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 $g:{\mathbb C}P^1\to {\mathbb C}P^n$ such that the inverse images of all its flattening points lie on the real line ${\mathbb R}P^1\subset {\mathbb C}P^1$ is real algebraic up to a linear fractional transformation of the image ${\mathbb C}P^n$. (By a flattening point $p$ on $g$ we mean a point at which the Frenet $n$-frame $(g',g'',...,g^{(n)})$ 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 $2,3$ 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