Irregular Shearlet Frames: Geometry and Approximation Properties

Recently, shearlet systems were introduced as a means to derive efficient encoding methodologies for anisotropic features in 2-dimensional data with a unified treatment of the continuum and digital setting. However, only very few construction strategies for discrete shearlet systems are known so far. In this paper, we take a geometric approach to this problem. Utilizing the close connection with group representations, we first introduce and analyze an upper and lower weighted shearlet density based on the shearlet group. We then apply this geometric measure to provide necessary conditions on the geometry of the sets of parameters for the associated shearlet systems to form a frame for L^2(\R^2), either when using all possible generators or a large class exhibiting some decay conditions. While introducing such a feasible class of shearlet generators, we analyze approximation properties of the associated shearlet systems, which themselves lead to interesting insights into homogeneous approximation abilities of shearlet frames. We also present examples, such a oversampled shearlet systems and co-shearlet systems, to illustrate the usefulness of our geometric approach to the construction of shearlet frames

Regional Indexes of Activity: Combining the Old with the New

This paper proposes a framework to construct indexes of activity which links two strands of the index literature – the traditional business cycle analysis and the latent variable approach. To illustrate the method, we apply the framework to Australian regional data, namely to two resource-rich and two service-based states. The results reveal differences in the evolution and drivers of economic activity across the four states. We also demonstrate the value of the Index in a broader context by using a structural vector autoregression (SVAR) approach to analyse the effects of shocks from the US and from China. This Index-SVAR approach facilitates a richer analysis because the unique feature of the index method proposed here allows impulse responses to be traced back to the components.Regional economic activity, coincident indicators, dynamic latent factor model

AN EMPLOYMENT EQUATION FOR AUSTRALIA: 1966-2001

We model the relationship between hours of work and employment and argue that unless actual hours are varying with a change in ‘standard hours’, actual hours should not appear in the long-run component of an equation for employment. If however standard hours are changing then it is desirable that this variable be incorporated into the employment equation. Our theoretical model yields an expression for the elasticity of employment with respect to standard hours which shows that the elasticity is related to the size of the premium for overtime. Using quarterly data for the period 1966:3 – 2001:3 we estimate a new employment equation for Australia incorporating standard hours of work. We find empirical support for our approach and we provide new estimates of the elasticity of employment with respect to the real wage and GDP. We also find a marked asymmetry in the response of employment to variations in real GDP and real wages in recession periods as against non-recession periods.Employment Determination, Demand for Labor, Australia

Coronal Thick Target Hard X Ray Emissions and Radio Emissions

Recently a distinctive class of hard X ray (HXR) sources located in the corona was found, which implies that the collisionally thick target model (CTTM) applies even to the corona. We investigated whether this idea can independently be verified by microwave radiations that have been known as the best companion to HXRs. The study is made for the GOES M2.3 class flare occurred on 2002 September 9 that were observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and the Owens Valley Solar Array (OVSA). Interpreting the observed energy dependent variation of HXR source size under the CTTM the coronal density should be as high as $5\times 10^{11}$ cm$^{-3}$ over the distance up to 12$"$. To explain the cut-off feature of microwave spectrum at 3 GHz, we however, need density no higher than $1\times 10^{11}$ cm$^{-3}$. Additional constraints need to be placed on temperature and magnetic field of the coronal source in order to reproduce the microwave spectrum as a whole. Firstly, a spectral feature called the Razin suppression requires the magnetic field in a range of 250--350 gauss along with high viewing angles around 75$^{\rm o}$. Secondly, to avoid excess fluxes at high frequencies due to the free-free emission that were not observed, we need a high temperature $\geq2\times 10^7$ K. These two microwave spectral features, Razzin suppression and free-free emissions, become more significant at regions of high thermal plasma density and are essential for validating and for determining additional parameters for the coronal HXR sources.Comment: APJ Letters, in pres

Real-time, step-wise, electrical detection of protein molecules using dielectrophoretically aligned SWNT-film FET aptasensors

Aptamer functionalized addressable SWNT-film arrays between cantilever electrodes were successfully developed for biosensor applications. Dielectrophoretically aligned SWNT suspended films made possible highly specific and rapid detection of target proteins with a large binding surface area. Thrombin aptamer immobilized SWNT-film FET biosensor resulted in a real-time, label-free, and electrical detection of thrombin molecules down to a concentration of ca. 7 pM with a step-wise rapid response time of several seconds.X113338sciescopu

On the numerical solution of the dynamically loaded hydrodynamic lubrication of the point contact problem

The transient analysis of hydrodynamic lubrication of a point-contact is presented. A body-fitted coordinate system is introduced to transform the physical domain to a rectangular computational domain, enabling the use of the Newton-Raphson method for determining pressures and locating the cavitation boundary, where the Reynolds boundary condition is specified. In order to obtain the transient solution, an explicit Euler method is used to effect a time march. The transient dynamic load is a sinusoidal function of time with frequency, fractional loading, and mean load as parameters. Results include the variation of the minimum film thickness and phase-lag with time as functions of excitation frequency. The results are compared with the analytic solution to the transient step bearing problem with the same dynamic loading function. The similarities of the results suggest an approximate model of the point contact minimum film thickness solution