122 research outputs found
On localization of pseudo-relativistic energy
We present a Kato-type inequality for bounded domain Omega \subset R^n, n>1.Comment: 17 page
Asymptotics of the Farey Fraction Spin Chain Free Energy at the Critical Point
We consider the Farey fraction spin chain in an external field . Using
ideas from dynamical systems and functional analysis, we show that the free
energy in the vicinity of the second-order phase transition is given,
exactly, by
Here is a reduced
temperature, so that the deviation from the critical point is scaled by the
Lyapunov exponent of the Gauss map, . It follows that
determines the amplitude of both the specific heat and susceptibility
singularities. To our knowledge, there is only one other microscopically
defined interacting model for which the free energy near a phase transition is
known as a function of two variables.
Our results confirm what was found previously with a cluster approximation,
and show that a clustering mechanism is in fact responsible for the transition.
However, the results disagree in part with a renormalisation group treatment
Quantization and Compressive Sensing
Quantization is an essential step in digitizing signals, and, therefore, an
indispensable component of any modern acquisition system. This book chapter
explores the interaction of quantization and compressive sensing and examines
practical quantization strategies for compressive acquisition systems.
Specifically, we first provide a brief overview of quantization and examine
fundamental performance bounds applicable to any quantization approach. Next,
we consider several forms of scalar quantizers, namely uniform, non-uniform,
and 1-bit. We provide performance bounds and fundamental analysis, as well as
practical quantizer designs and reconstruction algorithms that account for
quantization. Furthermore, we provide an overview of Sigma-Delta
() quantization in the compressed sensing context, and also
discuss implementation issues, recovery algorithms and performance bounds. As
we demonstrate, proper accounting for quantization and careful quantizer design
has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing
and Its Applications", 201
Towards a unified theory of Sobolev inequalities
We discuss our work on pointwise inequalities for the gradient which are
connected with the isoperimetric profile associated to a given geometry. We
show how they can be used to unify certain aspects of the theory of Sobolev
inequalities. In particular, we discuss our recent papers on fractional order
inequalities, Coulhon type inequalities, transference and dimensionless
inequalities and our forthcoming work on sharp higher order Sobolev
inequalities that can be obtained by iteration.Comment: 39 pages, made some changes to section 1
The Proper Dissipative Extensions of a Dual Pair
Let A and B be dissipative operators on a Hilbert space H and let (A,B) form a dual pair, i.e. A ? B*, resp. B ? A*. We present a method of determining the proper dissipative extensions C of this dual pair, i.e. A ? C ? B* provided that D(A) ? D(B) is dense in H. Applications to symmetric operators, symmetric operators perturbed by a relatively bounded dissipative operator and more singular differential operators are discussed. Finally, we investigate the stability of the numerical range of the different dissipative extensions
Measurement of the differential cross section for the production of an isolated photon with associated jet in ppbar collisions at sqrt(s)=1.96 TeV
The process ppbar -> photon + jet + X is studied using 1.0 fb^-1 of data
collected by the D0 detector at the Fermilab Tevatron ppbar collider at a
center-of-mass energy sqrt(s)=1.96 TeV. Photons are reconstructed in the
central rapidity region |y_gamma|<1.0 with transverse momenta in the range
30<Pt_gamma<400 GeV while jets are reconstructed in either the central
|y_jet|15 GeV.
The differential cross section d^3sigma/dPt_gamma dy_gamma dy_jet is measured
as a function of Pt_gamma in four regions, differing by the relative
orientations of the photon and the jet in rapidity. Ratios between the
differential cross sections in each region are also presented. Next-to-leading
order QCD predictions using different parameterizations of parton distribution
functions and theoretical scale choices are compared to the data. The
predictions do not simultaneously describe the measured normalization and
Pt_gamma dependence of the cross section in any of the four measured regions.Comment: 13 pages, 10 figure
Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE) Conceptual Design Report Volume 2: The Physics Program for DUNE at LBNF
The Physics Program for the Deep Underground Neutrino Experiment (DUNE) at the Fermilab Long-Baseline Neutrino Facility (LBNF) is described
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