907 research outputs found
Hilbert Functions of Filtered Modules
In this presentation we shall deal with some aspects of the theory of Hilbert
functions of modules over local rings, and we intend to guide the reader along
one of the possible routes through the last three decades of progress in this
area of dynamic mathematical activity. Motivated by the ever increasing
interest in this field, our goal is to gather together many new developments of
this theory into one place, and to present them using a unifying approach which
gives self-contained and easier proofs. In this text we shall discuss many
results by different authors, following essentially the direction typified by
the pioneering work of J. Sally. Our personal view of the subject is most
visibly expressed by the presentation of Chapters 1 and 2 in which we discuss
the use of the superficial elements and related devices. Basic techniques will
be stressed with the aim of reproving recent results by using a more elementary
approach. Over the past few years several papers have appeared which extend
classical results on the theory of Hilbert functions to the case of filtered
modules. The extension of the theory to the case of general filtrations on a
module has one more important motivation. Namely, we have interesting
applications to the study of graded algebras which are not associated to a
filtration, in particular the Fiber cone and the Sally-module. We show here
that each of these algebras fits into certain short exact sequences, together
with algebras associated to filtrations. Hence one can study the Hilbert
function and the depth of these algebras with the aid of the know-how we got in
the case of a filtration.Comment: 127 pages, revised version. Comments and remarks are welcom
Determinantal ideals and monomial curves in the three-dimensional space
We show that the defining ideal of every monomial curve in the affine or
projective three-dimensional space can be set-theoretically defined by three
binomial equations, two of which set-theoretically define a determinantal ideal
generated by the 2-minors of a matrix with monomial entries
The Ground State of the Pseudogap in Cuprate Superconductors
We present studies of the electronic structure of La2-xBaxCuO4, a system
where the superconductivity is strongly suppressed as static spin and charge
orders or "stripes" develop near the doping level of x=1/8. Using
angle-resolved photoemission and scanning tunneling microscopy, we detect an
energy gap at the Fermi surface with magnitude consistent with d-wave symmetry
and with linear density of states, vanishing only at four nodal points, even
when superconductivity disappears at x=1/8. Thus, the non-superconducting,
"striped" state at x=1/8 is consistent with a phase incoherent d-wave
superconductor whose Cooper pairs form spin/charge ordered structures instead
of becoming superconducting.Comment: This is the author's version of the wor
High-energy kink in high-temperature superconductors
In conventional metals, electron-phonon coupling, or the phonon-mediated
interaction between electrons, has long been known to be the pairing
interaction responsible for the superconductivity. The strength of this
interaction essentially determines the superconducting transition temperature
TC. One manifestation of electron-phonon coupling is a mass renormalization of
the electronic dispersion at the energy scale associated with the phonons. This
renormalization is directly observable in photoemission experiments. In
contrast, there remains little consensus on the pairing mechanism in cuprate
high temperature superconductors. The recent observation of similar
renormalization effects in cuprates has raised the hope that the mechanism of
high temperature superconductivity may finally be resolved. The focus has been
on the low energy renormalization and associated "kink" in the dispersion at
around 50 meV. However at that energy scale, there are multiple candidates
including phonon branches, structure in the spin-fluctuation spectrum, and the
superconducting gap itself, making the unique identification of the excitation
responsible for the kink difficult. Here we show that the low-energy
renormalization at ~50 meV is only a small component of the total
renormalization, the majority of which occurs at an order of magnitude higher
energy (~350 meV). This high energy kink poses a new challenge for the physics
of the cuprates. Its role in superconductivity and relation to the low-energy
kink remains to be determined.Comment: 13 pages, 4 figure
Measurement of an Exceptionally Weak Electron-Phonon Coupling on the Surface of the Topological Insulator BiSe Using Angle-Resolved Photoemission Spectroscopy
Gapless surface states on topological insulators are protected from elastic
scattering on non-magnetic impurities which makes them promising candidates for
low-power electronic applications. However, for wide-spread applications, these
states should have to remain coherent at ambient temperatures. Here, we studied
temperature dependence of the electronic structure and the scattering rates on
the surface of a model topological insulator, BiSe, by high resolution
angle-resolved photoemission spectroscopy. We found an extremely weak
broadening of the topological surface state with temperature and no anomalies
in the state's dispersion, indicating exceptionally weak electron-phonon
coupling. Our results demonstrate that the topological surface state is
protected not only from elastic scattering on impurities, but also from
scattering on low-energy phonons, suggesting that topological insulators could
serve as a basis for room temperature electronic devices.Comment: published version, 5 pages, 4 figure
Preliminary hidrological results from Sarennes glacier basin, French Alps
Located in the French Alps, Glacier de Sarennes is a small glacier which has its mass balance, measured since 1948. Now since 1992, the Snow Engineenng and Avalanche control department of Cemagref Grenoble measures water leve1 in the emissary of this glacier at the altitude of 2800 meters. The time step of these records is 10 minutes. The aim of this study is to realize the first hydrological assessment, despite having few records until now, to be able to control the new experimental discharge station, and to extract the first scientific results
Preliminary hidrological results from Sarennes glacier basin, French Alps
Located in the French Alps, Glacier de Sarennes is a small glacier which has its mass balance, measured since 1948. Now since 1992, the Snow Engineenng and Avalanche control department of Cemagref Grenoble measures water leve1 in the emissary of this glacier at the altitude of 2800 meters. The time step of these records is 10 minutes. The aim of this study is to realize the first hydrological assessment, despite having few records until now, to be able to control the new experimental discharge station, and to extract the first scientific results
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