164 research outputs found
Relative blocking in posets
Poset-theoretic generalizations of set-theoretic committee constructions are
presented. The structure of the corresponding subposets is described. Sequences
of irreducible fractions associated to the principal order ideals of finite
bounded posets are considered and those related to the Boolean lattices are
explored; it is shown that such sequences inherit all the familiar properties
of the Farey sequences.Comment: 29 pages. Corrected version of original publication which is
available at http://www.springerlink.com, see Corrigendu
ODE-methods in non-local equations
Non-local equations cannot be treated using classical ODE theorems.
Nevertheless, several new methods have been introduced in the non-local gluing
scheme of our previous article "On higher dimensional singularities for the
fractional Yamabe problem: a non-local Mazzeo-Pacard program"; we survey and
improve those, and present new applications as well. First, from the explicit
symbol of the conformal fractional Laplacian, a variation of constants formula
is obtained for fractional Hardy operators. We thus develop, in addition to a
suitable extension in the spirit of Caffarelli--Silvestre, an equivalent
formulation as an infinite system of second order constant coefficient ODEs.
Classical ODE quantities like the Hamiltonian and Wro\'nskian may then be
utilized. As applications, we obtain a Frobenius theorem and establish new
Poho\vzaev identities. We also give a detailed proof for the non-degeneracy of
the fast-decay singular solution of the fractional Lane-Emden equation.Comment: bibliography updated from previous versio
Quantum depinning of a pancake-vortex from a columnar defect
We consider the problem of the depinning of a weakly driven ()
pancake vortex from a columnar defect in a Josephson-coupled superconductor,
where denotes the force acting on the vortex ( is the critical
force).
The dynamics of the vortex is supposed to be of the Hall type. The Euclidean
action is calculated in the entire temperature range; the result
is universal and does not depend on the detailed form of the pinning potential.
We show that the transition from quantum to classical behavior is second-order
like with the temperature of the transition scaling like
Special attention is paid to the regime of applicability of our results, in
particular, the influence of the large vortex mass appearing in the superclean
limit is discussed.Comment: 11 pages, RevTeX, 4 figures inserte
Effective Actions and Phase Fluctuations in d-wave Superconductors
We study effective actions for order parameter fluctuations at low
temperature in layered d-wave superconductors such as the cuprates. The order
parameter lives on the bonds of a square lattice and has two amplitude and two
phase modes associated with it. The low frequency spectral weights for
amplitude and relative phase fluctuations is determined and found to be
subdominant to quasiparticle contributions. The Goldstone phase mode and its
coupling to density fluctuations in charged systems is treated in a
gauge-invariant manner. The Gaussian phase action is used to study both the
-axis Josephson plasmon and the more conventional in-plane plasmon in the
cuprates. We go beyond the Gaussian theory by deriving a coarse-grained quantum
XY model, which incorporates important cutoff effects overlooked in previous
studies. A variational analysis of this effective model shows that in the
cuprates, quantum effects of phase fluctuations are important in reducing the
zero temperature superfluid stiffness, but thermal effects are small for .Comment: Some numerical estimates corrected and figures changed. to appear in
PRB, Sept.1 (2000
Simultaneous Extraction of the Fermi constant and PMNS matrix elements in the presence of a fourth generation
Several recent studies performed on constraints of a fourth generation of
quarks and leptons suffer from the ad-hoc assumption that 3 x 3 unitarity holds
for the first three generations in the neutrino sector. Only under this
assumption one is able to determine the Fermi constant G_F from the muon
lifetime measurement with the claimed precision of G_F = 1.16637 (1) x 10^-5
GeV^-2. We study how well G_F can be extracted within the framework of four
generations from leptonic and radiative mu and tau decays, as well as from K_l3
decays and leptonic decays of charged pions, and we discuss the role of lepton
universality tests in this context. We emphasize that constraints on a fourth
generation from quark and lepton flavour observables and from electroweak
precision observables can only be obtained in a consistent way if these three
sectors are considered simultaneously. In the combined fit to leptonic and
radiative mu and tau decays, K_l3 decays and leptonic decays of charged pions
we find a p-value of 2.6% for the fourth generation matrix element |U_{e 4}|=0
of the neutrino mixing matrix.Comment: 19 pages, 3 figures with 16 subfigures, references and text added
refering to earlier related work, figures and text in discussion section
added, results and conclusions unchange
Unravelling the Genetics of Ischaemic Stroke
Hugh Markus discusses genetic factors in stroke risk, and emphasizes the importance of large sample studies and rigorous replication of results in genetic stroke research
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