The inverse electromagnetic scattering problem in a piecewise homogeneous medium

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation method. Inspired by a novel idea developed by Hahner [11], we prove that the penetrable interface between layers can be uniquely determined from a knowledge of the electric far field pattern for incident plane waves. Then, using the idea developed by Liu and Zhang [21], a new mixed reciprocity relation is obtained and used to show that the impenetrable obstacle with its physical property can also be recovered. Note that the wave numbers in the corresponding medium may be different and therefore this work can be considered as a generalization of the uniqueness result of [20].Comment: 19 pages, 2 figures, submitted for publicatio

Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Stäckel transform and 3D classification theory

This article is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat spaces. In the first part of the article we study the Stäckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different three-dimensional spaces. We show first that all superintegrable systems with nondegenerate potentials are multiseparable and then that each such system on any conformally flat space is Stäckel equivalent to a system on a constant curvature space. In the second part of the article we classify all the superintegrable systems that admit separation in generic coordinates. We find that there are eight families of these systems

Superintegrable Systems in Darboux spaces

Almost all research on superintegrable potentials concerns spaces of constant curvature. In this paper we find by exhaustive calculation, all superintegrable potentials in the four Darboux spaces of revolution that have at least two integrals of motion quadratic in the momenta, in addition to the Hamiltonian. These are two-dimensional spaces of nonconstant curvature. It turns out that all of these potentials are equivalent to superintegrable potentials in complex Euclidean 2-space or on the complex 2-sphere, via "coupling constant metamorphosis" (or equivalently, via Staeckel multiplier transformations). We present tables of the results

A versatile dual spot laser scanning confocal microscopy system for advanced fluorescence correlation spectroscopy analysis in living cell

A fluorescence correlation spectroscopy (FCS) system based on two independent measurement volumes is presented. The optical setup and data acquisition hardware are detailed, as well as a complete protocol to control the location, size and shape of the measurement volumes. A method that allows to monitor independently the excitation and collection efficiency distribution is proposed. Finally, a few examples of measurements that exploit the two spots in static and/or scanning schemes, are reported.Comment: Accepted for publication in Review of Scientific Instrumen

Comparison between Newton and response-surface methods

A supporting-point placement scheme is presented that is used for calculating function derivatives by the method of differences as well as a quadratic response-surface approximation. The placement scheme unifies the Newton (NM) and response-surface (RSM) methods in the limiting case when the point-set distance parameter for the RSM is chosen as small as that for obtaining the derivatives needed by the NM. Two new RSM minimization strategies with and without line searches are presented. The numerical performance of the algorithms is studied by using well-known test functions and the paths through the two-dimensional variables space are plotted for easier interpretation of the performance results. The results are compared with results of numerical experiments found in the literatur

Statistical Estimation of Quantum Tomography Protocols Quality

A novel operational method for estimating the efficiency of quantum state tomography protocols is suggested. It is based on a-priori estimation of the quality of an arbitrary protocol by means of universal asymptotic fidelity distribution and condition number, which takes minimal value for better protocol. We prove the adequacy of the method both with numerical modeling and through the experimental realization of several practically important protocols of quantum state tomography

Cost and Operational Evaluations of Centralized vs. Distributed Class IX Inventories

NPS NRP Technical ReportCost and Operational Evaluations of Centralized vs. Distributed Class IX InventoriesHQMC Installations and Logistics (I&L)This research is supported by funding from the Naval Postgraduate School, Naval Research Program (PE 0605853N/2098). https://nps.edu/nrpChief of Naval Operations (CNO)Approved for public release. Distribution is unlimited.