Minimum Forcing Sets for Miura Folding Patterns

We introduce the study of forcing sets in mathematical origami. The origami material folds flat along straight line segments called creases, each of which is assigned a folding direction of mountain or valley. A subset $F$ of creases is forcing if the global folding mountain/valley assignment can be deduced from its restriction to $F$. In this paper we focus on one particular class of foldable patterns called Miura-ori, which divide the plane into congruent parallelograms using horizontal lines and zig-zag vertical lines. We develop efficient algorithms for constructing a minimum forcing set of a Miura-ori map, and for deciding whether a given set of creases is forcing or not. We also provide tight bounds on the size of a forcing set, establishing that the standard mountain-valley assignment for the Miura-ori is the one that requires the most creases in its forcing sets. Additionally, given a partial mountain/valley assignment to a subset of creases of a Miura-ori map, we determine whether the assignment domain can be extended to a locally flat-foldable pattern on all the creases. At the heart of our results is a novel correspondence between flat-foldable Miura-ori maps and $3$-colorings of grid graphs.Comment: 20 pages, 16 figures. To appear at the ACM/SIAM Symp. on Discrete Algorithms (SODA 2015

Assessment of Unabated Facility Emission Potentials for Evaluating Airborne Radionuclide Monitoring Requirements at Pacific Northwest National Laboratory - 2007

Assessments were performed to evaluate compliance with the airborne radionuclide emission monitoring requirements in the National Emission Standards for Hazardous Air Pollutants (NESHAP – U.S. Code of Federal Regulations, Title 40, Part 61, Subpart H) and Washington Administrative Code (WAC) 246-247: Radiation Protection – Air Emissions. In these NESHAP assessments, potential unabated offsite doses were evaluated for emission locations at buildings that are part of the consolidated laboratory campus of the Pacific Northwest National Laboratory. This report describes the inventory-based methods and provides the results for the NESHAP assessment performed in 2007

Pacific Northwest National Laboratory Site Environmental Report for Calendar Year 2011

The PNNL Site Environmental Report for Calendar Year 2011 was prepared pursuant to the requirements of Department of Energy (DOE) Order 231.1B, "Environment, Safety and Health Reporting" to provide a synopsis of calendar year 2011 information related to environmental management performance and compliance efforts. It summarizes site compliance with federal, state, and local environmental laws, regulations, policies, directives, permits, and orders and environmental management performance

Every Large Point Set contains Many Collinear Points or an Empty Pentagon

We prove the following generalised empty pentagon theorem: for every integer $\ell \geq 2$, every sufficiently large set of points in the plane contains $\ell$ collinear points or an empty pentagon. As an application, we settle the next open case of the "big line or big clique" conjecture of K\'ara, P\'or, and Wood [\emph{Discrete Comput. Geom.} 34(3):497--506, 2005]

Pacific Northwest National Laboratory Facility Radionuclide Emission Points and Sampling Systems

Battelle—Pacific Northwest Division operates numerous research and development laboratories in Richland, Washington, including those associated with the Pacific Northwest National Laboratory (PNNL) on the Department of Energy’s Hanford Site that have the potential for radionuclide air emissions. The National Emission Standard for Hazardous Air Pollutants (NESHAP 40 CFR 61, Subparts H and I) requires an assessment of all effluent release points that have the potential for radionuclide emissions. Potential emissions are assessed annually. Sampling, monitoring, and other regulatory compliance requirements are designated based upon the potential-to-emit dose criteria found in the regulations. The purpose of this document is to describe the facility radionuclide air emission sampling program and provide current and historical facility emission point system performance, operation, and design information. A description of the buildings, exhaust points, control technologies, and sample extraction details is provided for each registered or deregistered facility emission point. Additionally, applicable stack sampler configuration drawings, figures, and photographs are provided

Vertex Pops and Popturns

This paper considers transformations of a planar polygon P according to two types of operations. A vertex pop (or a pop) reflects a vertex vi, i ∈ {1,..., n}, across the line through the two adjacent vertices vi−1 and vi+

Unfolding and Dissection of Multiple Cubes, Tetrahedra, and Doubly Covered Squares

In this paper, we introduce the notion of “rep-cube”: a net of a cube that can be divided into multiple polygons, each of which can be folded into a cube. This notion is inspired by the notion of polyomino and rep-tile; both are introduced by Solomon W. Golomb, and well investigated in the recreational mathematics society. We prove that there are infinitely many distinct rep-cubes. We also extend this notion to doubly covered squares and regular tetrahedra

Toward Unfolding Doubly Covered nn-Stars

info:eu-repo/semantics/publishe