Approximation with wave packets generated by a refinable function

We consider best -term approximation in with wave packets generated by a single refinable function. The main examples of wave packets are orthonormal wavelets, or more generally wavelet frames based on a multiresolution analysis (so-called framelets). The approximation classes associated with best -term approximation in for a large class of wave packets are completely characterized in terms of Besov spaces.

As an application of the main result, we show that for -term approximation in with elements from an oversampled version of a framelet system with compactly supported generators, the associated approximation classes turn out to be (essentially) Besov spaces.

     

Nonlinear approximation with general wave packets

We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete characterization of the approximation spaces is derived.     

Non-linear inverse scattering: high resolution quantitative breast tissue tomography

Recent published results in inverse scattering generally show the difficulty in dealing with moderate to high contrast inhomogeneities when employing linearized or iteratively linearized algorithms (e.g., distorted Born iterative method). This paper presents a fully nonlinear algorithm utilizing full wave field data, that results in ultrasound computed tomographic images from a laboratory breast scanner, and shows several such unique images from volunteer subjects. The forward problem, data collection process and inverse scattering algorithm used are discussed. A functional that represents the "best fit" between predicted and measured data is minimized, and therefore requires a very fast forward problem solver, Jacobian calculation, and gradient estimation, all of which are described. The data collection device is described. The algorithm and device yield quantitative estimates of human breast tissue in vivo. Several high resolution images, measuring ～150 by 150 wavelengths, obtained from the 2D inverse scattering algorithms, using data collected from a first prototype, are shown and discussed. The quantitative values are compared with previous published work.     

Recent developments in catalyst-related PEM fuel cell durability

Cost and durability remain the two major barriers to the widespread commercialization of polymer electrolyte membrane fuel cell (PEMFC)-based power systems, especially for the most impactful but challenging fuel cell electric vehicle (FCEV) application. Commercial FCEVs are now on the road; however, their PEMFC systems do not meet the cost targets established by the U.S. Department of Energy, primarily due to the high platinum loading needed on the cathode to achieve the requisite performance and lifetime. While the activities of a number of commercial Pt-based alloy cathode catalysts exceed the beginning-of-life (BOL) targets, these activities, and the overall cathode performance, degrade via a variety of mechanisms described herein. Degradation is mitigated in current FCEVs by utilizing a cathode catalyst with a lower BOL activity (e.g., much lower transition metal alloy content and larger BOL nanoparticle size), necessitating higher catalyst loadings, and through the utilization of system controls that avoid conditions known to exacerbate degradation processes, such as limiting the fuel cell stack voltage range. The design and development of active and robust materials and eliminating the need for vehicle mitigation strategies would greatly simplify the operating system, allowing for greater transient operation, avoiding large hybridization, and curtailing of fuel cell power. Although system mitigation strategies have provided the near-term pathway for FCEV commercialization, material-specific solutions are required to further reduce costs and improve operability and efficiency. Future material developments should focus on stabilization of the electrode structure and minimization of the catalyst particle susceptibility to dissolution caused by oxide formation and reduction over PEMFC cathode-relevant operating potentials plus minimization of support corrosion. Ex situ accelerated stress tests have provided insight into the processes responsible for material and performance degradation and will continue to provide useful information on the relative stability of materials and benchmarks for robust and stable materials-based solutions not requiring system mitigation strategies to achieve adequate lifetime.     

Pair Distribution Function from Liquid Jet Nanoparticle Suspension using Femtosecond X-ray Pulses

X-ray scattering data measured on femtosecond timescales at the SACLA X-ray Free Electron Laser (XFEL) facility on a suspension of HfO₂ nanoparticles in a liquid jet were used for pair distribution function (PDF) analysis. Despite a non-optimal experimental setup resulting in a modest Q_max of ~8 Å⁻¹, a promising PDF was obtained. The main features were reproduced when comparing the XFEL PDF to a PDF obtained from data measured at the PETRA III synchrotron light source. Refining structural parameters such as unit cell dimension and particle size from the XFEL PDF provided reliable values. Although the reachable Q_max limited the obtainable information, the present results indicate that good quality PDFs can be obtained on femtosecond timescales if the experimental conditions are further optimized. The study therefore encourages a new direction in ultrafast structural science where structural features of amorphous and disordered systems can be studied.     

