Raising and Lowering operators of spin-weighted spheroidal harmonics

In this paper we generalize the spin-raising and lowering operators of spin-weighted spherical harmonics to linear-in-$\gamma$ spin-weighted spheroidal harmonics where $\gamma$ is an additional parameter present in the second order ordinary differential equation governing these harmonics. One can then generalize these operators to higher powers in $\gamma$. Constructing these operators required calculating the $\ell$-, $s$- and $m$-raising and lowering operators (and various combinations of them) of spin-weighted spherical harmonics which have been calculated and shown explicitly in this paper

Soil bacteria and phosphates

Cover title.Includes bibliographical references

Band structure of W and Mo by empirical pseudopotential method

The empirical pseudopotential method (EPM) is used to calculate the band structure of tungsten and molybdenum. Agreement between the calculated reflectivity, density of states, density of states at the Fermi surface and location of the Fermi surface from this study and experimental measurements and previous calculations is good. Also the charge distribution shows the proper topological distribution of charge for a bcc crystal

A computer program for a line-by-line calculation of spectra from diatomic molecules and atoms assuming a Voight line profile

Computer program predicts the spectra resulting from electronic transitions of diatomic molecules and atoms in local thermodynamic equilibrium. The program produces a spectrum by accounting for the contribution of each rotational and atomic line considered

Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation

We present a novel analytic extraction of high-order post-Newtonian (pN) parameters that govern quasi-circular binary systems. Coefficients in the pN expansion of the energy of a binary system can be found from corresponding coefficients in an extreme-mass-ratio inspiral (EMRI) computation of the change $\Delta U$ in the redshift factor of a circular orbit at fixed angular velocity. Remarkably, by computing this essentially gauge-invariant quantity to accuracy greater than one part in $10^{225}$, and by assuming that a subset of pN coefficients are rational numbers or products of $\pi$ and a rational, we obtain the exact analytic coefficients. We find the previously unexpected result that the post-Newtonian expansion of $\Delta U$ (and of the change $\Delta\Omega$ in the angular velocity at fixed redshift factor) have conservative terms at half-integral pN order beginning with a 5.5 pN term. This implies the existence of a corresponding 5.5 pN term in the expansion of the energy of a binary system. Coefficients in the pN series that do not belong to the subset just described are obtained to accuracy better than 1 part in $10^{265-23n}$ at $n$th pN order. We work in a radiation gauge, finding the radiative part of the metric perturbation from the gauge-invariant Weyl scalar $\psi_0$ via a Hertz potential. We use mode-sum renormalization, and find high-order renormalization coefficients by matching a series in $L=\ell+1/2$ to the large-$L$ behavior of the expression for $\Delta U$. The non-radiative parts of the perturbed metric associated with changes in mass and angular momentum are calculated in the Schwarzschild gauge

Ten plays for primary grades

Thesis (Ed.M.)--Boston Universit

The Use of Agricultural Credit Facilities by 50 Negro Farm Families in Austin County, Texas

This study is limited to Negro farmers living and operating farms in Austin County. In this report, a brief description of the natural and human resources of the county are given in order to establish a background of the area covered. A description is also given of the established credit facilities in the county, both Government sponsored and private sources and their policies regarding credit to farm families. The purpose for which the study was made was to determine the reasons why the farm population is on a steady decline, the cause for sub-standard housing, to determine where farmers obtain their capitol for their farm operations and the rate of interest charged by the various lending agencies. This study was also necessary in order that the writer can get a better knowledge of the farmers problems in relation to capitol and will aid in the planning of a program where some of the problems stated can be worked on