479,158 research outputs found
Combinatorial proof for a stability property of plethysm coefficients
Plethysm coefficients are important structural constants in the representation the-
ory of the symmetric groups and general linear groups. Remarkably, some sequences
of plethysm coefficients stabilize (they are ultimately constants). In this paper we
give a new proof of such a stability property, proved by Brion with geometric representation theory techniques. Our new proof is purely combinatorial: we decompose
plethysm coefficients as a alternating sum of terms counting integer points in poly-
topes, and exhibit bijections between these sets of integer points.Ministerio de Ciencia e InnovaciĂłn MTM2010–19336Junta de AndalucĂa FQM–333Junta de AndalucĂa P12–FQM–269
Mathematical Logic: Proof Theory, Constructive Mathematics (hybrid meeting)
The Workshop "Mathematical Logic: Proof Theory,
Constructive Mathematics" focused on
proofs both as formal derivations in deductive systems as well as on
the extraction of explicit computational content from
given proofs in core areas of ordinary mathematics using proof-theoretic
methods. The workshop contributed to the following research strands: interactions between foundations and applications; proof mining; constructivity in classical logic; modal logic and provability logic; proof theory and theoretical computer science; structural proof theory
A critical test of the mode-coupling theory of the glass transition
The mode-coupling theory of the glass transition predicts the time evolution
of the intermediate scattering functions in viscous liquids on the sole basis
of the structural information encoded in two-point density correlations. We
provide a critical test of this property and show that the theory fails to
describe the qualitatively distinct dynamical behavior obtained in two model
liquids characterized by very similar pair correlation functions. Because we
use `exact' static information provided by numerical simulations, our results
are a direct proof that some important information about the dynamics of
viscous liquids is not captured by pair correlations, and is thus not described
by the mode-coupling theory, even in the temperature regime where the theory is
usually applied.Comment: 7 pages, 5 figures
Practical theories for service life prediction of critical aerospace structural components
A new second-order theory was developed for predicting the service lives of aerospace structural components. The predictions based on this new theory were compared with those based on the Ko first-order theory and the classical theory of service life predictions. The new theory gives very accurate service life predictions. An equivalent constant-amplitude stress cycle method was proposed for representing the random load spectrum for crack growth calculations. This method predicts the most conservative service life. The proposed use of minimum detectable crack size, instead of proof load established crack size as an initial crack size for crack growth calculations, could give a more realistic service life
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