67,777 research outputs found
Triangulated categories of mixed motives
This book discusses the construction of triangulated categories of mixed
motives over a noetherian scheme of finite dimension, extending Voevodsky's
definition of motives over a field. In particular, it is shown that motives
with rational coefficients satisfy the formalism of the six operations of
Grothendieck. This is achieved by studying descent properties of motives, as
well as by comparing different presentations of these categories, following and
extending insights and constructions of Deligne, Beilinson, Bloch, Thomason,
Gabber, Levine, Morel, Voevodsky, Ayoub, Spitzweck, R\"ondigs, {\O}stv{\ae}r,
and others. In particular, the relation of motives with -theory is addressed
in full, and we prove the absolute purity theorem with rational coefficients,
using Quillen's localization theorem in algebraic -theory together with a
variation on the Grothendieck-Riemann-Roch theorem. Using resolution of
singularities via alterations of de Jong-Gabber, this leads to a version of
Grothendieck-Verdier duality for constructible motivic sheaves with rational
coefficients over rather general base schemes. We also study versions with
integral coefficients, constructed via sheaves with transfers, for which we
obtain partial results. Finally, we associate to any mixed Weil cohomology a
system of categories of coefficients and well behaved realization functors,
establishing a correspondence between mixed Weil cohomologies and suitable
systems of coefficients. The results of this book have already served as ground
reference in many subsequent works on motivic sheaves and their realizations,
and pointers to the most recent developments of the theory are given in the
introduction.Comment: This is the final version. To appear in the series Springer
Monographs in Mathematic
Effect of Age and Food Novelty on Food Memory
The influence of age of the consumer and food novelty on incidentally learned food memory was investigated by providing a meal containing novel and familiar target items under the pretense of a study on hunger feelings to 34 young and 36 older participants in France and to 24 young and 20 older participants in Denmark and testing them a day later on recognition of the targets among a set of distractors that were variations of the target made by adding or subtracting taste (sour or sweet) or aroma (orange or red berry flavor). Memory was also tested by asking participants to indicate whether the target and the distractors were equal to or less or more intense than the remembered target in sourness sweetness and aroma. The results showed that when novelty is defined as whether people know or not a given product, it has a strong influence on memory performance, but that age did not, the elderly performing just as well as the young. The change in the distractors was more readily detected with familiar than with novel targets where the participants were still confused by the target itself. Special attention is given to the influence of the incidental learning paradigm on the outcome and to the ways in which it differs from traditional recognition experiments
The connection between elastic scattering cross sections and acoustic vibrations of an embedded nanoparticle
Arbitrary waves incident on a solid embedded nanoparticle are studied. The
acoustic vibrational frequencies are shown to correspond to the poles of the
scattering cross section in the complex frequency plane. The location of the
poles is unchanged even if the incident wave is nonplanar. A second approach
approximating the infinite matrix as a very large shell surrounding the
nanoparticle provides an alternate way of predicting the mode frequencies. The
wave function of the vibration is also provided.Comment: Accepted for publication in physica status solidi (c) (C) (2003)
WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Proceedings of Phonons200
Matrix inequalities from a two variables functional
Several matrix/operator inequalies are given. Most of them are unexpected
extensions of the Araki Log-majorization theorem, obtained thanks to a new
log-majorization for positive linear maps and normal operators (Theorem 2.9).
The main idea and technical tool is a two variables log-convex norm functional
(Theorem 1.2).Comment: Final version, to appear in International J. Math: Two corollaries on
Schur products have been added at the end of Section
Inelastic neutron scattering due to acoustic vibrations confined in nanoparticles: theory and experiment
The inelastic scattering of neutrons by nanoparticles due to acoustic
vibrational modes (energy below 10 meV) confined in nanoparticles is calculated
using the Zemach-Glauber formalism. Such vibrational modes are commonly
observed by light scattering techniques (Brillouin or low-frequency Raman
scattering). We also report high resolution inelastic neutron scattering
measurements for anatase TiO2 nanoparticles in a loose powder. Factors enabling
the observation of such vibrations are discussed. These include a narrow
nanoparticle size distribution which minimizes inhomogeneous broadening of the
spectrum and the presence of hydrogen atoms oscillating with the nanoparticle
surfaces which enhances the number of scattered neutrons.Comment: 3 figures, 1 tabl
Reaching optimally oriented molecular states by laser kicks
We present a strategy for post-pulse orientation aiming both at efficiency
and maximal duration within a rotational period. We first identify the
optimally oriented states which fulfill both requirements. We show that a
sequence of half-cycle pulses of moderate intensity can be devised for reaching
these target states.Comment: 4 pages, 3 figure
Integrability, quantization and moduli spaces of curves
This paper has the purpose of presenting in an organic way a new approach to
integrable (1+1)-dimensional field systems and their systematic quantization
emerging from intersection theory of the moduli space of stable algebraic
curves and, in particular, cohomological field theories, Hodge classes and
double ramification cycles. This methods are alternative to the traditional
Witten-Kontsevich framework and its generalizations by Dubrovin and Zhang and,
among other advantages, have the merit of encompassing quantum integrable
systems. Most of this material originates from an ongoing collaboration with A.
Buryak, B. Dubrovin and J. Gu\'er\'e
Existence and multiplicity for elliptic problems with quadratic growth in the gradient
We show that a class of divergence-form elliptic problems with quadratic
growth in the gradient and non-coercive zero order terms are solvable, under
essentially optimal hypotheses on the coefficients in the equation. In
addition, we prove that the solutions are in general not unique. The case where
the zero order term has the opposite sign was already intensively studied and
the uniqueness is the rule.Comment: To appear in Comm. PD
An algebra of deformation quantization for star-exponentials on complex symplectic manifolds
The cotangent bundle to a complex manifold is classically endowed
with the sheaf of \cor-algebras \W[T^*X] of deformation quantization, where
\cor\eqdot \W[\rmptt] is a subfield of \C[[\hbar,\opb{\hbar}]. Here, we
construct a new sheaf of \cor-algebras \TW[T^*X] which contains \W[T^*X]
as a subalgebra and an extra central parameter . We give the symbol calculus
for this algebra and prove that quantized symplectic transformations operate on
it. If is any section of order zero of \W[T^*X], we show that
\exp(t\opb{\hbar} P) is well defined in \TW[T^*X].Comment: Latex file, 24 page
Optimal rates of convergence for persistence diagrams in Topological Data Analysis
Computational topology has recently known an important development toward
data analysis, giving birth to the field of topological data analysis.
Topological persistence, or persistent homology, appears as a fundamental tool
in this field. In this paper, we study topological persistence in general
metric spaces, with a statistical approach. We show that the use of persistent
homology can be naturally considered in general statistical frameworks and
persistence diagrams can be used as statistics with interesting convergence
properties. Some numerical experiments are performed in various contexts to
illustrate our results
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