Laplace operators with eigenfunctions whose nodal set is a knot

We prove that, given any knot $\gamma$ in a compact 3-manifold M, there exists a Riemannian metric on M such that there is a complex-valued eigenfunction u of the Laplacian, corresponding to the first nontrivial eigenvalue, whose nodal set $u^{-1}(0)$ has a connected component given by $\gamma$. Higher dimensional analogs of this result will also be considered.Comment: 16 page

Dislocations of arbitrary topology in Coulomb eigenfunctions

For any finite link $L$ in $\mathbb{R}^3$ we prove the existence of a high-energy complex-valued eigenfunction of the hydrogen atom such that its nodal set contains a union of connected components diffeomorphic to $L$. This problem goes back to Berry, who constructed such eigenfunctions in the case where $L$ is the trefoil knot or the Hopf link and asked the question about the general result.Comment: 10 page

Development of a non-linear simulation for generic hypersonic vehicles - ASUHS1

A nonlinear simulation is developed to model the longitudinal motion of a vehicle in hypersonic flight. The equations of motion pertinent to this study are presented. Analytic expressions for the aerodynamic forces acting on a hypersonic vehicle which were obtained from Newtonian Impact Theory are further developed. The control surface forces are further examined to incorporate vehicle elastic motion. The purpose is to establish feasible equations of motion which combine rigid body, elastic, and aeropropulsive dynamics for use in nonlinear simulations. The software package SIMULINK is used to implement the simulation. Also discussed are issues needing additional attention and potential problems associated with the implementation (with proposed solutions)

Behavioral risk profiles of homeschooled adolescents in the United States: a nationally representative examination of substance use related outcomes

BACKGROUND: The homeschool population continues to grow in size and now accounts for 3.4% of all students in the United States. OBJECTIVE: Given the heterogeneous nature of the population, this study examines the relationship between different types of homeschoolers and a number of substance use related outcomes. METHODS: To conduct this study, we used pooled data (2002–2013) from the National Survey on Drug Use and Health (NSDUH). Respondents aged 12–17 who reported they had been homeschooled at any time during the previous 12 months were classified as homeschoolers (N = 1,321). Latent profile analysis (LPA) was conducted to identify latent subgroups of homeschoolers and multinomial regression was executed to assess the relationship between the subgroups and perceived substance use risk, availability, and past 12-month use. RESULTS: The LPA yielded four subgroups, which were summarized as (1) highly religious and engaged, (2) limited parental monitoring, (3) high parental warmth and support, and (4) secular permissive. Of these, the highly religious and engaged subgroup was the least likely to report using substances. CONCLUSION: The results underscore the variation that exists among homeschoolers and the importance of examining the relationship between different types of homeschoolers and outcomes of interest

Continuously Stratified Flow Dynamics Over a Hollow

Acoustic Doppler current profiles (ADCP) and density profiles were measured over three lower Chesapeake Bay bathymetric depressions (hollows) in order to determine the effects of a hollow on a continuously stratified flow. Measurements showed an acceleration of the near-bottom flow as it moved toward the deepest part of the hollows, in contrast to the deceleration expected from two-dimensional Bernoulli-type dynamics. The acceleration was attributed to lateral water intrusions that were most apparent during floods. The presence of lateral water intrusions was corroborated by observations in a transverse section that crossed the deepest part of the hollows. The observed deceleration of the along-hollow flow as it moved toward decreasing bathymetry was attributed to lateral flows toward the shoals. The current acceleration toward the deepest part of the hollows during flood, favored by vertical and lateral water intrusions, was deflected toward the right (looking landward) owing to Coriolis accelerations. In general during ebb and flood, the dynamics over the hollows could be explained with three-dimensional Bernoulli-type dynamics modified by Coriolis acceleration. At only one of the hollows, Cape Charles hollow, the sampling strategy allowed resolution of internal lee waves with periodicities of 1.42 h during flood and ebb tide periods. These internal waves were produced by the interaction of the sloping pycnocline and tidal currents. The formation of internal waves over the leeward side favored the development of vertical shear in the horizontal velocity. Large vertical shears enhanced turbulence and internal waves should have increased form drag resulting in locations in the water column of weakest along-hollow velocities. The phase of the semidiurnal tidal currents increased monotonically from the depth equivalent to the maximum depth of the shoals surrounding the hollow toward the bottom and surface, in contrast to the expected increment from bottom to surface over an estuary influenced by bottom friction

Gases

Unidad 21 de la serie Ciencias para la metalmecánica en la que se describen las características y propiedades de los gases, así como sus aplicaciones y usos en soldadura.Unit 21 of the Science series for metalworking in which the characteristics and properties of gases are described, as well as their applications and uses in welding.Introducción -- Objetivo terminal -- Gases -- Oxigeno -- Acetileno -- Propanona19 página

Hearing the Community: Evolution of a Nutrition and Physical Activity Program for African American Women to Improve Weight

Listening to the needs of the community is an important step toward reducing health disparities. Researchers may need to adjust their methods to maximize participation and benefit to the community. This report describes how the project team adjusted its approach to a weight loss intervention to support a community of African American women seeking to improve their health

Extensive Sensitivity Analysis and Parallel Stochastic Global Optimization Using Radial Basis Functions of Integrated Biorefineries under Operational Level Uncertainties

This work presents a decision-making framework for global optimization of detailed renewable energy processes considering technological uncertainty. The critical uncertain sources are identified with an efficient computational method for global sensitivity analysis, and are obtained in two different ways, simultaneously and independently per product pathway respect to the objective function. For global optimization, the parallel stochastic response surface method developed by Regis & Shoemaker (2009) is employed. This algorithm is based on the multi-start local metric stochastic response surface method explored by the same authors (2007a). The aforementioned algorithm uses as response surface model a radial basis function (RBF) for approximating the expensive simulation model. Once the RBF’s parameters are fitted, the algorithm selects multiple points to be evaluated simultaneously. The next point(s) to be evaluated in the expensive simulation are obtained based on their probability to attain a better result for the objective function. This approach represents a simplified oriented search. To evaluate the efficacy of this novel decision-making framework, a hypothetical multiproduct lignocellulosic biorefinery is globally optimized on its operational level. The obtained optimal points are compared with traditional optimization methods, e.g. Monte-Carlo simulation, and are evaluated for both proposed types of uncertainty calculated

Military service and crime: new evidence

BACKGROUND: Evidence indicates that a substantial proportion of military personnel are involved in high-risk and antisocial behaviors that place them at jeopardy for criminal justice system involvement. However, prior research on military service and crime has disproportionately focused on veterans from the Vietnam War era (1955–1975), and has tended to focus on either current or former military members. METHODS: This study employed data from a population-based study (i.e., National Study on Drug Use and Health [NSDUH] between 2002 and 2014). It systematically examines the prevalence of self-reported antisocial behaviors, criminal justice system involvement, and substance abuse among the US civilian population and military service members, including reservists (n = 2206) and those who reported having been separated or retired from military service (n = 20,551). These factors are further examined across the developmental spectrum of adulthood (ages 18–34, 35–49, and 50–64). RESULTS: Results showed that military members were more prone to lifetime arrests and overall substance misuse. However, additional findings emerged suggesting that, while the military population overall seems to be positively associated with higher criminal activity than that found in the civilian population, these findings were based on a specific subgroup of the veteran population. This subgroup is comprised of individuals who likely did not fit in with the military culture and were discharged from the military early in their careers. CONCLUSION: Additional research on identifying this subgroup of military members is encouraged to better concentrate on prevention and treatment measures