46 citations · 48 across the 8 of their papers we have counts for
8 papers
Mikhail Aleksandrovich Shubin. December 19, 1944 -- May 13, 2020
Maxim Braverman, Arnold Dikansky, Leonid Friedlander +8
The article is dedicated to thye memory of a distinguished mathematician Professor Misha Shubin
Diamond Twin
Toshikazu Sunada
As noticed in 2006 by the author of the present article, the hypothetical crystal---described by crystallographer F. Laves (1932) for the first time and designated ``Laves' graph o…
From Euclid to Riemann and Beyond
Toshikazu Sunada
The purpose of this essay is to trace the historical development of geometry while focusing on how we acquired mathematical tools for describing the "shape of the universe." More s…
Generalized Riemann sums
Toshikazu Sunada
The primary aim of this chapter is, commemorating the 150th anniversary of Riemann's death, to explain how the idea of {\it Riemann sum} is linked to other branches of mathematics.…
Topics on mathematical crystallography
Toshikazu Sunada
In July 2012 the General Assembly of the United Nations resolved that 2014 should be the International Year of Crystallography, 100 years since the award of the Nobel Prize for the…
Standard 2D Crystalline Patterns and Rational Points in Complex Quadrics
Toshikazu Sunada
A certain Diophantine problem and 2D crystallography are linked through the notion of standard realizations which was introduced originally in the study of random walks. In the dis…
Asymptotic behavior of quantum walks on the line
Toshikazu Sunada, Tatsuya Tate
This paper gives various asymptotic formulae for the transition probability associated with discrete time quantum walks on the real line. The formulae depend heavily on the `normal…
Geometric Theory of Lattice Vibrations and Specific Heat
Mikhail Shubin, Toshikazu Sunada
We discuss, from a geometric standpoint, the specific heat of a solid. This is a classical subject in solid state physics which dates back to a pioneering work by Einstein (1907) a…