Mean values of Dirichlet polynomials and applications to linear equations with prime variables

We prove a new mean-value theorem for Dirichlet polynomials with coefficients given by the von Mangoldt function. We then use our theorem to derive new estimates for certain exponential sums over primes. The latter have applications to additive problems with prime variables. In particular, we are able to improve on a recent result of J.Y. Liu and K.M. Tsang on the size of the solutions of linear equations with prime variables

GECKA3D: A 3D Game Engine for Commonsense Knowledge Acquisition

Commonsense knowledge representation and reasoning is key for tasks such as artificial intelligence and natural language understanding. Since commonsense consists of information that humans take for granted, gathering it is an extremely difficult task. In this paper, we introduce a novel 3D game engine for commonsense knowledge acquisition (GECKA3D) which aims to collect commonsense from game designers through the development of serious games. GECKA3D integrates the potential of serious games and games with a purpose. This provides a platform for the acquisition of re-usable and multi-purpose knowledge, and also enables the development of games that can provide entertainment value and teach players something meaningful about the actual world they live in

Nonlinear Preconditioning: How to use a Nonlinear Schwarz Method to Precondition Newton's Method

For linear problems, domain decomposition methods can be used directly as iterative solvers, but also as preconditioners for Krylov methods. In practice, Krylov acceleration is almost always used, since the Krylov method finds a much better residual polynomial than the stationary iteration, and thus converges much faster. We show in this paper that also for non-linear problems, domain decomposition methods can either be used directly as iterative solvers, or one can use them as preconditioners for Newton's method. For the concrete case of the parallel Schwarz method, we show that we obtain a preconditioner we call RASPEN (Restricted Additive Schwarz Preconditioned Exact Newton) which is similar to ASPIN (Additive Schwarz Preconditioned Inexact Newton), but with all components directly defined by the iterative method. This has the advantage that RASPEN already converges when used as an iterative solver, in contrast to ASPIN, and we thus get a substantially better preconditioner for Newton's method. The iterative construction also allows us to naturally define a coarse correction using the multigrid full approximation scheme, which leads to a convergent two level non-linear iterative domain decomposition method and a two level RASPEN non-linear preconditioner. We illustrate our findings with numerical results on the Forchheimer equation and a non-linear diffusion problem

A Molecular Line Survey of the Carbon-Rich Proto-Planetary Nebula AFGL 2688 in the 3mm and 1.3mm Windows

We present a spectral line survey of the proto-planetary nebula AFGL 2688 in the frequency ranges of 71-111 GHz, 157-160 GHz, and 218-267 GHz using the Arizona Radio Observatory 12m telescope and the Heinrich Hertz Submillimeter Telescope. A total of 143 individual spectral features associated with 32 different molecular species and isotopologues were identified. The molecules C3H, CH3CN, H2CO, H2CS, and HCO+ were detected for the first time in this object. By comparing the integrated line strengths of different transitions, we are able to determine the rotation temperatures, column densities, and fractional abundances of the detected molecules. The C, O, and N isotopic ratios in AFGL 2688 are compared with those in IRC+10216 and the Sun, and were found to be consistent with stellar nucleosynthesis theory. Through comparisons of molecular line strengths in asymptotic giant branch stars, proto-planetary nebulae, and planetary nebulae, we discuss the evolution in circumstellar chemistry in the late stages of evolution.Comment: 41 pages, 10 figures. Accepted for publication in Ap

The Transformation in Who is Expected to Work in the United States and How it Changed the Lives of Single Mothers and People with Disabilities

In the 1990s, social expectations of single mothers shifted towards the notion that most should, could, and would work, if given the proper incentives. This shift in expectations culminated in the passage of the Personal Responsibility and Work Opportunity Reconciliation Act in 1996, commonly known as welfare reform. As a result, ADFC/TANF caseloads fell along with cash transfers to single mothers who did not work. A decade later the earnings and household income of single mothers are significantly higher and moving more in synch with the U.S. economy. In stark contrast and despite espoused goals to the contrary, public policies toward working age men and women with disabilities have remained imbued with the notion that most cannot and thus, would not work, no matter what incentives they faced. As a result, SSDI/SSI expenditures and caseloads have increased and the earnings and household income of working age men and women with disabilities have fallen, leaving them even further behind the average working age American than they were a decade ago. Using data from the Current Population Survey we follow the economic well-being and employment of single mothers and working age men and women with disabilities over the past two major United States business cycles (1982-1993 and 1993-2004) and show that despite the dramatic decline in AFDC/TANF funding, single mothers’ economic well-being, labor earnings and employment all have risen substantially. In contrast, despite the dramatic increase in SSDI/SSI funding, the economic wellbeing of working age men and women with disabilities remained stagnant, as their labor earnings and employment plummeted.

Application of theoretical models to active and passive remote sensing of saline ice

The random medium model is used to interpret the polarimetric active and passive measurements of saline ice. The ice layer is described as a host ice medium embedded with randomly distributed inhomogeneities, and the underlying sea water is considered as a homogeneous half-space. The scatterers in the ice layer are modeled with an ellipsoidal correlation function. The orientation of the scatterers is vertically aligned and azimuthally random. The strong permittivity fluctuation theory is employed to calculate the effective permittivity and the distorted Born approximation is used to obtain the polarimetric scattering coefficients. We also calculate the thermal emissions based on the reciprocity and energy conservation principles. The effects of the random roughness at the air-ice, and ice-water interfaces are accounted for by adding the surface scattering to the volume scattering return incoherently. The above theoretical model, which has been successfully applied to analyze the radar backscatter data of the first-year sea ice near Point Barrow, AK, is used to interpret the measurements performed in the CRRELEX program