In this paper we prove an analogue of Mordell’s inequality for lattices in finite-dimensional complex or quaternionic Hermitian space that are modules over a maximal order in an imaginary quadratic number field or a totally definite rational quaternion algebra. This inequality implies that 16dimensional Barnes-Wall lattice has optimal density among all 16-dimensional lattices with Hurwitz struc...

First results are presented from an experiment that aims at the simultaneous determination of both transversal polarization components of electrons emitted in the decay of free neutrons – two observables that have never before been addressed experimentally. They reveal first-order sensitivity to real and imaginary parts of the exotic scalar and tensor interactions.

We study a two-level model coupled to the electromagnetic vacuum and to an external classic electric field with fixed frequency. The amplitude of the external electric field is supposed to vary very slow in time. Garrison and Wright [Phys. Lett. A128 (1988) 177] used the non-hermitian Hamiltonian approach to study the adiabatic limit of this model and obtained that the probability of this two-l...

It is argued that in hot gauge field theories, " Hard Thermal Loops " leading order calculations call for a definite sequence of angular averages and discontinuity (or Imaginary part prescription) operations, and run otherwise into incorrect results. The ten years old collinear singularity problem of hot QCD, provides a striking illustration of that fate.

We present a new algorithm for computing the ideal class group of an imaginary quadratic order which is based on the multiple polynomial version of the quadratic sieve factoring algorithm. Although no formal analysis is given, we conjecture that our algorithm has sub-exponential complexity, and computational experience shows that it is significantly faster in practice than existing algorithms.

In this paper we prove a version of Mordell’s inequality for lattices in finite-dimensional complex or quaternionic Hermitian space that are modules over a maximal order in an imaginary quadratic number field or a totally definite rational quaternion algebra. This inequality implies that 16dimensional Barnes-Wall lattice has optimal density among all 16-dimensional lattices with Hurwitz structu...

We improve Kolyvagin’s upper bound on the order of the p-primary part of the Shafarevich-Tate group of an elliptic curve of rank one over a quadratic imaginary field. In many cases, our bound is precisely the one predicted by the Birch and Swinnerton-Dyer conjectural formula.

The task of discriminating the motor imagery of different movements within the same limb using electroencephalography (EEG) signals is challenging because these imaginary movements have close spatial representations on the motor cortex area. There is, however, a pressing need to succeed in this task. The reason is that the ability to classify different same-limb imaginary movements could increa...

Weight functions with a parameter are introduced into an iteration process to increase the order of the convergence and enhance the behavior of the iteration process. The parameter can be chosen to restrict extraneous fixed points to the imaginary axis and provide the best basin of attraction. The process is demonstrated on several examples. Published by Elsevier Inc.

We give a classification of all principally polarized abelian surfaces that admit an (l, l)-isogeny to themselves, and show how to compute all the abelian surfaces that occur. We make the classification explicit in the simplest case l = 2. As part of our classification, we also show how to find all principally polarized abelian surfaces with multiplication by a given imaginary quadratic order.