Calculation of some determinants using the s-shifted factorial

Several determinants with gamma functions as elements are evaluated. This kind of determinants are encountered in the computation of the probability density of the determinant of random matrices. The s-shifted factorial is defined as a generalization for non-negative integers of the power function, the rising factorial (or Pochammer's symbol) and the falling factorial. It is a special case of polynomial sequence of the binomial type studied in combinatorics theory. In terms of the gamma function, an extension is defined for negative integers and even complex values. Properties, mainly composition laws and binomial formulae, are given. They are used to evaluate families of generalized Vandermonde determinants with s-shifted factorials as elements, instead of power functions.Comment: 25 pages; added section 5 for some examples of application

Representations of SU(1,1) in Non-commutative Space Generated by the Heisenberg Algebra

SU(1,1) is considered as the automorphism group of the Heisenberg algebra H. The basis in the Hilbert space K of functions on H on which the irreducible representations of the group are realized is explicitly constructed. The addition theorems are derived.Comment: Latex, 8 page

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Barriers to mental health care access for the individual in crisis.

The delivery system of health care to Americans is in crisis. As costs continue to escalate, and as access to services deteriorates, an increasing number of individuals in need of physical and mental health care are experiencing difficulty accessing the necessary services. Changes in economic resources have resulted in quantitative shifts in mental health service delivery. A greater number of individuals seek mental health services as a result of the stress and anxiety created from a threatened or actual loss of financial stability. This increase in demand for service comes at a time when mental health programs are experiencing a decrease in resources which has resulted in reduced access to services. The emergency mental health service utilization patterns and client characteristics have changed during the same period of time that the overall mental health care delivery system has undergone transformation. However, the changes in mental health care have not necessarily evolved out of careful rational planning, but rather as a response to chaotic shifts in the mental health system at large. The purpose of this study was to gather data about access to these mental health outpatient services as they related to client diagnostic characteristics, system ability to provide the service needed, and ability of the service to meet the client\u27s perceived need. The implications of the findings are clear. Access to services during a crisis was dependent upon system response, degree of psychopathology and a supportive environment. Any reform effort must include adequate crisis intervention and social services to meet the need of the changing population. Education for the general population and the professional would enhance understanding of the needs of the mentally ill and service availability

Spectra of Field Fluctuations in Braneworld Models with Broken Bulk Lorentz Invariance

We investigate five-dimensional braneworld setups with broken Lorentz invariance continuing the developments of our previous paper (arXiv:0712.1136), where a family of static self-tuning braneworld solutions was found. We show that several known braneworld models can be embedded into this family. Then we give a qualitative analysis of spectra of field fluctuations in backgrounds with broken Lorentz invariance. We also elaborate on one particular model and study spectra of scalar and spinor fields in it. It turns out that the spectra we have found possess very peculiar and unexpected properties.Comment: 30 pages, 8 figures, minor corrections, references added, note adde

Traffic related noise and air quality valuations: evidence from stated preference residential choice models

This paper reports on research which has estimated valuations of changes in traffic related noise levels and air quality and which contributes to the body of knowledge and to methodology in this area. There are several novel aspects of this research. Firstly, there have been relatively few stated preference studies of the monetary valuations of traffic related noise and air quality. A feature of this analysis is the examination of variations in values according to the size and sign of the environmental change, the currently experienced level of the attribute and various socio-economic factors. Secondly, the important issue of presentation is addressed, with two different methods used in the valuation of air quality and links made between valuations and physical measures. Thirdly, the results from stated preference and the contingent valuation method are compared. Finally, we bring together evidence from other studies and compare them with the findings obtained here

Analytical solutions of the Schr\"{o}dinger equation with the Woods-Saxon potential for arbitrary ll state

In this work, the analytical solution of the radial Schr\"{o}dinger equation for the Woods-Saxon potential is presented. In our calculations, we have applied the Nikiforov-Uvarov method by using the Pekeris approximation to the centrifugal potential for arbitrary $l$ states. The bound state energy eigenvalues and corresponding eigenfunctions are obtained for various values of $n$ and $l$ quantum numbers.Comment: 14 page

16-µJ pulse energy, picosecond, narrow-linewidth master oscillator power amplifier using direct amplification

We present a gain-switched-diode-seeded 1034.5nm master oscillator power amplifier, employing direct amplification through standard commercial Yb3+-doped fibres to generate 15.6µJ-pulse-energy, 126kW-peak-power, picosecond pulses with 3dB spectral bandwidth of 0.87nm