Theses & Reports
Contractor, Munir; Pradal, Christophe; Shasha, Dennis
Title: Platform Migrator
Author(s): Contractor, Munir; Pradal, Christophe; Shasha, Dennis
Currently, one of the major problems in software development and maintenance, specially in academia, is managing packages across time and systems. An application developed under a particular package manager using a certain set of packages does not always work reliably when ported to a different system or when abandoned for a period of time and picked up again with newer versions of the packages. In this report, we provide and describe Platform Migrator, a software that makes it easy to test applications across systems by identifying various packages in the base system, figuring out their corresponding equivalents in the new system and testing whether the software works as expected on the new system. Platform migrator can migrate software written and set up inside a conda environment to any Linux based system with conda or some other package manager. The philosophy of platform migrator is to identify a closure of the required dependencies for the software being migrated using the conda environment metadata and then use that closure to install the various dependencies on the target system. This documentation provides comprehensive details on how to use platform migrator and what it does internally to migrate software from one system to another. It also contains tutorials and case studies that can be replicated for better understanding of the process.
On the Solution of Elliptic Partial Differential Equations on Regions with Corners III: Curved Boundaries
Title: On the Solution of Elliptic Partial Differential Equations on Regions with Corners III: Curved Boundaries
Author(s): Serkh, Kirill
In this report we investigate the solution of boundary value problems for elliptic partial differential equations on domains with corners. Previously, we observed that when, in the case of polygonal domains, the boundary value problems are formulated as boundary integral equations of classical potential theory, the solutions are representable by series of certain elementary functions. Here, we extend this observation to the general case of regions with boundaries consisting of analytic curves meeting at corners. We show that the solutions near the corners have the same leading terms as in the polygonal case, plus a series of corrections involving products of the leading terms with integer powers and powers of logarithms. Furthermore, we show that if the curve in the vicinity of a corner approximates a polygon to order \(k\), then the correction added to the leading terms will vanish like \(O(t^k)\), where \(t\) is the distance from the corner.