564 research outputs found
Generating functions associated to Frobenius algebras
We introduce a generating function associated to the homogeneous generators
of a graded algebra that measures how far is this algebra from being finitely
generated. For the case of some algebras of Frobenius endomorphisms we describe
this generating function explicitly as a rational function.Comment: 15 pages. Published in Linear Algebra App
Computing the support of local cohomology modules
For a polynomial ring , we present a method to compute the
characteristic cycle of the localization for any nonzero polynomial that avoids a direct computation of as a -module. Based on this
approach, we develop an algorithm for computing the characteristic cycle of the
local cohomology modules for any ideal using the
\v{C}ech complex. The algorithm, in particular, is useful for answering
questions regarding vanishing of local cohomology modules and computing
Lyubeznik numbers. These applications are illustrated by examples of
computations using our implementation of the algorithm in Macaulay~2.Comment: 15 page
-modules, Bernstein-Sato polynomials and -invariants of direct summands
We study the structure of -modules over a ring which is a direct
summand of a polynomial or a power series ring with coefficients over a
field. We relate properties of -modules over to -modules over . We
show that the localization and the local cohomology module
have finite length as -modules over . Furthermore, we show the existence
of the Bernstein-Sato polynomial for elements in . In positive
characteristic, we use this relation between -modules over and to
show that the set of -jumping numbers of an ideal is
contained in the set of -jumping numbers of its extension in . As a
consequence, the -jumping numbers of in form a discrete set of
rational numbers. We also relate the Bernstein-Sato polynomial in with the
-thresholds and the -jumping numbers in .Comment: 24 pages. Comments welcome
On some local cohomology spectral sequences
We introduce a formalism to produce several families of spectral sequences
involving the derived functors of the limit and colimit functors over a finite
partially ordered set. The first type of spectral sequences involves the left
derived functors of the colimit of the direct system that we obtain applying a
family of functors to a single module. For the second type we follow a
completely different strategy as we start with the inverse system that we
obtain by applying a covariant functor to an inverse system. The spectral
sequences involve the right derived functors of the corresponding limit. We
also have a version for contravariant functors. In all the introduced spectral
sequences we provide sufficient conditions to ensure their degeneration at
their second page. As a consequence we obtain some decomposition theorems that
greatly generalize the well-known decomposition formula for local cohomology
modules given by Hochster.Comment: 63 pages, comments are welcome. To appear in International
Mathematics Research Notice
El nou mecanisme de dosificació
Premis Pharmanews-Fedefarma 2016Des de temps immemorials, l'estudi de la cinètica dels fà rmacs dins de l'organisme ha
estat i és un dels problemes principals ja que cada substà ncia té un perfil concret i és
complicat concloure patrons de comportament. Si no s'estudia correctament aquesta
cinètica, pot haver-hi infradosificació o sobredosificació. En el cas de la
infradosificació, el resultat majorità riament serà la ineficà cia del fà rmac ja que el
pacient, en principi, no desenvoluparà cap resposta. En un cas de sobredosificació, es
pot comprometre la salut del pacient
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