The Relative Occupational Success of Blacks and Whites

macroeconomics, occupational success

Homecoming 2015

Photos of Homecoming 201

Closed-form sums for some perturbation series involving associated Laguerre polynomials

Infinite series sum_{n=1}^infty {(alpha/2)_n / (n n!)}_1F_1(-n, gamma, x^2), where_1F_1(-n, gamma, x^2)={n!_(gamma)_n}L_n^(gamma-1)(x^2), appear in the first-order perturbation correction for the wavefunction of the generalized spiked harmonic oscillator Hamiltonian H = -d^2/dx^2 + B x^2 + A/x^2 + lambda/x^alpha 0 0, A >= 0. It is proved that the series is convergent for all x > 0 and 2 gamma > alpha, where gamma = 1 + (1/2)sqrt(1+4A). Closed-form sums are presented for these series for the cases alpha = 2, 4, and 6. A general formula for finding the sum for alpha/2 = 2 + m, m = 0,1,2, ..., in terms of associated Laguerre polynomials, is also provided.Comment: 16 page

Gravitating semirelativistic N-boson systems

Analytic energy bounds for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N(p_i^2 + m^2)^{1/2} - sum_{1=i<j}^N v/r_{ij}, with v>0, are derived by use of Jacobi relative coordinates. For gravity v=c/N, these bounds are substantially tighter than earlier bounds and they are shown to coincide with known results in the nonrelativistic limit.Comment: 7 pages, 2 figures It is now proved that the reduced Hamiltonian is bounded below by the simple N/2 Hamiltonia

Duration of antibody response following vaccination against feline immunodeficiency virus

Objectives: Recently, two point-of-care (PoC) feline immunodeficiency virus (FIV) antibody test kits (Witness and Anigen Rapid) were reported as being able to differentiate FIV-vaccinated from FIV-infected cats at a single time point, irrespective of the gap between testing and last vaccination (0–7 years). The aim of the current study was to investigate systematically anti-FIV antibody production over time in response to the recommended primary FIV vaccination series. Methods: First, residual plasma from the original study was tested using a laboratory-based ELISA to determine whether negative results with PoC testing were due to reduced as opposed to absent antibodies to gp40. Second, a prospective study was performed using immunologically naive client-owned kittens and cats given a primary FIV vaccination series using a commercially available inactivated whole cell/inactivated whole virus vaccine (Fel-O-Vax FIV, three subcutaneous injections at 4 week intervals) and tested systematically (up to 11 times) over 6 months, using four commercially available PoC FIV antibody kits (SNAP FIV/FeLV Combo [detects antibodies to p15/p24], Witness FeLV/FIV [gp40], Anigen Rapid FIV/FeLV [p24/gp40] and VetScan FeLV/FIV Rapid [p24]). Results: The laboratory-based ELISA showed cats from the original study vaccinated within the previous 0–15 months had detectable levels of antibodies to gp40, despite testing negative with two kits that use gp40 as a capture antigen (Witness and Anigen Rapid kits). The prospective study showed that antibody testing with SNAP Combo and VetScan Rapid was positive in all cats 2 weeks after the second primary FIV vaccination, and remained positive for the duration of the study (12/12 and 10/12 cats positive, respectively). Antibody testing with Witness and Anigen Rapid was also positive in a high proportion of cats 2 weeks after the second primary FIV vaccination (8/12 and 7/12, respectively), but antibody levels declined below the level of detection in most cats (10/12) by 1 month after the third (final) primary FIV vaccination. All cats tested negative using Witness and Anigen Rapid 6 months after the third primary FIV vaccination. Conclusions and relevance: This study has shown that a primary course of FIV vaccination does not interfere with FIV antibody testing in cats using Witness and Anigen Rapid, provided primary vaccination has not occurred within the previous 6 months. Consequently, Witness and Anigen Rapid antibody test kits can be used reliably to determine FIV infection status at the time of annual booster FIV vaccination to help detect ‘vaccine breakthroughs’ and in cats that have not received a primary course of FIV vaccination within the preceding 6 months. The duration of antibody response following annual booster FIV vaccination and the resulting effect on antibody testing using PoC kits needs to be determined by further research. The mechanism(s) for the variation in FIV antibody test kit performance remains unclear

Asymptotic iteration method for eigenvalue problems

An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y'' = lambda(x) y' + s(x) y is introduced, where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to Schroedinger type problems, including some with highly singular potentials, are presented.Comment: 14 page

Semirelativistic stability of N-boson systems bound by 1/r pair potentials

We analyze a system of self-gravitating identical bosons by means of a semirelativistic Hamiltonian comprising the relativistic kinetic energies of the involved particles and added (instantaneous) Newtonian gravitational pair potentials. With the help of an improved lower bound to the bottom of the spectrum of this Hamiltonian, we are able to enlarge the known region for relativistic stability for such boson systems against gravitational collapse and to sharpen the predictions for their maximum stable mass.Comment: 11 pages, considerably enlarged introduction and motivation, remainder of the paper unchange

Exact solutions for semirelativistic problems with non-local potentials

It is shown that exact solutions may be found for the energy eigenvalue problem generated by the class of semirelativistic Hamiltonians of the form H = sqrt{m^2+p^2} + hat{V}, where hat{V} is a non-local potential with a separable kernel of the form V(r,r') = - sum_{i=1}^n v_i f_i(r)g_i(r'). Explicit examples in one and three dimensions are discussed, including the Yamaguchi and Gauss potentials. The results are used to obtain lower bounds for the energy of the corresponding N-boson problem, with upper bounds provided by the use of a Gaussian trial function.Comment: 13 pages, 3 figure

Perturbation expansions for a class of singular potentials

Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is applied and extended to obtain non-power perturbation expansions for a class of singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha > 2), known as generalized spiked harmonic oscillators. The perturbation expansions developed here are valid for small values of the coupling lambda > 0, and they extend the results which Harrell obtained for the spiked harmonic oscillator A = 0. Formulas for the the excited-states are also developed.Comment: 23 page