297 research outputs found
Regulator constants and the parity conjecture
The p-parity conjecture for twists of elliptic curves relates multiplicities
of Artin representations in p-infinity Selmer groups to root numbers. In this
paper we prove this conjecture for a class of such twists. For example, if E/Q
is semistable at 2 and 3, K/Q is abelian and K^\infty is its maximal pro-p
extension, then the p-parity conjecture holds for twists of E by all orthogonal
Artin representations of Gal(K^\infty/Q). We also give analogous results when
K/Q is non-abelian, the base field is not Q and E is replaced by an abelian
variety. The heart of the paper is a study of relations between permutation
representations of finite groups, their "regulator constants", and
compatibility between local root numbers and local Tamagawa numbers of abelian
varieties in such relations.Comment: 50 pages; minor corrections; final version, to appear in Invent. Mat
Stationary Black Holes with Static and Counterrotating Horizons
We show that rotating dyonic black holes with static and counterrotating
horizon exist in Einstein-Maxwell-dilaton theory when the dilaton coupling
constant exceeds the Kaluza-Klein value. The black holes with static horizon
bifurcate from the static black holes. Their mass decreases with increasing
angular momentum, their horizons are prolate.Comment: 4 pages, 6 figure
Classtalk: A Classroom Communication System for Active Learning
This pdf file is an article describing the advantages of using Classtalk technology in the classroom to enhance classroom communication. Classtalk technology cab facilitate the presentation of questions for small group work, collec the student answers and then display histograms showing how the class answered. This new communication technology can help instructors create a more interactive, student centered classroom, especially when teaching large courses. The article describes Classtalk as a very useful tool not only for engaging students in active learning, but also for enhancing the overall communication within the classroom. This article is a selection from the electronic Journal for Computing in Higher Education. Educational levels: Graduate or professional
3D heterotic string theory: new approach and extremal solutions
We develop a new formalism for the bosonic sector of low-energy heterotic
string theory toroidally compactified to three dimensions. This formalism is
based on the use of some single non-quadratic real matrix potential which
transforms linearly under the action of subgroup of the three-dimensional
charging symmetries. We formulate a new charging symmetry invariant approach
for the symmetry generation and straightforward construction of asymptotically
flat solutions. Finally, using the developed approach and the established
formal analogy between the heterotic and Einstein-Maxwell theories, we
construct a general class of the heterotic string theory extremal solutions of
the Israel-Wilson-Perjes type. This class is asymptotically flat and charging
symmetry complete; it includes the extremal solutions constructed before and
possesses the non-trivial bosonic string theory limit.Comment: 20 pages in Late
Ranks of twists of elliptic curves and Hilbert's Tenth Problem
In this paper we investigate the 2-Selmer rank in families of quadratic
twists of elliptic curves over arbitrary number fields. We give sufficient
conditions on an elliptic curve so that it has twists of arbitrary 2-Selmer
rank, and we give lower bounds for the number of twists (with bounded
conductor) that have a given 2-Selmer rank. As a consequence, under appropriate
hypotheses we can find many twists with trivial Mordell-Weil group, and
(assuming the Shafarevich-Tate conjecture) many others with infinite cyclic
Mordell-Weil group. Using work of Poonen and Shlapentokh, it follows from our
results that if the Shafarevich-Tate conjecture holds, then Hilbert's Tenth
Problem has a negative answer over the ring of integers of every number field.Comment: Minor changes. To appear in Inventiones mathematica
From thermal rectifiers to thermoelectric devices
We discuss thermal rectification and thermoelectric energy conversion from
the perspective of nonequilibrium statistical mechanics and dynamical systems
theory. After preliminary considerations on the dynamical foundations of the
phenomenological Fourier law in classical and quantum mechanics, we illustrate
ways to control the phononic heat flow and design thermal diodes. Finally, we
consider the coupled transport of heat and charge and discuss several general
mechanisms for optimizing the figure of merit of thermoelectric efficiency.Comment: 42 pages, 22 figures, review paper, to appear in the Springer Lecture
Notes in Physics volume "Thermal transport in low dimensions: from
statistical physics to nanoscale heat transfer" (S. Lepri ed.
Undecidability in number theory
These lecture notes cover classical undecidability results in number theory,
Hilbert's 10th problem and recent developments around it, also for rings other
than the integers. It also contains a sketch of the authors result that the
integers are universally definable in the rationals.Comment: 48 pages. arXiv admin note: text overlap with arXiv:1011.342
Metal enrichment processes
There are many processes that can transport gas from the galaxies to their
environment and enrich the environment in this way with metals. These metal
enrichment processes have a large influence on the evolution of both the
galaxies and their environment. Various processes can contribute to the gas
transfer: ram-pressure stripping, galactic winds, AGN outflows, galaxy-galaxy
interactions and others. We review their observational evidence, corresponding
simulations, their efficiencies, and their time scales as far as they are known
to date. It seems that all processes can contribute to the enrichment. There is
not a single process that always dominates the enrichment, because the
efficiencies of the processes vary strongly with galaxy and environmental
properties.Comment: 18 pages, 8 figures, accepted for publication in Space Science
Reviews, special issue "Clusters of galaxies: beyond the thermal view",
Editor J.S. Kaastra, Chapter 17; work done by an international team at the
International Space Science Institute (ISSI), Bern, organised by J.S.
Kaastra, A.M. Bykov, S. Schindler & J.A.M. Bleeke
Self-assembled InAs quantum dot formation on GaAs ring-like nanostructure templates
The evolution of InAs quantum dot (QD) formation is studied on GaAs ring-like nanostructures fabricated by droplet homo-epitaxy. This growth mode, exclusively performed by a hybrid approach of droplet homo-epitaxy and Stransky-Krastanor (S-K) based QD self-assembly, enables one to form new QD morphologies that may find use in optoelectronic applications. Increased deposition of InAs on the GaAs ring first produced a QD in the hole followed by QDs around the GaAs ring and on the GaAs (100) surface. This behavior indicates that the QDs prefer to nucleate at locations of high monolayer (ML) step density
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