A family of fourth-order superintegable systems with rational potentials related to Painlev\'e VI

We discuss a family of Hamiltonians given by particular rational extensions of the singular oscillator in two-dimensions. The wave functions of these Hamiltonians can be expressed in terms of products of Laguerre and exceptional Jacobi polynomials. We show that these systems are superintegrable and admit an integral of motion that is of fourth-order. As such systems have been classified, we see that these potential satisfy a non-linear equation related to Painlev\'e VI. We begin by demonstrating the process with the simpler example of rational extensions of the harmonic oscillator and use the classification of third-order superintegrable systems to connect these families with the known solutions of Painlev\'e IV associated with Hermite polynomials

A high-wavenumber boundary-element method for an acoustic scattering problem

In this paper we show stability and convergence for a novel Galerkin boundary element method approach to the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data. This problem models, for example, outdoor sound propagation over inhomogeneous flat terrain. To achieve a good approximation with a relatively low number of degrees of freedom we employ a graded mesh with smaller elements adjacent to discontinuities in impedance, and a special set of basis functions for the Galerkin method so that, on each element, the approximation space consists of polynomials (of degree $\nu$) multiplied by traces of plane waves on the boundary. In the case where the impedance is constant outside an interval $[a,b]$, which only requires the discretization of $[a,b]$, we show theoretically and experimentally that the $L_2$ error in computing the acoustic field on $[a,b]$ is ${\cal O}(\log^{\nu+3/2}|k(b-a)| M^{-(\nu+1)})$, where $M$ is the number of degrees of freedom and $k$ is the wavenumber. This indicates that the proposed method is especially commendable for large intervals or a high wavenumber. In a final section we sketch how the same methodology extends to more general scattering problems

Remote sensing research for agricultural applications

Materials and methods used to characterize selected soil properties and agricultural crops in San Joaquin County, California are described. Results show that: (1) the location and widths of TM bands are suitable for detecting differences in selected soil properties; (2) the number of TM spectral bands allows the quantification of soil spectral curve form and magnitude; and (3) the spatial and geometric quality of TM data allows for the discrimination and quantification of within field variability of soil properties. The design of the LANDSAT based multiple crop acreage estimation experiment for the Idaho Department of Water Resources is described including the use of U.C. Berkeley's Survey Modeling Planning Model. Progress made on Peditor software development on MIDAS, and cooperative computing using local and remote systems is reported as well as development of MIDAS microcomputer systems

Sexual violence in post-conflict Liberia: survivors and their care.

Using routine data from three clinics offering care to survivors of sexual violence (SV) in Monrovia, Liberia, we describe the characteristics of SV survivors and the pattern of SV and discuss how the current approach could be better adapted to meet survivors' needs. There were 1500 survivors seeking SV care between January 2008 and December 2009. Most survivors were women (98%) and median age was 13 years (Interquartile range: 9-17 years). Sexual aggression occurred during day-to-day activities in 822 (55%) cases and in the survivor's home in 552 (37%) cases. The perpetrator was a known civilian in 1037 (69%) SV events. Only 619 (41%) survivors sought care within 72 h. The current approach could be improved by: effectively addressing the psychosocial needs of child survivors, reaching male survivors, targeting the perpetrators in awareness and advocacy campaigns and reducing delays in seeking care

Modelling radiation-induced cell cycle delays

Ionizing radiation is known to delay the cell cycle progression. In particular after particle exposure significant delays have been observed and it has been shown that the extent of delay affects the expression of damage such as chromosome aberrations. Thus, to predict how cells respond to ionizing radiation and to derive reliable estimates of radiation risks, information about radiation-induced cell cycle perturbations is required. In the present study we describe and apply a method for retrieval of information about the time-course of all cell cycle phases from experimental data on the mitotic index only. We study the progression of mammalian cells through the cell cycle after exposure. The analysis reveals a prolonged block of damaged cells in the G2 phase. Furthermore, by performing an error analysis on simulated data valuable information for the design of experimental studies has been obtained. The analysis showed that the number of cells analyzed in an experimental sample should be at least 100 to obtain a relative error less than 20%.Comment: 19 pages, 11 figures, accepted for publication in Radiation and Environmental Biophysic

