The Erwin Schrr Odinger International Institute for Mathematical Physics Some Examples in One{dimensional \geometric" Scattering Some Examples in One-dimensional \geometric" Scattering

Evolution of the first eigenvalue of buckling problem on Riemannian manifold under Ricci flow

Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...

The Erwin Schrr Odinger International Institute for Mathematical Physics Rayleigh{type Isoperimetric Inequality with a Homogeneous Magnetic Field Rayleigh-type Isoperimetric Inequality with a Homogeneous Magnetic Eld

We prove that the two dimensional free magnetic Schrr odinger operator, with a xed constant magnetic eld and Dirichlet boundary conditions on a planar domain with a given area, attains its smallest possible eigenvalue if the domain is a disk. We also give some rough bounds on the lowest magnetic eigenvalue of the disk. Running title: Magnetic Rayleigh-type inequality.

The Erwin Schrr Odinger International Institute for Mathematical Physics K{theory of Noncommutative Lattices K-theory of Noncommutative Lattices

Noncommutative lattices have been recently used as nite topological approximations in quantum physical models. As a rst step in the construction of bundles and characteristic classes over such noncommutative spaces, we shall study their K-theory. We shall do it algebraically, by studying the algebraic K-theory of the associated algebras of`continuous functions' which turn out to be noncommutati...

The Erwin Schrr Odinger International Institute for Mathematical Physics Martingale-diierence Random Fields Limit Theorems and Some Applications Martingale-diierence Random Fields. Limit Theorems and Some Applications

The Erwin Schrr Odinger International Institute for Mathematical Physics Quasifree Second Quantization and Its Relation to Noncommutative Geometry Quasifree Second Quantization and Its Relation to Noncommutative Geometry

Schwinger terms of current algebra can be identiied with nontrivial cyclic cocycles of a Fredholm module. We discuss its temperature dependence. Similar anomalies may occur also in spin systems. In simple examples already an operator{valued cocycle shows up.