The Enforcement of Ohio's Litter Control Laws

PDF pages: 7

Proceedings Community Leader's Litter Control Workshop

PDF pages: 5

Kernel Approximation on Manifolds I: Bounding the Lebesgue Constant

The purpose of this paper is to establish that for any compact, connected C^{\infty} Riemannian manifold there exists a robust family of kernels of increasing smoothness that are well suited for interpolation. They generate Lagrange functions that are uniformly bounded and decay away from their center at an exponential rate. An immediate corollary is that the corresponding Lebesgue constant will be uniformly bounded with a constant whose only dependence on the set of data sites is reflected in the mesh ratio, which measures the uniformity of the data. The analysis needed for these results was inspired by some fundamental work of Matveev where the Sobolev decay of Lagrange functions associated with certain kernels on \Omega \subset R^d was obtained. With a bit more work, one establishes the following: Lebesgue constants associated with surface splines and Sobolev splines are uniformly bounded on R^d provided the data sites \Xi are quasi-uniformly distributed. The non-Euclidean case is more involved as the geometry of the underlying surface comes into play. In addition to establishing bounded Lebesgue constants in this setting, a "zeros lemma" for compact Riemannian manifolds is established.Comment: 33 pages, 2 figures, new title, accepted for publication in SIAM J. on Math. Ana

Hypervelocity scramjet combustor-nozzle analysis and design

The progress report for the grant entitled 'Hypervelocity of Scramjet Combustor-Nozzle Analysis and Design' is presented. The three main tasks in the program are combustor modeling study, development of anaylsis capabilities for hypersonic scramjet nozzles, and development of optimum design methods for hypersonic scramjet nozzles. The research performed was documented in a series of technical publications and presentations at various conferences. A brief description of the research in each of the above three areas and a list of the resulting technical publications are included

Observations on North Dakota Sponges (Haplosclerina: Spongillidae) and Sisyrids (Neuroptera: Sisyridae)

Factors influencing occurrence, distribution, and ecology of sponges and sisyrids are discussed, with emphasis on northeastern North Dakota. New state records for North Dakota sponges, Eunapius Jraguis Leidy and Ephydatia fluviatilis L. and the sisyrids, Sisyra vicaria (Hagen) and Climacia areolaris (Hagen), and new county records for C. areolaris in northwestern Minnesota and Eunapius fragilis in northeastern North Dakota are reported. A rare association of the parasite, S. vicaria with the host, Ephydatia fluviatilis is also reported. Some physicochcmical relations of Eunapius fragilis found in the Forest River, North Dakota, are discussed

Kinematic structure for robust mechanical architectures in robotic planetary exploration

This paper describes new research into the kinematic structure of autonomous robotic systems, and into the associated design processes. The approach aims to develop novel insights and applicable tools and techniques for designing advanced mechanical architectures for planetary exploration systems. These should provide enhanced functionality for tackling complex autonomous operations, and improved levels of robustness in the face of the inevitable system faults

Discreteness and the transmission of light from distant sources

We model the classical transmission of a massless scalar field from a source to a detector on a background causal set. The predictions do not differ significantly from those of the continuum. Thus, introducing an intrinsic inexactitude to lengths and durations - or more specifically, replacing the Lorentzian manifold with an underlying discrete structure - need not disrupt the usual dynamics of propagation.Comment: 16 pages, 1 figure. Version 2: reference adde

The Hausdorff dimension of random walks and the correlation length critical exponent in Euclidean field theory

We study the random walk representation of the two-point function in statistical mechanics models near the critical point. Using standard scaling arguments we show that the critical exponent $\nu$ describing the vanishing of the physical mass at the critical point is equal to $\nu_\theta/ d_w$. $d_w$ is the Hausdorff dimension of the walk. $\nu_\theta$ is the exponent describing the vanishing of the energy per unit length of the walk at the critical point. For the case of O(N) models, we show that $\nu_\theta=\varphi$, where $\varphi$ is the crossover exponent known in the context of field theory. This implies that the Hausdorff dimension of the walk is $\varphi/\nu$ for O(N) models.Comment: 11 pages (plain TeX