On the Two Spectra Inverse Problem for Semi-Infinite Jacobi Matrices

We present results on the unique reconstruction of a semi-infinite Jacobi operator from the spectra of the operator with two different boundary conditions. This is the discrete analogue of the Borg-Marchenko theorem for Schr{\"o}dinger operators in the half-line. Furthermore, we give necessary and sufficient conditions for two real sequences to be the spectra of a Jacobi operator with different boundary conditions.Comment: In this slightly revised version we have reworded some of the theorems, and we updated two reference

Views of the Chiral Magnetic Effect

My personal views of the Chiral Magnetic Effect are presented, which starts with a story about how we came up with the electric-current formula and continues to unsettled subtleties in the formula. There are desirable features in the formula of the Chiral Magnetic Effect but some considerations would lead us to even more questions than elucidations. The interpretation of the produced current is indeed very non-trivial and it involves a lot of confusions that have not been resolved.Comment: 19 pages, no figure; typos corrected, references significantly updated, to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye

Eliminate Exams in Intro to Flight with Portfolios? An Update After 6 Years of Improvement

A portfolio can be an extremely powerful tool to determine the degree of learning experienced by a student throughout the semester, and to coax the student into a higher level of reflective learning and meta-cognition not generally possible by studying for and taking the traditional in-class, timed final exam. Portfolios have been common in art, photography, journalism, business, architecture and other professions for quite some time. Strong justification can be found in learning theory for using Portfolios in engineering. Even though engineering design provides the most immediately obvious application of portfolios within engineering, different kinds of portfolios can be implemented across the engineering curriculum. This paper will briefly discuss what an engineering portfolio is in the context of an Introduction to Flight course given to sophomore year students at the University of Dayton. The paper will describe in detail what has been learned in 6 years of implementing portfolios in Intro to Flight. By the time the students submit their portfolios, almost all of the students are extremely positive about the entire portfolio experience. Most importantly, the portfolios elucidate the level of understanding and comprehension of the breadth and depth of the subject being examined for the student and instructor in a manner not possible through the use of a traditional in-class timed final exam. Portfolios provide an individualistic and creative outlet for assessment that leads to self-motivated and energized students. Finally, portfolios frequently cause a paradigm shift in student expectations for learning by shifting responsibility for the learning to the student which promotes a tendency towards life-long learning practices