Topics in harmonic analysis and partial differential equations: extension theorems and geometric maximum principles

Title from PDF of title page (University of Missouri--Columbia, viewed on May 13, 2013).The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.Thesis advisor: Dr. Marius MitreaIncludes bibliographical references.Vita.M.A. University of Missouri--Columbia 2011.Dissertations, Academic -- University of Missouri--Columbia -- Mathematics."May 2011"The present thesis consists of two main parts. In the first part, we prove that a function defined on a closed subset of a geometrically doubling quasi-metric space which satisfies a Hölder-type condition may be extended to the entire space with preservation of regularity. The proof proceeds along the lines of the original work of Whitney in 1934 and yields a linear extension operator. A similar extension result is also proved in the absence of the geometrically doubling hypothesis, albeit the resulting extension procedure is nonlinear in this case. The results presented in this part are based upon work done in collaboration M. Mitrea. In the second part of the thesis we prove that an open, proper, nonempty subset of ℝn is a locally Lyapunov domain if and only if it satisfies a uniform hour-glass condition. The latter is a property of a purely geometrical nature, which amounts to the ability of threading the boundary, at any location, in between the two rounded components of a certain fixed region, whose shape resembles that of an ordinary hour-glass, suitably re-positioned. The limiting cases of the result are as follows: Lipschitz domains may be characterized by a uniform double cone condition, whereas domains of class ℂ1,1 may be characterized by a uniform two-sided ball condition. Additionally, we discuss a sharp generalization of the Hopf-Oleinik boundary point principle for domains satisfying a one-sided, interior pseudo-ball condition, for semi-elliptic operators with singular drift. This, in turn, is used to obtain a sharp version of Hopf's Strong Maximum Principle for second-order, non-divergence form differential operators with singular drift. This part of my thesis originates from a recent paper in collaboration with D. Brigham, V. Maz'ya, M. Mitrea, and E. Ziad e

Privacy and Cloud Computing in Public Schools

Today, data driven decision-making is at the center of educational policy debates in the United States. School districts are increasingly turning to rapidly evolving technologies and cloud computing to satisfy their educational objectives and take advantage of new opportunities for cost savings, flexibility, and always-available service among others. As public schools in the United States rapidly adopt cloud-computing services, and consequently transfer increasing quantities of student information to third-party providers, privacy issues become more salient and contentious. The protection of student privacy in the context of cloud computing is generally unknown both to the public and to policy-makers. This study thus focuses on K-12 public education and examines how school districts address privacy when they transfer student information to cloud computing service providers. The goals of the study are threefold: first, to provide a national picture of cloud computing in public schools; second, to assess how public schools address their statutory obligations as well as generally accepted privacy principles in their cloud service agreements; and, third, to make recommendations based on the findings to improve the protection of student privacy in the context of cloud computing. Fordham CLIP selected a national sample of school districts including large, medium and small school systems from every geographic region of the country. Using state open public record laws, Fordham CLIP requested from each selected district all of the district’s cloud service agreements, notices to parents, and computer use policies for teachers. All of the materials were then coded against a checklist of legal obligations and privacy norms. The purpose for this coding was to enable a general assessment and was not designed to provide a compliance audit of any school district nor of any particular vendor.https://ir.lawnet.fordham.edu/clip/1001/thumbnail.jp

Privacy and Cloud Computing in Public Schools

Today, data driven decision-making is at the center of educational policy debates in the United States. School districts are increasingly turning to rapidly evolving technologies and cloud computing to satisfy their educational objectives and take advantage of new opportunities for cost savings, flexibility, and always-available service among others. As public schools in the United States rapidly adopt cloud-computing services, and consequently transfer increasing quantities of student information to third-party providers, privacy issues become more salient and contentious. The protection of student privacy in the context of cloud computing is generally unknown both to the public and to policy-makers. This study thus focuses on K-12 public education and examines how school districts address privacy when they transfer student information to cloud computing service providers. The goals of the study are threefold: first, to provide a national picture of cloud computing in public schools; second, to assess how public schools address their statutory obligations as well as generally accepted privacy principles in their cloud service agreements; and, third, to make recommendations based on the findings to improve the protection of student privacy in the context of cloud computing. Fordham CLIP selected a national sample of school districts including large, medium and small school systems from every geographic region of the country. Using state open public record laws, Fordham CLIP requested from each selected district all of the district’s cloud service agreements, notices to parents, and computer use policies for teachers. All of the materials were then coded against a checklist of legal obligations and privacy norms. The purpose for this coding was to enable a general assessment and was not designed to provide a compliance audit of any school district nor of any particular vendor.https://ir.lawnet.fordham.edu/clip/1001/thumbnail.jp

