Formulation of a distortion index based on peak compressor pressure ratios

In order to effectively use a compressor face total-pressure distortion index as a measure of inlet-engine compatibility, a correlation of distortion amplitude with stall margin must be developed with minimal scatter. A recent analysis of data recorded in extensive distortion screen tests with the J85-GE-13 turbojet engine has resulted in a correlation based on compressor discharge pressure ratioed to the minimum pressure at the compressor face. Simply by determining compressor stall lines with a single hub radial distortion pattern, a single tip radial pattern, and with undistorted inflow, the overall compressor pressure ratio at stall for even the most complex distortion pattern was found to be predictable

Elliptical Weighted HOLICs for Weak Lensing Shear Measurement. part1:Definitions and isotropic PSF correction

We develop a new method to estimate gravitational shear by adopting an elliptical weight function to measure background galaxy images. In doing so, we introduce a new concept of "zero plane" which is an imaginal source plane where shapes of all sources are perfect circles, and regard the intrinsic shear as the result of an imaginal lensing distortion. This makes the relation between the observed shear, the intrinsic shear and lensing distortion more simple and thus higher-order calculation more easy. The elliptical weight function allows us to measure the mutiplemoment of shape of background galaxies more precisely by weighting highly to brighter parts of image and moreover to reduce systematic error due to insufficient expansion of the weight function in the original approach of KSB. Point Spread Function(PSF) correction in E-HOLICs methods becomes more complicated than those in KSB methods. In this paper we studied isotropic PSF correction in detail. By adopting the lensing distortion as the ellipticity of the weight function, we are able to show that the shear estimation in E-HOLICs method reduces to solve a polynomial in the absolute magnitude of the distortion. We compare the systematic errors between our approach and KSB using STEP2 simulation. It is confirmed that KSB method overestimate the input shear for images with large ellipticities, and E-HOLICs correctly estimate the input shear even for such images. Anisotropic PSF correction and analysis of real data will be presented in forthcoming paper.Comment: 30 pages, 8 figures, submitted to Ap

Semiclassical estimates of the cut-off resolvent for trapping perturbations

This paper is devoted to the study of a semiclassical "black box" operator $P$. We estimate the norm of its resolvent truncated near the trapped set by the norm of its resolvent truncated on rings far away from the origin. For $z$ in the unphysical sheet with $- h |ln h| < Im z < 0$, we prove that this estimate holds with a constant $h |Im z|^{-1} e^{C|Im z|/h}$. We also obtain analogous bounds for the resonances states of $P$. These results hold without any assumption on the trapped set neither any assumption on the multiplicity of the resonances.Comment: 19 page

Existence of Dirac resonances in the semi-classical limit

We study the existence of quantum resonances of the three-dimensional semiclassical Dirac operator perturbed by smooth, bounded and real-valued scalar potentials V decaying like ⟨x⟩−δ at infinity for some δ>0. By studying analytic singularities of a certain distribution related to V and by combining two trace formulas, we prove that the perturbed Dirac operators possess resonances near supV+1 and infV−1. We also provide a lower bound for the number of resonances near these points expressed in terms of the semiclassical parameter

Complex absorbing potential method for Stark resonances

We characterize the resonances of Stark Hamiltonians by the complex absorbing potential method. Namely, we prove that the Stark resonances are the limit points of complex eigenvalues of the Stark Hamiltonian with a quadratic complex absorbing potential when the absorbing coefficient tends to zero. The proof employs the complex distortion outside a cone introduced in the previous work by the author. Potentials with local singularities such as the Coulomb potential are allowed as perturbations.Comment: 14 page

Energy-Efficient Data Acquisition in Wireless Sensor Networks through Spatial Correlation

The application of Wireless Sensor Networks (WSNs) is restrained by their often-limited lifetime. A sensor node's lifetime is fundamentally linked to the volume of data that it senses, processes and reports. Spatial correlation between sensor nodes is an inherent phenomenon to WSNs, induced by redundant nodes which report duplicated information. In this paper, we report on the design of a distributed sampling scheme referred to as the 'Virtual Sampling Scheme' (VSS). This scheme is formed from two components: an algorithm for forming virtual clusters, and a distributed sampling method. VSS primarily utilizes redundancy of sensor nodes to get only a subset to sense the environment at any one time. Sensor nodes that are not sensing the environment are in a low-power sleep state, thus conserving energy. Furthermore, VSS balances the energy consumption amongst nodes by using a round robin method