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

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

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

Fast-Gated 16 x 16 SPAD Array With 16 on-Chip 6 ps Time-to-Digital Converters for Non-Line-of-Sight Imaging

We present the design and characterization of a fully-integrated array of 16 x 16 Single-Photon Avalanche Diodes (SPADs) with fast-gating capabilities and 16 on-chip 6 ps time-to-digital converters, which has been embedded in a compact imaging module. Such sensor has been developed for Non-Line-Of-Sight imaging applications, which require: i) a narrow instrument response function, for a centimeter-accurate single-shot precision; ii) fast-gated SPADs, for time-filtering of directly reflected photons; iii) high photon detection probability, for acquiring faint signals undergoing multiple scattering events. Thanks to a novel multiple differential SPAD-SPAD sensing approach, SPAD detectors can be swiftly activated in less than 500 ps and the full-width at half maximum of the instrument response function is always less than 75 ps (60 ps on average). Temporal responses are consistently uniform throughout the gate window, showing just few picoseconds of time dispersion when 30 ns gate pulses are applied, while the differential non-linearity is as low as 250 fs. With a photon detection probability peak of 70% at 490 nm, a fill-factor of 9.6% and up to 1.6 . 10(8) photon time-tagging measurements per second, such sensor fulfills the demand for fully-integrated imaging solutions optimized for non-line-of-sight imaging applications, enabling to cut exposure times while also optimizing size, weight, power and cost, thus paving the way for further scaled architectures

Magnetic tunneling junctions with the Heusler compound Co_2Cr_{0.6}Fe_{0.4}Al

The Heusler alloy is used as an electrode of magnetic tunneling junctions. The junctions are deposited by magnetron dc sputtering using shadow mask techniques with AlO_{x} as a barrier and cobalt as counter electrode. Measurements of the magnetoresistive differential conductivity in a temperature range between 4K and 300K are shown. An analysis of the barrier properties applying the Simmons model to the bias dependent junction conductivity is performed. VSM measurements were carried out to examine the magnetic properties of the samples.Comment: 3 pages, 3 figures submitted to JMMM (proceedings of JEMS04

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