stokes Equations

In this paper, we obtain a blow up criterion for classical solutions to the 3-D compressible Naiver-Stokes equations just in terms of the gradient of the velocity, similar to the Beal-Kato-Majda criterion for the ideal incompressible flow. In addition, initial vacuum is allowed in our case.Comment: 25 page

The Migration of Elites in a Borderless World: Citizenship as an Incentive for Professionals and Managers?

Der Artikel geht der Frage nach, inwiefern die geöffneten Türen für die Immigration Hochqualifizierter in den OECD-Ländern tatsächlich zu einer verstärkten Migrationsbewegung führen. Die Analyse von Daten zu Eliten- und Hochqualifiziertenmigration in Ostasien, Europa und den USA führt zu dem Ergebnis, dass diese dem Muster einer „brain circulation“ folgt und die Staatsbürgerrechte dabei keine entscheidende Rolle spielen