Privacy and Cloud Computing in Public Schools

Today, data driven decision-making is at the center of educational policy debates in the United States. School districts are increasingly turning to rapidly evolving technologies and cloud computing to satisfy their educational objectives and take advantage of new opportunities for cost savings, flexibility, and always-available service among others. As public schools in the United States rapidly adopt cloud-computing services, and consequently transfer increasing quantities of student information to third-party providers, privacy issues become more salient and contentious. The protection of student privacy in the context of cloud computing is generally unknown both to the public and to policy-makers. This study thus focuses on K-12 public education and examines how school districts address privacy when they transfer student information to cloud computing service providers. The goals of the study are threefold: first, to provide a national picture of cloud computing in public schools; second, to assess how public schools address their statutory obligations as well as generally accepted privacy principles in their cloud service agreements; and, third, to make recommendations based on the findings to improve the protection of student privacy in the context of cloud computing. Fordham CLIP selected a national sample of school districts including large, medium and small school systems from every geographic region of the country. Using state open public record laws, Fordham CLIP requested from each selected district all of the district’s cloud service agreements, notices to parents, and computer use policies for teachers. All of the materials were then coded against a checklist of legal obligations and privacy norms. The purpose for this coding was to enable a general assessment and was not designed to provide a compliance audit of any school district nor of any particular vendor.https://ir.lawnet.fordham.edu/clip/1001/thumbnail.jp

Shear wave velocities in the Pampean flat-slab region from Rayleigh wave tomography: Implications for slab and upper mantle hydration

The Pampean flat-slab region, located in central Argentina and Chile between 29° and 34°S, is considered a modern analog for Laramide flat-slab subduction within western North America. Regionally, flat-slab subduction is characterized by the Nazca slab descending to ∼100 km depth, flattening out for ∼300 km laterally before resuming a more “normal” angle of subduction. Flat-slab subduction correlates spatially with the track of the Juan Fernandez Ridge, and is associated with the inboard migration of deformation and the cessation of volcanism within the region. To better understand flat-slab subduction we combine ambient-noise tomography and earthquake-generated surface wave measurements to calculate a regional 3D shear velocity model for the region. Shear wave velocity variations largely relate to changes in lithology within the crust, with basins and bedrock exposures clearly defined as low- and high-velocity regions, respectively. We argue that subduction-related hydration plays a significant role in controlling shear wave velocities within the upper mantle. In the southern part of the study area, where normal-angle subduction is occurring, the slab is visible as a high-velocity body with a low-velocity mantle wedge above it, extending eastward from the active arc. Where flat-slab subduction is occurring, slab velocities increase to the east while velocities in the overlying lithosphere decrease, consistent with the slab dewatering and gradually hydrating the overlying mantle. The hydration of the slab may be contributing to the excess buoyancy of the subducting oceanic lithosphere, helping to drive flat-slab subduction

Detección y extracción de muestras falladas usando visión artificial y un brazo robótico

Se realizó un trabajo de investigación con la finalidad de detectar y extraer muestras fallidas usando visión artificial y un brazo robótico con el supuesto que dicha actividad logre una disminución de los costos y mejora en la optimización de procesos en el control de la calidad, mediante el reconocimiento de patrones RGB. El estudio tuvo carácter experimental y analítico. En el desarrollo del procesamiento se hizo uso del algoritmo matemático CBIR y la teoría RGB. El prototipo trabaja con un total de 6 tipos de imágenes, se realizaron 10 pruebas por imagen. El brazo robótico se tardó en promedio 0,33 segundos, para la identificación del error, mientras que el ojo humano promedio se tardó 17 segundos. También se corroboro lo que distintos autores como Sandoval, Silva. L. han realizado y recomendado en investigaciones similares; sin embargo, algo que no se ha podido concluir satisfactoriamente en las otras investigaciones es la variación de los colores, lo cual se mejoró en nuestro proyecto haciendo uso del teorema RGB. Asimismo, se utilizó un identificador bayesiano, como herramienta estadística para identificar características discriminantes con un error porcentual menor a 5%. Se determinó que el proyecto trabaja de manera óptima logrando una certeza de 97,5% en el primer nivel, de 96,41% en el segundo nivel y de 95,35% en el tercer nivel