12,929 research outputs found
Making proofs without Modus Ponens: An introduction to the combinatorics and complexity of cut elimination
This paper is intended to provide an introduction to cut elimination which is
accessible to a broad mathematical audience. Gentzen's cut elimination theorem
is not as well known as it deserves to be, and it is tied to a lot of
interesting mathematical structure. In particular we try to indicate some
dynamical and combinatorial aspects of cut elimination, as well as its
connections to complexity theory. We discuss two concrete examples where one
can see the structure of short proofs with cuts, one concerning feasible
numbers and the other concerning "bounded mean oscillation" from real analysis
Measuring the LISA test mass magnetic proprieties with a torsion pendulum
Achieving the low frequency LISA sensitivity requires that the test masses
acting as the interferometer end mirrors are free-falling with an unprecedented
small degree of deviation. Magnetic disturbances, originating in the
interaction of the test mass with the environmental magnetic field, can
significantly deteriorate the LISA performance and can be parameterized through
the test mass remnant dipole moment and the magnetic susceptibility
. While the LISA test flight precursor LTP will investigate these effects
during the preliminary phases of the mission, the very stringent requirements
on the test mass magnetic cleanliness make ground-based characterization of its
magnetic proprieties paramount. We propose a torsion pendulum technique to
accurately measure on ground the magnetic proprieties of the LISA/LTP test
masses.Comment: 6 pages, 3 figure
Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories
For a split, simply connected, semisimple Lie group of rank
and the maximal compact subgroup of , we give a method for computing
Iwasawa coordinates of using the Chevalley generators and the Steinberg
presentation. When is a scalar coset for a supergravity theory in
dimensions , we determine the action of the integral form
on . We give explicit results for the action of the
discrete --duality groups and on the
scalar cosets and
for type IIB supergravity
in ten dimensions and 11--dimensional supergravity in dimensions,
respectively. For the former, we use this to determine the discrete U--duality
transformations on the scalar sector in the Borel gauge and we describe the
discrete symmetries of the dyonic charge lattice. We determine the
spectrum--generating symmetry group for fundamental BPS solitons of type IIB
supergravity in dimensions at the classical level and we propose an
analog of this symmetry at the quantum level. We indicate how our methods can
be used to study the orbits of discrete U--duality groups in general
Quantifying signals with power-law correlations: A comparative study of detrended fluctuation analysis and detrended moving average techniques
Detrended fluctuation analysis (DFA) and detrended moving average (DMA) are
two scaling analysis methods designed to quantify correlations in noisy
non-stationary signals. We systematically study the performance of different
variants of the DMA method when applied to artificially generated long-range
power-law correlated signals with an {\it a-priori} known scaling exponent
and compare them with the DFA method. We find that the scaling
results obtained from different variants of the DMA method strongly depend on
the type of the moving average filter. Further, we investigate the optimal
scaling regime where the DFA and DMA methods accurately quantify the scaling
exponent , and how this regime depends on the correlations in the
signal. Finally, we develop a three-dimensional representation to determine how
the stability of the scaling curves obtained from the DFA and DMA methods
depends on the scale of analysis, the order of detrending, and the order of the
moving average we use, as well as on the type of correlations in the signal.Comment: 15 pages, 16 figure
What is the true charge transfer gap in parent insulating cuprates?
A large body of experimental data point towards a charge transfer instability
of parent insulating cuprates to be their unique property. We argue that the
true charge transfer gap in these compounds is as small as 0.4-0.5\,eV rather
than 1.5-2.0\,eV as usually derived from the optical gap measurements. In fact
we deal with a competition of the conventional (3d) ground state and a
charge transfer (CT) state with formation of electron-hole dimers which evolves
under doping to an unconventional bosonic system. Our conjecture does provide
an unified standpoint on the main experimental findings for parent cuprates
including linear and nonlinear optical, Raman, photoemission, photoabsorption,
and transport properties anyhow related with the CT excitations. In addition we
suggest a scenario for the evolution of the CuO planes in the CT unstable
cuprates under a nonisovalent doping.Comment: 13 pages, 5 figures, submitted to PR
Thermal gradient-induced forces on geodetic reference masses for LISA
The low frequency sensitivity of space-borne gravitational wave observatories
will depend critically on the geodetic purity of the trajectories of orbiting
test masses. Fluctuations in the temperature difference across the enclosure
surrounding the free-falling test mass can produce noisy forces through several
processes, including the radiometric effect, radiation pressure, and
outgassing. We present here a detailed experimental investigation of thermal
gradient-induced forces for the LISA gravitational wave mission and the LISA
Pathfinder, employing high resolution torsion pendulum measurements of the
torque on a LISA-like test mass suspended inside a prototype of the LISA
gravitational reference sensor that will surround the test mass in orbit. The
measurement campaign, accompanied by numerical simulations of the radiometric
and radiation pressure effects, allows a more accurate and representative
characterization of thermal-gradient forces in the specific geometry and
environment relevant to LISA free-fall. The pressure dependence of the measured
torques allows clear identification of the radiometric effect, in quantitative
agreement with the model developed. In the limit of zero gas pressure, the
measurements are most likely dominated by outgassing, but at a low level that
does not threaten the LISA sensitivity goals.Comment: 21 pages, 16 figures, submitted to Physical Review
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