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

Epitaxial Co2Cr0.6Fe0.4Al thin films and magnetic tunneling junctions

Epitaxial thin films of the theoretically predicted half metal Co2Cr0.6Fe0.4Al were deposited by dc magnetron sputtering on different substrates and buffer layers. The samples were characterized by x-ray and electron beam diffraction (RHEED) demonstrating the B2 order of the Heusler compound with only a small partition of disorder on the Co sites. Magnetic tunneling junctions with Co2Cr0.6Fe0.4Al electrode, AlOx barrier and Co counter electrode were prepared. From the Julliere model a spin polarisation of Co2Cr0.6Fe0.4Al of 54% at T=4K is deduced. The relation between the annealing temperature of the Heusler electrodes and the magnitude of the tunneling magnetoresistance effect was investigated and the results are discussed in the framework of morphology and surface order based of in situ STM and RHEED investigations.Comment: accepted by J. Phys. D: Appl. Phy

On the symbolic powers of binomial edge ideals

We show that under some conditions, if the initial ideal in$_<(I)$ of an ideal $I$ in a polynomial ring has the property that its symbolic and ordinary powers coincide, then the ideal $I$ shares the same property. We apply this result to prove the equality between symbolic and ordinary powers for binomial edge ideals with quadratic Gr\"obner basis

Asymptotics for models of non-stationary diffusion in domains with a surface distribution of obstacles

We consider a time-dependent model for the diffusion of a substance through an incompressible fluid in a perforated domain ??, urn:x-wiley:mma:media:mma5323:mma5323-math-0001 with n?=?3,4. The fluid flows in a domain containing a periodical set of ?obstacles? (?\??) placed along an inner (n???1)?dimensional manifold urn:x-wiley:mma:media:mma5323:mma5323-math-0002. The size of the obstacles is much smaller than the size of the characteristic period ?. An advection term appears in the partial differential equation linking the fluid velocity with the concentration, while we assume a nonlinear adsorption law on the boundary of the obstacles. This law involves a monotone nonlinear function ? of the concentration and a large adsorption parameter. The ?critical adsorption parameter? depends on the size of the obstacles , and, for different sizes, we derive the time?dependent homogenized models. These models contain a ?strange term? in the transmission conditions on ?, which is a nonlinear function and inherits the properties of ?. The case in which the fluid velocity and the concentration do not interact is also considered for n???3.The authors would like to thank the anonymous referees for their careful reading of the manupscript and useful comments. The work has been partially supported by MINECO, MTM2013-44883-P

Powers of componentwise linear ideals

We give criteria for graded ideals to have the property that all their powers are componentwise linear. Typical examples to which our criteria can be applied include the vertex cover ideals of certain finite graphs

Insights into the Structure of Dot@Rod and Dot@Octapod CdSe@CdS Heterostructures

CdSe@CdS dot@rods with diameter around 6 nm and length of either 20, 27, or 30 nm and dot@octapods with pod diameters of ?15 nm and lengths of ?50 nm were investigated by X-ray absorption spectroscopy. These heterostructures are prepared by seed-mediated routes, where the structure, composition, and morphology of the CdSe nanocrystals used as a seed play key roles in directing the growth of the second semiconducting domain. The local structural environment of all the elements in the CdSe@CdS heterostructures was investigated at the Cd, S, and Se K-edges by taking advantage of the selectivity of X-ray absorption spectroscopy, and was compared to pure reference compounds. We found that the structural features of dot@rods are independent of the size of the rods. These structures can be described as made of a CdSe dot and a CdS rod, both in the wurtzite phase with a high crystallinity of both the core and the rod. This result supports the effectiveness of high temperature colloidal synthesis in promoting the formation of core@shell nanocrystals with very low defectivity. On the other hand, data on the CdSe@CdS with octapod morphology suggest the occurrence of a core composed of a CdSe cubic sphalerite phase with eight pods made of CdS wurtzite phase. Our findings are compared to current models proposed for the design of functional heterostructures with controlled nanoarchitecture

Seasonal and interannual variability of the surface circulation in the eastern Gulf of Cadiz (SW Iberia)

11 páginas, 6 figuras, 1 tabla.An 11-year (1996–2007) time series of current meter observations representative of the open sea circulation; a 4-year (2001–2005) time series of current meter records over the continental shelf and in situ data during different seasons have been compared in order to study the seasonal and interannual variability of the surface circulation in the eastern Gulf of Cadiz. The open sea velocity observations indicate southeastward flow along the northern continental slope of the Gulf of Cadiz, compatible with anticyclonic circulation, during most of the year and more intense during summer months. Flow reversals (northwestward circulation) at seasonal time scales in late autumn and early winter (preferably December and January) are a rather recurrent feature with variable intensity depending on the year. Anticyclonic circulation is associated with westerlies, whereas flow reversals usually take place under easterly episodes, suggesting wind-driven circulation. Negative North Atlantic Oscillation indices (indicative of southward displacement of the Azores high) are also linked to the reversals. Changes in this mainly wind-driven large-scale surface circulation are echoed by the shelf circulation: the coastal countercurrent that closes the mesoscale cyclonic cell over the eastern shelf in spring-summer (upwelling season) is replaced by and eastward current in autumn and winter.We acknowledge CANIGO (MAS3-PL95-0443) European-funded project and, particularly, Guillermo Díaz Del Río for CTD data and the UIB-IMEDEA (Special Action CICYT, REN2000-2599-E) for the software used for the optimal interpolation. Partial support from CTM2006–02326 (Ministry of Science and Technology) and P07-RNM-02938 (Junta de Andalucía) Spanish-funded projects and the Consejeria de Agricultura y Pesca of the Junta de Andalucia are also acknowledged.Peer reviewe