Quadrics on complex Riemannian spaces of constant curvature, separation of variables, and the Gaudin magnet
Integrable systems that are connected with orthogonal separation of variables in complex Riemannian spaces of constant curvature are considered herein. An isomorphism with the hyperbolic Gaudin magnet, previously pointed out by one of the authors, extends to coordinates of this type. The complete classification of these separable coordinate systems is provided by means of the corresponding L matrices for the Gaudin magnet. The limiting procedures (or e calculus) which relate various degenerate orthogonal coordinate systems play a crucial role in the classification of all such systems.

title: Lie theory and separation of variables. 7. The harmonic oscillator in elliptic coordinates and Ince polynomials
abstract: As a continuation of Paper 6 we study the separable basis eigenfunctions and their relationships for the harmonic oscillator Hamiltonian in two space variables with special emphasis on products of Ince polynomials, the eigenfunctions obtained when one separates variables in elliptic coordinates. The overlaps connecting this basis to the polar and Cartesian coordinate bases are obtained by computing in a simpler Bargmann Hilbert space model of the problem. We also show that Ince polynomials are intimately connected with the representation theory of SU (2), the group responsible for the eigenvalue degeneracy of the oscillator Hamiltonian.

title: Lie theory and separation of variables. 11. The EPD equation
abstract: We show that the Euler–Poisson–Darboux equation {∂tt−∂rr−[(2m+1)/r]∂r}Θ=0 separates in exactly nine coordinate systems corresponding to nine orbits of symmetric second‐order operators in the enveloping algebra of SL(2,R), the symmetry group of this equation. We employ techniques developed in earlier papers from this series and use the representation theory of SL(2,R) to derive special function identities relating the separated solutions. We also show that the complex EPD equation separates in exactly five coordinate systems corresponding to five orbits of symmetric second‐order operators in the enveloping algebra of SL(2,C).

title: Separation of variables in Einstein spaces. I. Two ignorable and one null coordinate
abstract: Computes and classifies all Einstein spaces and their corresponding coordinate systems such that the Hamilton-Jacobi equation admits a separation of variables with two ignorable and one essential null coordinates. The authors find that all such spaces correspond to plane-fronted gravitational waves of Petrov type N. They also give necessary conditions which a general space-time must have in order to admit coordinates of the type studied. Furthermore, the integrability conditions for Helmholtz (Schrodinger) separability are completely solved.

title: Complete sets of commuting operators and O (3) scalars in the enveloping algebra of SU (3)
abstract: We consider the ``missing label'' problem for basis vectors of SU(3) representations in a basis corresponding to the group reduction SU(3)⊃O(3)⊃O(2). We prove that only two independent O (3) scalars exist in the enveloping algebra of S U (3), in addition to the obvious ones, namely the angular momentum L2 and the two SU(3) Casimir operators C(2) and C(3). Any one of these two operators (of third and fourth order in the generators) can be added to C(2), C(3), L2, and L3 to form a complete set of commuting operators. The eigenvalues of the third and fourth order scalars X(3) and X(4) are calculated analytically or numerically for many cases of physical interest. The methods developed in this article can be used to resolve a missing label problem for any semisimple group G, when reduced to any semisimple subgroup H.

title: Superintegrability on the two-dimensional hyperboloid. II
abstract: In this work we examine the basis functions for classical and quantum mechanical systems on the two-dimensional hyperboloid that admit separation of variables in at least two coordinate systems. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup spherical coordinate cases, and the details of the structure of the quadratic symmetry algebras.

title: Neutrino and antineutrino inclusive charged-current cross section measurements with the MINOS near detector
abstract: This thesis presents the measurement of energy dependence of the neutrino-nucleon inclusive charged current cross section on an isoscalar target in the range 3-50 GeV for neutrinos and 5-50 GeV energy range for antineutrinos. The data set was collected with the MINOS Near Detector using the wide band NuMI beam at Fermilab. The size of the charged current sample is 1.94 x 10{sup 6} neutrino events and 1.60 x 10{sup 5} antineutrino events. The flux has been extracted using a low hadronic energy sub-sample of the charged current events. The energy dependence of the cross section is obtained by dividing the charged current sample with the extracted flux. The neutrino and antineutrino cross section exhibits a linear dependence on energy at high energy but shows deviations from linear behavior at low energy. We also present a measurement of the ratio of antineutrino to neutrino inclusive cross section.

title: A RESEARCH AND DEVELOPMENT PROGRAM TO CONTINUE THE DEVELOPMENT OF PRECISION INSTRUMENTATION FOR THE STUDY OF MUONS IN THE TeV REGION

title: MPS Data Acquisition System
abstract: A description is given of the data acquisition system used with the multiparticle spectrometer facility at Brookhaven. Detailed information is provided on that part of the system which connects the detectors to the data handler; namely, the detector electronics, device controller, and device port optical isolator.

title: Development of Large Area Integrated Silicon Tracking Elements for the LHC Luminosity Upgrade
abstract: A natural upgrade of the CERN LHC would be to increase the luminosity to 1035 cm-2s-1. For charged particle tracking at this Super-LHC, all-silicon systems are considered appropriate. For tracking in an upgraded ATLAS detector, outside a radius of 20 cm, large area integrated elements ("staves") containing silicon strip detectors are under design and development. Each stave would hold of order 30 individual modules and contain integrated electrical services, mechanical support, and cooling. Prototype tests of such staves are reported here including studies of noise, interference, and a comparison of power distribution by parallel and serial current flow. Mechanical design and simulation on full length staves are presented as well.

title: Search for the disappearance of muon antineutrinos in the NuMI neutrino beam
abstract: We report constraints on muon antineutrino oscillation parameters that were obtained by using the two MINOS detectors to measure the 7% antineutrino component of the NuMI neutrino beam. In the Far Detector, we select 130 events in the charged-current muon antineutrino sample, compared to a prediction of 136.4 +/- 11.7(stat) ^{+10.2}_{-8.9}(syst) events under the assumption |dm2bar|=2.32x10^-3 eV^2, snthetabar=1.0. A fit to the two-flavor oscillation approximation constrains |dm2bar|<3.37x10^-3 eV^2 at the 90% confidence level with snthetabar=1.0.