70 research outputs found
Formal Proof of SCHUR Conjugate Function
The main goal of our work is to formally prove the correctness of the key
commands of the SCHUR software, an interactive program for calculating with
characters of Lie groups and symmetric functions. The core of the computations
relies on enumeration and manipulation of combinatorial structures. As a first
"proof of concept", we present a formal proof of the conjugate function,
written in C. This function computes the conjugate of an integer partition. To
formally prove this program, we use the Frama-C software. It allows us to
annotate C functions and to generate proof obligations, which are proved using
several automated theorem provers. In this paper, we also draw on methodology,
discussing on how to formally prove this kind of program.Comment: To appear in CALCULEMUS 201
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Estimating worst case failure dependency with partial knowledge of the difficulty function
For systems using software diversity, well-established theories show that the expected probability of failure on demand (pfd) for two diverse program versions failing together will generally differ from what it would be if they failed independently. This is explained in terms of a “difficulty function” that varies between demands on the system. This theory gives insight, but no specific prediction unless we have some means to quantify the difficulty function. This paper presents a theory leading to a worst case measure of “average failure dependency” between diverse software, given only partial knowledge of the difficulty function. It also discusses the possibility of estimating the model parameters, with one approach based on an empirical analysis of previous systems implemented as logic networks, to support pre-development estimates of expected gain from diversity. The approach is illustrated using a realistic safety system example
Charge-density wave formation in Sr_{14}Cu_{24}O_{41}
The electrodynamic response of the spin-ladder compound
SrCaCuO () has been studied from
radiofrequencies up to the infrared. At temperatures below 250 K a pronounced
absorption peak appears around 12 cm in SrCuO for
the radiation polarized along the chains/ladders ().
In addition a strongly temperature dependent dielectric relaxation is observed
in the kHz - MHz range. We explain this behavior by a charge density wave which
develops in the ladders sub-system and produces a mode pinned at 12 cm.
With increasing Ca doping the mode shifts up in frequency and eventually
disappears for because the dimensionality of the system crosses over from
one to two dimensions, giving way to the superconducting ground state under
pressure.Comment: One name added to author list 4 pages, 2 figures, email:
[email protected]
Stability of condensate in superconductors
According to the BCS theory the superconducting condensate develops in a
single quantum mode and no Cooper pairs out of the condensate are assumed. Here
we discuss a mechanism by which the successful mode inhibits condensation in
neighboring modes and suppresses a creation of noncondensed Cooper pairs. It is
shown that condensed and noncondensed Cooper pairs are separated by an energy
gap which is smaller than the superconducting gap but large enough to prevent
nucleation in all other modes and to eliminate effects of noncondensed Cooper
pairs on properties of superconductors. Our result thus justifies basic
assumptions of the BCS theory and confirms that the BCS condensate is stable
with respect to two-particle excitations
Projective dynamics and first integrals
We present the theory of tensors with Young tableau symmetry as an efficient
computational tool in dealing with the polynomial first integrals of a natural
system in classical mechanics. We relate a special kind of such first
integrals, already studied by Lundmark, to Beltrami's theorem about
projectively flat Riemannian manifolds. We set the ground for a new and simple
theory of the integrable systems having only quadratic first integrals. This
theory begins with two centered quadrics related by central projection, each
quadric being a model of a space of constant curvature. Finally, we present an
extension of these models to the case of degenerate quadratic forms.Comment: 39 pages, 2 figure
Linear extension sums as valuations on cones
33 pagesInternational audienceThe geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset
A measurement of the tau mass and the first CPT test with tau leptons
We measure the mass of the tau lepton to be 1775.1+-1.6(stat)+-1.0(syst.) MeV
using tau pairs from Z0 decays. To test CPT invariance we compare the masses of
the positively and negatively charged tau leptons. The relative mass difference
is found to be smaller than 3.0 10^-3 at the 90% confidence level.Comment: 10 pages, 4 figures, Submitted to Phys. Letts.
Measurement of the B0 Lifetime and Oscillation Frequency using B0->D*+l-v decays
The lifetime and oscillation frequency of the B0 meson has been measured
using B0->D*+l-v decays recorded on the Z0 peak with the OPAL detector at LEP.
The D*+ -> D0pi+ decays were reconstructed using an inclusive technique and the
production flavour of the B0 mesons was determined using a combination of tags
from the rest of the event. The results t_B0 = 1.541 +- 0.028 +- 0.023 ps, Dm_d
= 0.497 +- 0.024 +- 0.025 ps-1 were obtained, where in each case the first
error is statistical and the second systematic.Comment: 17 pages, 4 figures, submitted to Phys. Lett.
First Measurement of Z/gamma* Production in Compton Scattering of Quasi-real Photons
We report the first observation of Z/gamma* production in Compton scattering
of quasi-real photons. This is a subprocess of the reaction e+e- to
e+e-Z/gamma*, where one of the final state electrons is undetected.
Approximately 55 pb-1 of data collected in the year 1997 at an e+e-
centre-of-mass energy of 183 GeV with the OPAL detector at LEP have been
analysed. The Z/gamma* from Compton scattering has been detected in the
hadronic decay channel. Within well defined kinematic bounds, we measure the
product of cross-section and Z/gamma* branching ratio to hadrons to be
(0.9+-0.3+-0.1) pb for events with a hadronic mass larger than 60 GeV,
dominated by (e)eZ production. In the hadronic mass region between 5 GeV and 60
GeV, dominated by (e)egamma* production, this product is found to be
(4.1+-1.6+-0.6) pb. Our results agree with the predictions of two Monte Carlo
event generators, grc4f and PYTHIA.Comment: 18 pages, LaTeX, 5 eps figures included, submitted to Physics Letters
WW Production Cross Section and W Branching Fractions in e+e- Collisions at 189 GeV
From a data sample of 183 pb^-1 recorded at a center-of-mass energy of roots
= 189 GeV with the OPAL detector at LEP, 3068 W-pair candidate events are
selected. Assuming Standard Model W boson decay branching fractions, the W-pair
production cross section is measured to be sigmaWW = 16.30 +- 0.34(stat.) +-
0.18(syst.) pb. When combined with previous OPAL measurements, the W boson
branching fraction to hadrons is determined to be 68.32 +- 0.61(stat.) +-
0.28(syst.) % assuming lepton universality. These results are consistent with
Standard Model expectations.Comment: 22 pages, 5 figures, submitted to Phys. Lett.
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