31,396 research outputs found
Majorana states in a p-wave superconducting ring
The spectrum of excitations of the chiral superconducting ring with internal
and external radii, comparable with coherence length, trapping a unit flux is
calculated. We find within the Bogoliubov-deGennes approach that there exists a
pair of precisely zero energy states. They are not protected by topology, but
are stable under certain deformations of the system. We discuss the ways to
tune the system so that it grows into such a "Majorana disk". This condition
has a character of a resonance phenomenon
Problems around polynomials - the good, the bad and the ugly ...
This is a list of several open problems dealing mainly with univariate
polynomials.Comment: 7 pages, no figure
First steps towards total reality of meromorphic functions
It was earlier conjectured by the second and the third authors that any
rational curve such that the inverse
images of all its flattening points lie on the real line is real algebraic up to a linear fractional transformation of
the image . (By a flattening point on we mean a point
at which the Frenet -frame is degenerate.) Below we
extend this conjecture to the case of meromorphic functions on real algebraic
curves of higher genera and settle it for meromorphic functions of degrees
and several other cases.Comment: 10 pages, 1 figur
Responses to comments and elaborations of previous posts III
This post is dedicated to the memory of Rabbi Chaim Flom, late rosh yeshiva of Yeshivat Ohr David in Jerusalem. I first met Rabbi Flom thirty years ago when he became my teacher at the Hebrew Youth Academy of Essex County (now known as the Joseph Kushner Hebrew Academy; unfortunately, another one of my teachers from those years also passed away much too young, Rabbi Yaakov Appel). When he first started teaching he was known as Mr. Flom, because he hadn't yet received semikhah (Actually, he had some sort of semikhah but he told me that he didn't think it was adequate to be called "Rabbi" by the students.) He was only at the school a couple of years and then decided to move to Israel to open his yeshiva. I still remember his first parlor meeting which was held at my house. Rabbi Flom was a very special man. Just to give some idea of this, ten years after leaving the United States he was still in touch with many of the students and even attended our weddings. He would always call me when he came to the U.S. and was genuinely interested to hear about my family and what I was working on. He will be greatly missed
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