Shellable weakly compact subsets of C[0,1]C[0,1]

We show that for every weakly compact subset $K$ of $C[0,1]$ with finite Cantor-Bendixson rank, there is a reflexive Banach lattice $E$ and an operator $T:E\rightarrow C[0,1]$ such that $K\subseteq T(B_E)$. On the other hand, we exhibit an example of a weakly compact set of $C[0,1]$ homeomorphic to $\omega^\omega+1$ for which such $T$ and $E$ cannot exist. This answers a question of M. Talagrand in the 80's.Comment: 13 page

Cumulative Risk and a Call for Action in Environmental Justice Communities

Health disparities, social inequalities, and environmental injustice cumulatively affect individual and community vulnerability and overall health; yet health researchers, social scientists and environmental scientists generally study them separately. Cumulative risk assessment in poor, racially segregated, economically isolated and medically underserved communities needs to account for their multiple layers of vulnerability, including greater susceptibility, greater exposure, less preparedness to cope, and less ability to recover in the face of exposure. Recommendations for evidence-based action in environmental justice communities include: reducing pollution in communities of highest burden; building on community resources; redressing inequality when doing community-based research; and creating a screening framework to identify communities of greatest risk

Water splits to degrade two-dimensional group-IV monochalcogenides in nanoseconds

The experimental exfoliation of layered group-IV monochalcogenides --semiconductors isostructural to black phosphorus-- using processes similar to those followed in the production of graphene or phosphorene has turned out unsuccessful thus far, as if the chemical degradation observed in black phosphorus was aggravated in these monochalcogenides. Here, we document a facile dissociation of water by these materials within ten nanoseconds from room-temperature Car-Parrinello molecular dynamics calculations under standard temperature and pressure conditions. These results suggest that humidity must be fully eradicated to exfoliate monolayers successfully, for instance, by placing samples in a hydrophobic solution during mechanical exfoliation. From another materials perspective, these two-dimensional materials that create individual hydrogen ions out of water without illumination may become relevant for applications in hydrogen production and storage.Comment: This document is the Accepted Manuscript version of Published Work that appeared in final form in ACS Central Science, copyright American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work please use the following link: https://pubs.acs.org/doi/10.1021/acscentsci.8b0058

Geodesic Forests in the Last-Passage Percolation

The aim of this article is to study the forest composed by point-to-line geodesics in the last-passage percolation model with exponential weights. We will show that the location of the root can be described in terms of the maxima of a random walk, whose distribution will depend on the geometry of the substrate (line). For flat substrates, we will get power law behaviour of the height function, study its scaling limit, and describe it in terms of variational problems involving the Airy process.Comment: 20 page

Ticket to Work: Choosing the Right Employment Network

The purpose of this guide is to educate New Yorkers with disabilities who have a Ticket to Work from the Social Security Administration on how to secure the services and supports to go to work by choosing an Employment Network

The convex hull of a Banach-Saks set

A subset $A$ of a Banach space is called Banach-Saks when every sequence in $A$ has a Ces{\`a}ro convergent subsequence. Our interest here focusses on the following problem: is the convex hull of a Banach-Saks set again Banach-Saks? By means of a combinatorial argument, we show that in general the answer is negative. However, sufficient conditions are given in order to obtain a positive result.Comment: 29 page

Supplemental Security Income: Calculating the Impact of Earnings on Benefits

The purpose of this guide is to educate New Yorkers with disabilities about the impact of earnings on Supplemental Security Income benefits

Negative results for approximation using single layer and multilayer feedforward neural networks

We prove a negative result for the approximation of functions defined on compact subsets of $\mathbb{R}^d$ (where $d \geq 2$) using feedforward neural networks with one hidden layer and arbitrary continuous activation function. In a nutshell, this result claims the existence of target functions that are as difficult to approximate using these neural networks as one may want. We also demonstrate an analogous result (for general $d \in \mathbb{N}$) for neural networks with an \emph{arbitrary} number of hidden layers, for activation functions that are either rational functions or continuous splines with finitely many pieces.Comment: 12 pages, submitted to a Journa

Dynamic analysis and control PID path of a model type gantry crane

This paper presents an alternate form for the dynamic modelling of a mechanical system that simulates in real life a gantry crane type, using Euler's classical mechanics and Lagrange formalism, which allows find the equations of motion that our model describe. Moreover, it has a basic model design system using the SolidWorks software, based on the material and dimensions of the model provides some physical variables necessary for modelling. In order to verify the theoretical results obtained, a contrast was made between solutions obtained by simulation in SimMechanics-Matlab and Euler-Lagrange equations system, has been solved through Matlab libraries for solving equation's systems of the type and order obtained. The force is determined, but not as exerted by the spring, as this will be the control variable. The objective to bring the mass of the pendulum from one point to another with a specified distance without the oscillation from it, so that, the answer is overdamped. This article includes an analysis of PID control in which the equations of motion of Euler-Lagrange are rewritten in the state space, once there, they were implemented in Simulink to get the natural response of the system to a step input in F and then draw the desired trajectories

Fundamental units of length and time

Ideal rods and clocks are defined as an infinitesimal symmetry of the spacetime. Since no a priori geometric structure is considered, all the possible models of spacetime are obtained.Comment: Part of the results of this article has been announced at the meeting ``XXIV International Workshop on the Fundamental Problems of High Energy Physics and Field Theory'' 27-29 June 2001, Protvino, Russi