All Teleportation and Dense Coding Schemes

We establish a one-to-one correspondence between (1) quantum teleportation schemes, (2) dense coding schemes, (3) orthonormal bases of maximally entangled vectors, (4) orthonormal bases of unitary operators with respect to the Hilbert-Schmidt scalar product, and (5) depolarizing operations, whose Kraus operators can be chosen to be unitary. The teleportation and dense coding schemes are assumed to be ``tight'' in the sense that all Hilbert spaces involved have the same finite dimension d, and the classical channel involved distinguishes d^2 signals. A general construction procedure for orthonormal bases of unitaries, involving Latin Squares and complex Hadamard Matrices is also presented.Comment: 21 pages, LaTe

Magneto-structural properties of the layered quasi-2D triangular-lattice antiferromagnets Cs2_2CuCl4−x_{4-x}Brx_x for x{x} = 0,1,2 and 4

We present a study of the magnetic susceptibility $\chi_{mol}$ under variable hydrostatic pressure on single crystals of Cs$_2$CuCl$_{4-x}$Br$_x$. This includes the border compounds \textit{x} = 0 and 4, known as good realizations of the distorted triangular-lattice spin-1/2 Heisenberg antiferromagnet, as well as the isostructural stoichiometric systems Cs$_2$CuCl$_{3}$Br$_1$ and Cs$_2$CuCl$_{2}$Br$_2$. For the determination of the exchange coupling constants $J$ and $J^{\prime}$, $\chi_{mol}$ data were fitted by a $J-J^{\prime}$ model \cite{Schmidt2015}. Its application, validated for the border compounds, yields a degree of frustration $J^{\prime}$/$J$ = 0.47 for Cs$_2$CuCl$_3$Br$_1$ and $J^{\prime}$/$J$ $\simeq$ 0.63 - 0.78 for Cs$_2$CuCl$_2$Br$_2$, making these systems particular interesting representatives of this family. From the evolution of the magnetic susceptibility under pressure up to about 0.4\,GPa, the maximum pressure applied, two observations were made for all the compounds investigated here. First, we find that the overall energy scale, given by $J_c = (J^2$ + $J^{\prime 2}$)$^{1/2}$, increases under pressure, whereas the ratio $J^{\prime}$/$J$ remains unchanged in this pressure range. These experimental observations are in accordance with the results of DFT calculations performed for these materials. Secondly, for the magnetoelastic coupling constants, extraordinarily small values are obtained. We assign these observations to a structural peculiarity of this class of materials

A portable neutron spectroscope (NSPECT) for detection, imaging and identification of nuclear material

We have developed, fabricated and tested a prototype imaging neutron spectrometer designed for real-time neutron source location and identification. Real-time detection and identification is important for locating materials. These materials, specifically uranium and transuranics, emit neutrons via spontaneous or induced fission. Unlike other forms of radiation (e.g. gamma rays), penetrating neutron emission is very uncommon. The instrument detects these neutrons, constructs images of the emission pattern, and reports the neutron spectrum. The device will be useful for security and proliferation deterrence, as well as for nuclear waste characterization and monitoring. The instrument is optimized for imaging and spectroscopy in the 1-20 MeV range. The detection principle is based upon multiple elastic neutron-proton scatters in organic scintillator. Two detector panel layers are utilized. By measuring the recoil proton and scattered neutron locations and energies, the direction and energy spectrum of the incident neutrons can be determined and discrete and extended sources identified. Event reconstruction yields an image of the source and its location. The hardware is low power, low mass, and rugged. Its modular design allows the user to combine multiple units for increased sensitivity. We will report the results of laboratory testing of the instrument, including exposure to a calibrated Cf-252 source. Instrument parameters include energy and angular resolution, gamma rejection, minimum source identification distances and times, and projected effective area for a fully populated instrument