The use of manipulatives and education materials to teach young children about science and conservation

The purpose of this project is a preliminary evaluation of the usage and the effectiveness of the Splash Zone Family Kit to help instill a love of the ocean. The kit consists educational materials given to families of Monterey and Santa Cruz Head Start communities. The materials are used not only in the school center but also at the Monterey Bay Aquarium which the families visit. The redundancy of the materials in different settings is implied as an important component to instilling a love of a nature and an eventual conservation ethic. This project studied the impact, use and conversations around these materials

On the Relationship between the One-Corner Problem and the M−M-Corner Problem for the Vortex Filament Equation

In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a regular M-corner polygon as initial datum can be explained at infinitesimal times as the superposition of M one-corner initial data. This fact is mainly sustained with the calculation of the speed of the center of mass; in particular, we show that several conjectures made at the numerical level are in agreement with the theoretical expectations. Moreover, due to the spatial periodicity, the evolution of VFE at later times can be understood as the nonlinear interaction of infinitely many filaments, one for each corner; and this interaction turns out to be some kind of nonlinear Talbot effect. We also give very strong numerical evidence of the transfer of energy and linear momentum for the M-corner case; and the numerical experiments carried out provide new arguments that support the multifractal character of the trajectory defined by one of the corners of the initial polygon

The Vortex Filament Equation as a Pseudorandom Generator

In this paper, we consider the evolution of the so-called vortex filament equation (VFE), $$X_t = X_s \wedge X_{ss},$$ taking a planar regular polygon of M sides as initial datum. We study VFE from a completely novel point of view: that of an evolution equation which yields a very good generator of pseudorandom numbers in a completely natural way. This essential randomness of VFE is in agreement with the randomness of the physical phenomena upon which it is based

Vortex filament equation for a regular polygon

In this paper, we study the evolution of the vortex filament equation,$$X_t = X_s \wedge X_{ss},$$with $X(s, 0)$ being a regular planar polygon. Using algebraic techniques, supported by full numerical simulations, we give strong evidence that $X(s, t)$ is also a polygon at any rational time; moreover, it can be fully characterized, up to a rigid movement, by a generalized quadratic Gau$\beta$ sum. We also study the fractal behaviour of $X(0, t)$, relating it with the so-called Riemann's non-differentiable function, that was proved by Jaffard to be a multifractal

Vortex Filament Equation for a regular polygon in the hyperbolic plane

The aim of this article is twofold. First, we show the evolution of the vortex filament equation (VFE) for a regular planar polygon in the hyperbolic space. Unlike in the Euclidean space, the planar polygon is open and both of its ends grow exponentially, which makes the problem more challenging from a numerical point of view. However, with fixed boundary conditions, a finite difference scheme and a fourth-order Runge--Kutta method in time, we show that the numerical solution is in complete agreement with the one obtained from algebraic techniques. Second, as in the Euclidean case, we claim that, at infinitesimal times, the evolution of VFE for a planar polygon as the initial datum can be described as a superposition of several one-corner initial data. As a consequence, not only can we compute the speed of the center of mass of the planar polygon, but the relationship also allows us to compare the time evolution of any of its corners with that in the Euclidean case

On the Evolution of the Vortex Filament Equation for regular M-polygons with nonzero torsion

In this paper, we consider the evolution of the Vortex Filament equa- tion (VFE): Xt = Xs ∧ Xss, taking M-sided regular polygons with nonzero torsion as initial data. Us- ing algebraic techniques, backed by numerical simulations, we show that the solutions are polygons at rational times, as in the zero-torsion case. However, unlike in that case, the evolution is not periodic in time; more- over, the multifractal trajectory of the point X(0,t) is not planar, and appears to be a helix for large times. These new solutions of VFE can be used to illustrate numerically that the smooth solutions of VFE given by helices and straight lines share the same instability as the one already established for circles. This is accomplished by showing the existence of variants of the so-called Rie- mann’s non-differentiable function that are as close to smooth curves as desired, when measured in the right topology. This topology is motivated by some recent results on the well-posedness of VFE, which prove that the selfsimilar solutions of VFE have finite renormalized energy

Numerical approximation of the fractional Laplacian on R using orthogonal families

