Solving Potential Scattering Equations without Partial Wave Decomposition

Considering two-body integral equations we show how they can be dimensionally reduced by integrating exactly over the azimuthal angle of the intermediate momentum. Numerical solution of the resulting equation is feasible without employing a partial-wave expansion. We illustrate this procedure for the Bethe-Salpeter equation for pion-nucleon scattering and give explicit details for the one-nucleon-exchange term in the potential. Finally, we show how this method can be applied to pion photoproduction from the nucleon with $\pi N$ rescattering being treated so as to maintain unitarity to first order in the electromagnetic coupling. The procedure for removing the azimuthal angle dependence becomes increasingly complex as the spin of the particles involved increases.Comment: 15 pages, 4 figure

What Should EDA Fund? Developing a Model for Pre-Assessment of Economic Development Investments

This paper describes the completion of a “comprehensive study of regionalism” that was conducted by a joint team of economists and economic development specialists for the Economic Development Administration (EDA). The project consisted of two main activities: an examination of the factors associated with economic development success and the creation of a practical interactive tool for EDA project assessment and comparison. Findings from surveys, interviews, and project case studies are discussed in terms of their support for a positive relationship between successful economic development efforts and factors such as leadership and private investment. Also, the authors discuss the creation of a quantitative assessment model utilizing well-known approaches such as economic impact multipliers and cluster theory. The primary contribution of this work to the existing body of EDA-focused research and evaluation literature is introducing a means of using standardized scores, also known as z-scores, to compare and assess economic development projects across both industries and regions.regional economic development, economic impact, assessment model, EDA, z-score

Near infrared spectroscopy of the type IIn SN 2010jl: evidence for high velocity ejecta

The Type IIn supernova SN 2010jl was relatively nearby and luminous, allowing detailed studies of the near-infrared (NIR) emission. We present 1 - 2.4 micron spectroscopy over the age range of 36 - 565 days from the earliest detection of the supernova. On day 36, the H lines show an unresolved narrow emission component along with a symmetric broad component that can be modeled as the result of electron scattering by a thermal distribution of electrons. Over the next hundreds of days, the broad components of the H lines shift to the blue by 700 km/s, as is also observed in optical lines. The narrow lines do not show a shift, indicating they originate in a different region. He I 1.0830 and 2.0587 micron lines both show an asymmetric broad emission component, with a shoulder on the blue side that varies in prominence and velocity from -5500 km/s on day 108 to -4000 km/s on day 219. This component may be associated with the higher velocity flow indicated by X-ray observations of the supernova. The absence of the feature in the H lines suggests that this is from a He rich ejecta flow. The He I 1.0830 micron feature has a narrow P Cygni line, with absorption extending to ~100 km/s and strengthening over the first 200 days, and an emission component which weakens with time. At day 403, the continuum emission becomes dominated by a blackbody spectrum with a temperature of ~1900 K, suggestive of dust emission.Comment: 17 pages, 18 figure

Inexpensive and Portable System for Dexterous High-Density Myoelectric Control of Multiarticulate Prostheses

Multiarticulate bionic arms are now capable of mimicking the endogenous movements of the human hand. 3D-printing has reduced the cost of prosthetic hands themselves, but there is currently no low-cost alternative to dexterous electromyographic (EMG) control systems. To address this need, we developed an inexpensive (~$675) and portable EMG control system by integrating low-cost microcontrollers with an EMG acquisition device. We validated signal acquisition by comparing the signal-to-noise ratio (SNR) of our system with that of a high-end research-grade system. We also demonstrate the ability to use the low-cost control system for proportional and independent control of various prosthetic hands in real-time. We found that the SNR of the low-cost control system was statistically no worse than 44% of the SNR of a research-grade control system. The RMSEs of predicted hand movements (from a modified Kalman filter) were typically a few percent better than, and not more than 6% worse than, RMSEs of a research-grade system for up to six degrees of freedom when only relatively few (six) EMG electrodes were used. However, RMSEs were generally higher than RMSEs of research-grade systems that utilize considerably more (32) EMG electrodes, guiding future work towards increasing electrode count. Successful instantiation of this low-cost control system constitutes an important step towards the commercialization and wide-spread availability of dexterous bionic hands.Comment: IEEE EMBC 202

The Weiss conjecture and weak norms

In this note we show that for analytic semigroups the so-called Weiss condition of uniform boundedness of the operators Re(\lambda)^\einhalb C(\lambda+A)^{-1}, \qquad Re(\lambda)>0 on the complex right half plane and weak Lebesgue $L^{2,\infty}$--admissibility are equivalent. Moreover, we show that the weak Lebesgue norm is best possible in the sense that it is the endpoint for the 'Weiss conjecture' within the scale of Lorentz spaces $L^{p,q}$