Linear resolutions of powers and products

The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms and Borel fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi deformation

Absolutely Koszul algebras and the Backelin-Roos property

We study absolutely Koszul algebras, Koszul algebras with the Backelin-Roos property and their behavior under standard algebraic operations. In particular, we identify some Veronese subrings of polynomial rings that have the Backelin-Roos property and conjecture that the list is indeed complete. Among other things, we prove that every universally Koszul ring defined by monomials has the Backelin-Roos property

Cynoglossum clandestinum Desf. (Boraginaceae), a new especies for the flora of the Catalan Countries

Es dóna a conèixer una localitat nova de Cynoglossum clandestinum Desf. a la comarca de la Vall d’Albaida, que representa una novetat per a la flora dels Països Catalans. Es realitzen comentaris sobre els caràcters morfològics, l’hàbitat i l’estat de conservació. Es discuteix també sobre la seva inclusió en alguna de les categories del Decret 70/2009, que inclou el «Catàleg Valencià d’Espècies de Flora Amenaçada».Cynoglossum clandestinum Desf. has been found in Catalan Countries for the first time. Several comments on the morphological characterization, the habitat and the convervation estatus are reported. We discussed about the need to include it in the Decree 70/2009, in which includes the “Valencian Catalogue of Threatened Plant Species”

Cynoglossum clandestinum Desf. (Boraginaceae), una espècie nova per a la flora dels Països Catalans

Es dóna a conèixer una localitat nova de Cynoglossum clandestinum Desf. a la comarca de la Vall d'Albaida, que representa una novetat per a la flora dels Països Catalans. Es realitzen comentaris sobre els caràcters morfològics, l'hàbitat i l'estat de conservació. Es discuteix també sobre la seva inclusió en alguna de les categories del Decret 70/2009, que inclou el «Catàleg Valencià d'Espècies de Flora Amenaçada».Cynoglossum clandestinum Desf. has been found in Catalan Countries for the first time. Several comments on the morphological characterization, the habitat and the convervation estatus are reported. We discussed about the need to include it in the Decree 70/2009, in which includes the "Valencian Catalogue of Threatened Plant Species"

Suggestive hypothesis on a case report: Patient presenting with cyclical ovarian cysts coupled to increased cholestatic enzymes

We describe the case of a childbearing-age woman presenting with spontaneous recurrent functional ovarian cysts and, more interestingly, chronic and asymptomatic elevation of cholestatic parameters. The patient showed no history of chronic viral infections, immunological and metabolic disorders, alcohol abuse and environmental toxins exposition. Hepatic ultrasonography and cholangio-pancreatography-magnetic-resonance excluded any morphological and structural abnormalities, while liver biopsy evidenced only minimal and not specific features of inflammation. Cholestasis indices obtained prompt recovery after each cycle of synthetic hormone therapy, implanted to treat functional ovarian cysts. She has continuously experienced the off-therapy asynchronous recurrence of liver laboratory abnormalities and functional ovarian cysts. The favorable effect of the synthetic hormone therapy to obtaining a stable recovery of this unexplained long-lasting cholestatic syndrome could be likely explained by downregulation of an endogenous ovarian overproduction, although estrogen-regulated local intracellular transduction pathways cannot be excluded

Brillouin light scattering study of Co2_{2}Cr0.6_{0.6}Fe0.4_{0.4}Al and Co2_{2}FeAl Heusler compounds

The thermal magnonic spectra of Co$_{2}$Cr$_{0.6}$Fe$_{0.4}$Al (CCFA) and Co$_2$FeAl were investigated using Brillouin light scattering spectroscopy (BLS). For CCFA, the exchange constant A (exchange stiffness D) is found to be 0.48 $\mu$erg/cm (203 meV A$^2$), while for Co$_2$FeAl the corresponding values of 1.55 $\mu$erg/cm (370 meV A$^2$) were found. The observed asymmetry in the BLS spectra between the Stokes and anti-Stokes frequencies was assigned to an interplay between the asymmetrical profiles of hybridized Damon-Esbach and perpendicular standing spin-wave modes, combined with the optical sensitivity of the BLS signal to the upper side of the CCFA or Co$_2$FeAl film

Towards an on-chip platform for the controlled application of forces via magnetic particles: A novel device for mechanobiology

In-vitro tests and analyses are of fundamental importance for investigating biological mechanisms in cells and bio-molecules. The controlled application of forces to activate specific bio-pathways and investigate their effects, mimicking the role of the cellular environment, is becoming a prominent approach in this field. In this work, we present a non-invasive magnetic on-chip platform which allows for the manipulation of magnetic particles, through micrometric magnetic conduits of Permalloy patterned on-chip. We show, from simulations and experiments, that this technology permits to exert a finely controlled force on magnetic beads along the chip surface. This force can be tuned from few to hundreds pN by applying a variable external magnetic field

Deterministically Computing Reduction Numbers of Polynomial Ideals

We discuss the problem of determining reduction number of a polynomial ideal I in n variables. We present two algorithms based on parametric computations. The first one determines the absolute reduction number of I and requires computation in a polynomial ring with (n-dim(I))dim(I) parameters and n-dim(I) variables. The second one computes via a Grobner system the set of all reduction numbers of the ideal I and thus in particular also its big reduction number. However,it requires computations in a ring with n.dim(I) parameters and n variables.Comment: This new version replaces the earlier version arXiv:1404.1721 and it has been accepted for publication in the proceedings of CASC 2014, Warsaw, Polna