Combined calculi for photon orbital and spin angular momenta

Context. Wavelength, photon spin angular momentum (PSAM), and photon orbital angular momentum (POAM), completely describe the state of a photon or an electric field (an ensemble of photons). Wavelength relates directly to energy and linear momentum, the corresponding kinetic quantities. PSAMand POAM, themselves kinetic quantities, are colloquially known as polarization and optical vortices, respectively. Astrophysical sources emit photons that carry this information. Aims. PSAM characteristics of an electric field (intensity) are compactly described by the Jones (Stokes/Mueller) calculus. Similarly, I created calculi to represent POAM characteristics of electric fields and intensities in an astrophysical context. Adding wavelength dependence to all of these calculi is trivial. The next logical steps are to 1) form photon total angular momentum (PTAM = POAM + PSAM) calculi; 2) prove their validity using operators and expectation values; and 3) show that instrumental PSAM can affect measured POAM values for certain types electric fields. Methods. I derive the PTAM calculi of electric fields and intensities by combining the POAM and PSAM calculi. I show how these quantities propagate from celestial sphere to image plane. I also form the PTAMoperator (the sum of the POAMand PSAMoperators), with and without instrumental PSAM, and calculate the corresponding expectation values. Results. Apart from the vector, matrix, dot product, and direct product symbols, the PTAM and POAM calculi appear superficially identical. I provide tables with all possible forms of PTAM calculi. I prove that PTAM expectation values are correct for instruments with and without instrumental PSAM. I also show that POAM measurements of "unfactored" PTAM electric fields passing through non-zero instrumental circular PSAM can be biased. Conclusions. The combined PTAM calculi provide insight into how to mathematically model PTAM sources and calibrate POAMand PSAM- induced POAM measurement errors

Training benefits consequent to 8-weeks of kettlebell training

This study was designed to examine the changes in aerobic capacity and muscular strength consequent to 8 weeks of kettlebell training. Seventeen subjects (9 males, 8 females) completed 1 repetition maximum (1RM) testing for one-arm shoulder press, leg press, upright row, and handgrip strength. Subjects then performed an 8-minute kettlebell VO2max snatch test to determine aerobic capacity. Testing was done before and after the 8-week training program. The 8-week kettlebell training program consisted of kettlebell snatches, swings, Turkish get-ups, and variations of the three fundamental movements. Each training session consisting of a 5-minute warm-up, 40 minute exercise session, and 10 minute cool-down. Following the training program, the experimental group demonstrated significant (p<0.05) improvements in VO2max (13.8%), leg strength (14.8%), and grip strength (13.9%) compared to the control group. No significant changes were found in the upright row or shoulder press between groups. The results show that an 8-week kettlebell training program is an effective way to improve muscular strength and aerobic capacity

How good are projection methods for convex feasibility problems?

We consider simple projection methods for solving convex feasibility problems. Both successive and sequential methods are considered, and heuristics to improve these are suggested. Unfortunately, particularly given the large literature which might make one think otherwise, numerical tests indicate that in general none of the variants considered are especially effective or competitive with more sophisticated alternatives

The fully residually F quotients of F*<x,y>

We describe the fully residually F; or limit groups relative to F; (where F is a free group) that arise from systems of equations in two variables over F that have coefficients in F.Comment: 64 pages, 2 figures. Following recommendations from a referee, the paper has been completely reorganized and many small mistakes have been corrected. There were also a few gaps in the earlier version of the paper that have been fixed. In particular much of the content of Section 8 in the previous version had to be replaced. This paper is to appear in Groups. Geom. Dy

Default Estimation for Low-Default Portfolios

The problem in default probability estimation for low-default portfolios is that there is little relevant historical data information. No amount of data processing can fix this problem. More information is required. Incorporating expert opinion formally is an attractive option.

Determination of ferroelectric compositional phase transition using novel virtual crystal approach

We employ a new method for studying compositionally disordered ferroelectric oxides. This method is based on the virtual crystal approximation (VCA), in which two or more component potentials are averaged into a composite atomic potential. In our method, we construct a virtual atom with the correctly averaged atomic size and atomic eigenvalues. We have used our new method to study the composition dependent phase transition in Pb(Zr_{1-x}Ti_x)O_3 lying between x=0.5 and x=0.4. We correctly predict the experimentally determined phase transition from the tetragonal phase to a low-temperature rhombohedral phase between these two compositions.Comment: 7 pages, 2 figures, Proceedings for Fundamental Physics of Ferroelectrics, Aspen, CO February 13-20, 200

Calculation of the Anisotropic Coefficients of Thermal Expansion: A First-Principles Approach

Predictions of the anisotropic coefficients of thermal expansion are needed to not only compare to experimental measurement, but also as input for macroscopic modeling of devices which operate over a large temperature range. While most current methods are limited to isotropic systems within the quasiharmonic approximation, our method uses first-principles calculations and includes anharmonic effects to determine the temperature-dependent properties of materials. These include the lattice parameters, anisotropic coefficients of thermal expansion, isothermal bulk modulus, and specific heat at constant pressure. Our method has been tested on two compounds (Cu and AlN) and predicts thermal properties which compare favorably to experimental measurement over a wide temperature range.Comment: 8 pages, 9 figures, 1 tabl