A Holder Continuous Nowhere Improvable Function with Derivative Singular Distribution

We present a class of functions $\mathcal{K}$ in $C^0(\R)$ which is variant of the Knopp class of nowhere differentiable functions. We derive estimates which establish \mathcal{K} \sub C^{0,\al}(\R) for 0<\al<1 but no $K \in \mathcal{K}$ is pointwise anywhere improvable to C^{0,\be} for any \be>\al. In particular, all $K$'s are nowhere differentiable with derivatives singular distributions. $\mathcal{K}$ furnishes explicit realizations of the functional analytic result of Berezhnoi. Recently, the author and simulteously others laid the foundations of Vector-Valued Calculus of Variations in $L^\infty$ (Katzourakis), of $L^\infty$-Extremal Quasiconformal maps (Capogna and Raich, Katzourakis) and of Optimal Lipschitz Extensions of maps (Sheffield and Smart). The "Euler-Lagrange PDE" of Calculus of Variations in $L^\infty$ is the nonlinear nondivergence form Aronsson PDE with as special case the $\infty$-Laplacian. Using $\mathcal{K}$, we construct singular solutions for these PDEs. In the scalar case, we partially answered the open $C^1$ regularity problem of Viscosity Solutions to Aronsson's PDE (Katzourakis). In the vector case, the solutions can not be rigorously interpreted by existing PDE theories and justify our new theory of Contact solutions for fully nonlinear systems (Katzourakis). Validity of arguments of our new theory and failure of classical approaches both rely on the properties of $\mathcal{K}$.Comment: 5 figures, accepted to SeMA Journal (2012), to appea

Virtual Shaping on NACA 0015 by Means of a High Momentum Coefficient Synthetic Jet

Results concerning flow control on a NACA 0015 airfoil using high power synthetic jets are presented for low incidences and for Reynolds numbers ranging from 132000 to 425000. The forcing was operated through a spanwise slit positioned near the leading edge at x/c=1.25% or at x/c=10% on the upper surface. Static pressure distribution measurements around the airfoil, wake surveys and smoke flow visualizations were performed. Pressure distributions were significantly modified around the injection location, showing an area of intense suction which increased the lift and strongly affected the drag. Flow visualizations highlighted that the intense suction was due to a virtual shaping effect caused by the formation of a recirculation bubble capable of displacing the streamlines. Low momentum deficits in the wake velocity distributions and, in certain conditions, jet-like flow was observed for the forced cases. Finally, a scaling law relating the bubble size to the forcing intensity is propose

Charged Vortices in High Temperature Superconductors Probed by NMR

We report a first experimental evidence that a vortex in the high temperature superconductors (HTSC) traps a finite electric charge from the high resolution measurements of the nuclear quadrupole frequencies. In slightly overdoped YBa_2Cu_3O_7 the vortex is negatively charged by trapping electrons, while in underdoped YBa_2Cu_4O_8 it is positively charged by expelling electrons. The sign of the trapped charge is opposite to the sign predicted by the conventional BCS theory. Moreover, in both materials, the deviation of the magnitude of the charge from the theory is also significant. These unexpected features can be attributed to the novel electronic structure of the vortex in HTSC.Comment: 6 pages, 7 figures, to be published in Phys Rev.

Syntaxin 5 Is Required for Copper Homeostasis in Drosophila and Mammals

Copper is essential for aerobic life, but many aspects of its cellular uptake and distribution remain to be fully elucidated. A genome-wide screen for copper homeostasis genes in Drosophila melanogaster identified the SNARE gene Syntaxin 5 (Syx5) as playing an important role in copper regulation; flies heterozygous for a null mutation in Syx5 display increased tolerance to high dietary copper. The phenotype is shown here to be due to a decrease in copper accumulation, a mechanism also observed in both Drosophila and human cell lines. Studies in adult Drosophila tissue suggest that very low levels of Syx5 result in neuronal defects and lethality, and increased levels also generate neuronal defects. In contrast, mild suppression generates a phenotype typical of copper-deficiency in viable, fertile flies and is exacerbated by co-suppression of the copper uptake gene Ctr1A. Reduced copper uptake appears to be due to reduced levels at the plasma membrane of the copper uptake transporter, Ctr1. Thus Syx5 plays an essential role in copper homeostasis and is a candidate gene for copper-related disease in humans

Prosociality in business: a human empowerment framework

This study introduces a human empowerment framework to better understand why some businesses are more socially oriented than others in their policies and activities. Building on Welzel’s theory of emancipation, we argue that human empowerment—comprised of four components: action resources, emancipative values, social movement activity, and civic entitlements—enables, motivates, and entitles individuals to pursue social goals for their businesses. Using a sample of over 15,000 entrepreneurs from 43 countries, we report strong empirical evidence for two ecological effects of the framework components on prosociality. We find that human empowerment (1) lifts entrepreneurs’ willingness to choose a social orientation for their business, and (2) reinforces the gender effect on prosociality in business activity. We discuss the human empowerment framework’s added value in understanding how modernization processes fully leverage the potential of social business activities for societies

Role of Homer Proteins in the Maintenance of Sleep-Wake States

Sleep is an evolutionarily conserved process that is linked to diurnal cycles and normal daytime wakefulness. Healthy sleep and wakefulness are integral to a healthy lifestyle; this occurs when an organism is able to maintain long bouts of both sleep and wake. Homer proteins, which function as adaptors for group 1 metabotropic glutamate receptors, have been implicated in genetic studies of sleep in both Drosophila and mouse. Drosophila express a single Homer gene product that is upregulated during sleep. By contrast, vertebrates express Homer as both constitutive and immediate early gene (H1a) forms, and H1a is up-regulated during wakefulness. Genetic deletion of Homer in Drosophila results in fragmented sleep and in failure to sustain long bouts of sleep, even under increased sleep drive. However, deletion of Homer1a in mouse results in failure to sustain long bouts of wakefulness. Further evidence for the role of Homer1a in the maintenance of wake comes from the CREB alpha delta mutant mouse, which displays a reduced wake phenotype similar to the Homer1a knockout and fails to up-regulate Homer1a upon sleep loss. Homer1a is a gene whose expression is induced by CREB. Sustained behaviors of the sleep/wake cycle are created by molecular pathways that are distinct from those for arousal or short bouts, and implicate an evolutionarily-conserved role for Homer in sustaining these behaviors