New zero free regions for the derivatives of the Riemann zeta function

The main aim of this paper is twofold. First we generalize, in a novel way, most of the known non-vanishing results for the derivatives of the Riemann zeta function by establishing the existence of an infinite sequence of regions in the right half-plane where these derivatives cannot have any zeros; and then, in the rare regions of the complex plane that do contain zeros of the k-th derivative of the zeta function, we describe a unexpected phenomenon, which implies great regularities in their zero distributions. In particular, we prove sharp estimates for the number of zeros in each of these new critical strips, and we explain how they converge, in a very precise, periodic fashion, to their central, critical lines, as k increases. This not only shows that the zeros are not randomly scattered to the right of the line Re(s)=1, but that, in many respects, their two-dimensional distribution eventually becomes much simpler and more predictable than the one-dimensional behavior of the zeros of the zeta function on the line Re(s)=1/2

Computation of 2-groups of positive classes of exceptional number fields

We present an algorithm for computing the 2-group of the positive divisor classes of a number field F in case F has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel WK2(F) in K2(F) for such number fields

Thermal, electric and spin transport in superconductor/ferromagnetic-insulator structures

A ferromagnetic insulator (FI) attached to a conventional superconductor (S) changes drastically the properties of the latter. Specifically, the exchange field at the FI/S interface leads to a splitting of the superconducting density of states. If S is a superconducting film, thinner than the superconducting coherence length, the modification of the density of states occurs over the whole sample. The co-existence of the exchange splitting and superconducting correlations in S/FI structures leads to striking transport phenomena that are of interest for applications in thermoelectricity, superconducting spintronics and radiation sensors. Here we review the most recent progress in understanding the transport properties of FI/S structures by presenting a complete theoretical framework based on the quasiclassical kinetic equations. We discuss the coupling between the electronic degrees of freedom, charge, spin and energy, under non-equilibrium conditions and its manifestation in thermoelectricity and spin-dependent transport.Comment: 117 pages, 33 figures. arXiv admin note: substantial text overlap with arXiv:1706.0824

Computation of 2-groups of narrow logarithmic divisor classes of number fields

We present an algorithm for computing the 2-group of narrow logarithmic divisor classes of degree 0 for number fields F. As an application, we compute in some cases the 2-rank of the wild kernel WK2(F)

Application of object tracking in video recordings to the observation of mice in the wild

We give an overview of methods used to track moving objects in video and describe how information about animal behavior can be extracted from tracking data. We discuss how computer-aided observation can be used to identify and pre-select potentially interesting video sequences from large amounts of video data for further observation, as well as directly analyze extracted data. We examine how this analysis can be used to study animal behavior. As an example, we examine thermal video recorded from free-living, nocturnal, wild mice in the genus Peromyscus