Manifolds with bounded integral curvature and no positive eigenvalue lower bounds

We provide an explicit construction of a sequence of closed surfaces with uniform bounds on the diameter and on $L^p$ norms of the curvature, but without a positive lower bound on the first non-zero eigenvalue of the Laplacian $\lambda_1$. This example shows that the assumption of smallness of the $L^p$ norm of the curvature is a necessary condition to derive Lichnerowicz and Zhong-Yang type estimates under integral curvature conditions

Computation of surf. mechanics

In differential geometry, surfaces of revolution form a large class of illuminating examples. These surfaces are also useful in applications, where the assumption of rotational symmetry can simplify a modeling problem substantially. Particularly for some problems in biology, one might want to simulate the deformation of such surfaces. One discretized model based on interpolation by linear segments has been presented previously in the literature. We present a new model based on interpolation by arcs of parabolas in a way that properly generalizes the previous approach; a third model which is useful as a benchmark is obtained as a special case. We present the results of the simulation and discuss the models' performance and error properties

E-TRIALS: Developing a Web Application For Educational Research

As online learning becomes more common, significant interest in educational research has grown at WPI and other universities. One platform for online learning, ASSISTments, is unique for its built-in capacity for research. We outline the issues inherent to ASSISTments' randomized controlled trial features, including scattered documentation, opaque features, and a high reliance on human intervention by the ASSISTments research team. Considering these issues, and coupled with a project based on design thinking and user research, we propose a series of remedies for these faults, presenting a design for an E-TRIALS web application that will address them. Development of this newly designed web application has begun and the tool will ultimately replace the existing testbed infrastructure