In this paper, using well-known complex variable techniques, we compute explicitly, in terms of the F12 Gaussian hypergeometric function, the one-dimensional fractional Laplacian of the complex Higgins functions, the complex Christov functions, and their sine-like and cosine-like versions. Then, after studying the asymptotic behavior of the resulting expressions, we discuss the numerical difficulties in their implementation, and develop a method using arbitrary-precision arithmetic that computes them accurately. We also explain how to create the differentiation matrices associated to the complex Higgins functions and to the complex Christov functions, and study their condition numbers. In this regard, we show how arbitrary-precision arithmetic is the natural tool to deal with ill-conditioned systems. Finally, we simulate numerically the fractional nonlinear Schrödinger equation using the developed tools

A pseudospectral method for the one-dimensional fractional Laplacian on R

In this paper, we propose a novel pseudospectral method to approximate accurately and efficiently the fractional Laplacian without using truncation. More precisely, given a bounded regular function defined over R, we map the unbounded domain into a finite one, and represent the resulting function as a trigonometric series. Therefore, the central point of this paper is the computation of the fractional Laplacian of an elementary trigonometric function. As an application of the method, we also do the simulation of Fisher's equation with fractional Laplacian in the monostable case

Uncovering the Cultural Narratives and Environmental Identities of Latina/o Environmental Professionals and Beyond

The environmental movement needs people from communities of color and the differing perspectives they provide. Latinas/os are one of the largest communities of color in the US, and their numbers continue to grow. However, mainstream environmental organizations have failed to engage this community in authentic ways. The lack of meaningful opportunities for activation of existing resources for Latina/o environmental identity, specifically Latina/o values and perspectives, may be the reason why this has not happened. This research project incorporates three elements reported in three manuscripts: 1) a critical review of the last decade of research (N=39) that brings together into one publication what is known about Latina/o environmental identity in both the peer review and "gray" literature of polling. A LatCrit theoretical framework shapes that review and serves to identify key constructs necessary for any analysis of Latina/o environmental identities, specifically the constructs of intersectionality, multidisciplinarity, and interdisciplinarity. 2) Biographical interviews (N=28) employing a visible thinking routine -- concept mapping -- explores firsthand the environmental identity and environmental values of Latina/o environmental professionals from around the US focusing specifically on the significant life events these professionals include in their narratives. The narratives of Latina/o environmental professionals are explored in light of similarities and differences with the "master narratives" of mainstream environmentalism in the US. Two themes that emerged from the narratives that are not traditionally part of the narratives of mainstream environmental professionals were the values of familismo and conscientização. Finally, 3) a widely used existing instrument, the Environmental Identity scale (EID), was modified to include questions about significant themes that emerged from the interviews and literature review. This expanded instrument was administered to Latinas/os living in the Pacific Northwest (N= 149) and the results are analyzed in light of whether the EID in its current or expanded form can be a useful tool for documenting the experience of Latinas/os in the US. In order to authentically engage the Latina/o community and thus to remain relevant, the mainstream environmental movement must acknowledge how different Latina/o identities intersect with structures of privilege in the US and provide proenvironmental behaviors that affirm these identities

Global compliance with hepatitis b vaccine birth dose and factors related to timely schedule. A literature review

Objectives: Identify global barriers for delivery of hepatitis B vaccine birth dose. Methods: A search for cross sectional studies published between January 2001 and December 2017 was conducted using the following Mesh terms: "Vaccination"[Mesh], "Mass Vaccination"[Mesh], "Hepatitis B"[Mesh], "Hepatitis B virus"[Mesh], "Hepatitis B Surface Antigens"[Mesh]. Databases consulted included: PUBMED, SCIELO, EMBASE and BIREME. To evaluate the quality of studies, we used an adapted version of the Newcastle-Ottawa Quality Assessment Scale for cross sectional studies. Results: An initial list of 6,789 articles were generated by the combination of search terms. After reviewing titles and abstracts, they were reduced to 134 for full reading, and 22 studies were included in the barriers analysis. The region with more references was Western Pacific while eastern Mediterranean had the lowest. Being born outside of a health facility and weakness of outreach vaccination service seems to be the most important an cited factors related to underperformance of birth dose delivery. In developed countries, hospital policies on birth dose vaccination was the main factor associated to no vaccintion with the birth dose. Conclusions: New ways to deliver hepatitis B vaccines to neonates being born at home or outside health facilities should be envisaged and applied, if the goal of eliminating perinatal transmission of hepatitis B is to be achieved