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

DD-modules, Bernstein-Sato polynomials and FF-invariants of direct summands

We study the structure of $D$-modules over a ring $R$ which is a direct summand of a polynomial or a power series ring $S$ with coefficients over a field. We relate properties of $D$-modules over $R$ to $D$-modules over $S$. We show that the localization $R_f$ and the local cohomology module $H^i_I(R)$ have finite length as $D$-modules over $R$. Furthermore, we show the existence of the Bernstein-Sato polynomial for elements in $R$. In positive characteristic, we use this relation between $D$-modules over $R$ and $S$ to show that the set of $F$-jumping numbers of an ideal $I\subseteq R$ is contained in the set of $F$-jumping numbers of its extension in $S$. As a consequence, the $F$-jumping numbers of $I$ in $R$ form a discrete set of rational numbers. We also relate the Bernstein-Sato polynomial in $R$ with the $F$-thresholds and the $F$-jumping numbers in $R$.Comment: 24 pages. Comments welcome

El nou mecanisme de dosificació

Premis Pharmanews-Fedefarma 2016Des de temps immemorials, l'estudi de la cinètica dels fàrmacs dins de l'organisme ha estat i és un dels problemes principals ja que cada substància 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 majoritàriament serà la ineficàcia del fàrmac ja que el pacient, en principi, no desenvoluparà cap resposta. En un cas de sobredosificació, es pot comprometre la salut del pacient