Providing Real-World Experiences: the Virginia Tech Externship for Mathematics Specialists

We describe the structure and implementation of the yearlong Externship experience associated with the Mathematics Specialist program at Virginia Polytechnic Institute & State University (Virginia Tech). We discuss the assignments and experiences included in the Externship, the alignment of those experiences with the job description developed by the Virginia Mathematics and Science Coalition Task Force, and teacher comments on the effectiveness of their Externship experiences [1]

Life inside black holes

We consider test planet and photon orbits of the third kind inside a black hole, which are stable, periodic and neither come out of the black hole nor terminate at the singularity. Interiors of supermassive black holes may be inhabited by advanced civilizations living on planets with the third-kind orbits. In principle, one can get information from the interiors of black holes by observing their white hole counterparts.Comment: 4 pages, 2 figure

Address by Professor David B. Wilkins, Washington and Lee University School of Law Commencement Exercises, May 5, 2018

Professor David B. Wilkins of Harvard Law School delivered an invited address to the Washington and Lee Law Class of 2018 at their commencement ceremony. Following the conclusion of the ceremony, Dean Brant Hellwig secured Professor Wilkins\u27 gracious permission to publish the address in the Washington and Lee Law Review, and provides a written introduction to Professor Wilkins\u27 speech here. Professor Wilkins undertook considerable research in crafting a commencement address that incorporated several prominent figures from the history W&L Law and the University. His speech highlighted not only the contributions of George Washington and Robert E. Lee, for whom the University is named, but also two of the Law School’s most prominent alumni: John W. Davis, former Solicitor General of the United States, President of the American Bar Association, and founder of the Davis Polk law firm; and Supreme Court Justice Lewis F. Powell, Jr

Multi-k magnetic structures in USb_{0.9}Te_{0.1} and UAs_{0.8}Se_{0.2} observed via resonant x-ray scattering at the U M4 edge

Experiments with resonant photons at the U M4 edge have been performed on a sample of USb_{0.9}Te_{0.1}, which has an incommensurate magnetic structure with k = 0.596(2) reciprocal lattice units. The reflections of the form , as observed previously in a commensurate k = 1/2 system [N. Bernhoeft et al., Phys. Rev. B 69 174415 (2004)] are observed, removing any doubt that these occur because of multiple scattering or high-order contamination of the incident photon beam. They are clearly connected with the presence of a 3k configuration. Measurements of the reflections from the sample UAs_{0.8}Se_{0.2} in a magnetic field show that the transition at T* ~ 50 K is between a low-temperature 2k and high-temperature 3k state and that this transition is sensitive to an applied magnetic field. These experiments stress the need for quantitative theory to explain the intensities of these reflections.Comment: submitted to Phys. Rev.

Image Processing Failure and Deep Learning Success in Lawn Measurement

Lawn area measurement is an application of image processing and deep learning. Researchers have been used hierarchical networks, segmented images and many other methods to measure lawn area. Methods effectiveness and accuracy varies. In this project Image processing and deep learning methods has been compared to find the best way to measure the lawn area. Three Image processing methods using OpenCV has been compared to Convolutional Neural network which is one of the most famous and effective deep learning methods. We used Keras and TensorFlow to estimate the lawn area. Convolutional Neural Network or shortly CNN shows very high accuracy (94-97%) for this purpose. In image processing methods, Thresholding with 80-87% accuracy and Edge detection are effective methods to measure the lawn area but Contouring with 26-31% accuracy does not calculate the lawn area successfully. We may conclude that deep learning methods especially CNN could be the best detective method comparing to image processing and other deep learning techniques

Resonant X-Ray Scattering on the M-Edge Spectra from Triple-k Structure Phase in U_{0.75}Np_{0.25}O_{2} and UO_{2}

We derive an expression for the scattering amplitude of resonant x-ray scattering under the assumption that the Hamiltonian describing the intermediate state preserves spherical symmetry. On the basis of this expression, we demonstrate that the energy profile of the RXS spectra expected near U and Np M_4 edges from the triple-k antiferromagnetic ordering phase in UO_{2} and U_{0.75}Np_{0.25}O_{2} agree well with those from the experiments. We demonstrate that the spectra in the \sigma-\sigma' and \sigma-\pi' channels exhibit quadrupole and dipole natures, respectively.Comment: 3 pages, 3 figures, to be published in J. Phys. Soc. Jpn. Supp