Relating phase transition heat capacity to thermal conductivity and effusivity in Cu2Se

Accurate measurement of thermal conductivity is essential to determine the thermoelectric figure‐of‐merit, zT. Near the phase transition of Cu₂Se at 410 K, the transport properties change rapidly with temperature, and there is a concurrent peak in measured heat capacity from differential scanning calorimetry (DSC). Interpreting the origin as a broad increase in heat capacity or as a transient resulted in a three‐fold difference in the reported zT in two recent publications. To resolve this discrepancy, thermal effusivity was deduced from thermal conductivity and diffusivity measurements via the transient plane source (TPS) method and compared with that calculated from thermal diffusivity and the two interpretations of the DSC data for heat capacity. The comparison shows that the DSC measurement gave the heat capacity relevant for calculation of the thermal conductivity of Cu₂Se. The thermal conductivity calculated this way follows the electronic contribution to thermal conductivity closely, and hence the main cause of the zT peak is concluded to be the enhanced Seebeck coefficient. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Frame Decomposition of Decomposition Spaces

A new construction of tight frames for with flexible time-frequency localization is considered. The frames can be adapted to form atomic decompositions for a large family of smoothness spaces on a class of so-called decomposition spaces. The decomposition space norm can be completely characterized by a sparseness condition on the frame coefficients. As examples of the general construction, new tight frames yielding decompositions of Besov space, anisotropic Besov spaces, α-modulation spaces, and anisotropic α-modulation spaces are considered. Finally, curvelet-type tight frames are constructed on      

Sex as a Risk Factor for Solar Ultraviolet Radiation Exposure?–Dosimetry in Danish Outdoor Workers

Solar ultraviolet radiation (UVR) exposure is a known risk factor for the development of skin cancer. Heterogeneity in solar UVR exposure may explain the diversity in skin cancer incidence between men and women. This, however, has not previously been investigated in Danish outdoor workers using UVR dosimetry. The aim of this study was to evaluate sex differences in solar UVR dosimetry in Danish outdoor workers on working and leisure days. A cross-sectional design was used to collect dosimetry data during the Danish summer season (May to September). Analysis was based on an electronic questionnaire and dosimetry data from 450 outdoor workers (88 women, 362 men). Dosimetry data were reported as standard erythema dose (SED). The daily median SED (Interquartile range) on working days was 1.6 (2.5) in men and 1.5 (2.1) in women while on leisure days it was 0.5 (1.4) in men and 0.6 (1.3) in women. Analysis by multiple linear regression did not show any association between daily median SED and sex on either working or leisure days. In conclusion, solar UVR exposure in Danish outdoor workers did not vary according to sex.     

Boundedness for pseudodifferential operators on multivariate α-modulation spaces

The α-modulation spaces M ^s,α _p,q (R ^d ), α∈[0,1], form a family of spaces that contain the Besov and modulation spaces as special cases. In this paper we prove that a pseudodifferential operator σ(x,D) with symbol in the Hörmander class S ^b _ρ,0 extends to a bounded operator σ(x,D):M ^s,α _p,q (R ^d )→M ^s-b,α _p,q (R ^d ) provided 0≤α≤ρ≤1, and 1<p,q<∞. The result extends the well-known result that pseudodifferential operators with symbol in the class S ^b _1,0 maps the Besov space B ^s _p,q (R ^d ) into B ^s-b _p,q (R ^d ).     

Investigation of the correlation between stoichiometry and thermoelectric properties in a PtSb2 single crystal

The thermoelectric properties of a PtSb(2) single crystal containing a stoichiometric gradient were investigated. The gradient was produced by employing a Stockbarger synthesis technique. The gradient was observed through the use of spatial resolved Seebeck coefficient measurements and verified utilizing X-Ray Diffraction and Energy Dispersive X-Ray Spectroscopy. The correlation between Pt/Sb ratio and physical property parameters--Seebeck coefficient, mobility, resistivity and charge carrier concentration--was studied. Elemental analysis by Energy Dispersive X-Ray Spectroscopy, X-Ray Fluorescence and Inductively Coupled Plasma revealed Sb deficiency in the crystal, which explains the observed high charge carrier concentration and metallic properties. The transport properties were measured in the temperature range T = 20-300 K on a polycrystalline sample. Furthermore, ab initio theoretical calculations have been conducted to support the interpretation of the measurements.