Randomized UMD Banach spaces and decoupling inequalities for stochastic integrals

In this paper we prove the equivalence of decoupling inequalities for stochastic integrals and one-sided randomized versions of the UMD property of a Banach space as introduced by Garling.

     

Nitroxyl free radical binding to Si(1 0 0): a combined scanning tunneling microscopy and computational modeling study

The ultra-high vacuum scanning tunneling microscope (UHV-STM) was used to investigate the addition of the 2,2,6,6-tetramethyl-1-piperidinyloxy (TEMPO) radical to the Si(1 0 0) surface. Room temperature studies performed on clean Si(1 0 0)-2 × 1 confirm the proposed binding of the unpaired valence electron associated with the singly occupied molecular orbital (SOMO) of the molecule with a Si dangling bond. A strong bias dependence in the topography of isolated molecules was observed in the range of −2.0 to +2.5 V. Semiempirical and density functional calculations of TEMPO bound to a three-dimer silicon cluster model yield occupied state density isosurfaces below the highest occupied (HOMO) and unoccupied state densities isosurfaces above the lowest unoccupied molecular orbital (LUMO) which trend in qualitative agreement with the bias dependent STM topography. Furthermore, the placement of TEMPO molecules on dangling bonds was controlled with atomic precision on the monohydride Si(1 0 0) surface via electron stimulated desorption of H, demonstrating the compatibility of nitroxyl free radical binding chemistries with nanopatterning techniques such as feedback controlled lithography.     

Quasiperiodic motions in superquadratic time-periodic potentials

It is shown that for a large class of potentials on the line with superquadratic growth at infinity and with the additional time-periodic dependence all possible motions under the influence of such potentials are bounded for all time and that most (in a precise sense) motions are in fact quasiperiodic. The class of potentials includes, as very particular examples, the exponential, polynomial and much more. This extends earlier results and gives an answer to a problem posed by Littlewood in the mid 1960's. Along the way machinery is developed for estimating the action-angle transformation directly in terms of the potential and also some apparently new identities involving singular integrals are derived.     

The Hard Lefschetz Theorem and the topology of semismall maps

A line bundle on a complex projective manifold is said to be lef if one of its powers is globally generated and defines a semismall map in the sense of Goresky-MacPherson. As in the case of ample bundles the first Chern class of lef line bundles satisfies the Hard Lefschetz Theorem and the Hodge-Riemann Bilinear Relations. As a consequence, we prove a generalization of the Grauert contractibility criterion: the Hodge Index Theorem for semismall maps, Theorem 2.4.1. For these maps the Decomposition Theorem of Beilinson, Bernstein and Deligne is equivalent to the non-degeneracy of certain intersection forms associated with a stratification. This observation, joint with the Hodge Index Theorem for semismall maps gives a new proof of the Decomposition Theorem for the direct image of the constant sheaf. A new feature uncovered by our proof is that the intersection forms involved are definite.     

A note on theβ-measure for digraph competitions

Digraph games are cooperative TU-games associated to digraph competitions: domination structures that can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles for a group of individuals within the framework of social choice theory. Brink and Gilles (2000) defined theβ-measure of a digraph competition as the Shapley value of the corresponding digraph game. This paper provides a new characterization of theβ-measure.     

Aggregation effects in maximum covering models

The level of aggregation is critical in discrete location analyses as it affects the level of data collection required, computation times and the usefulness of the analyses. We examine the effects of three alternative nodal aggregation schemes on (i) the model's solution times, (ii) the locational decisions indicated by the maximum covering model, (iii) the coverage provided by the aggregate solutions compared with the optimal solutions, and (iv) the coverage predicted by the aggregate model compared with the coverage that results from using the aggregate model's facility sites and the disaggregate demands. The results suggest that considerable aggregation can be tolerated without incurring large errors in total coverage, but that location errors are introduced at moderate levels of aggregation. The magnitude of these errors is significantly affected by the aggregation scheme employed.     

Optimal bounds for ratios of eigenvalues of one-dimensional Schrödinger operators with Dirichlet boundary conditions and positive potentials

Consider the Schrödinger equation –u+V(x)u=u on the intervalI, whereV(x)0 forxI and where Dirichlet boundary conditions are imposed at the endpoints ofI. We prove the optimal bound

Quantification of copper and zinc species fractions in legume seeds extracts by SEC/ICP-MS: validation and uncertainty estimation

Fractions of Cu and Zn species in legume samples (common white bean, pea, chick pea and lentil seeds and defatted soybean flour) were analysed by on-line hyphenation of size exclusion chromatography and inductively coupled plasma-mass spectrometry. Samples were extracted by 0.02 mol l⁻¹ Tris–HCl buffer solution, pH 7.5. The extraction efficiency lay in the region 60–90 and 60–80% for Cu and Zn, respectively. Quantification of elements in the individual chromatographic fractions was carried out by isotope dilution (ID) and external calibration (EC) techniques. For ID analysis the chromatographic effluent was mixed with the flow of ⁶⁵Cu and ⁶⁸Zn isotope enriched solution and the isotope ratio values ⁶³Cu/⁶⁵Cu and (⁶⁴Zn+⁶⁶Zn)/⁶⁸Zn were measured. In the case of EC technique calibration solutions of elements were injected to the flow of mobile phase by the second injector. Prior entering detector the effluent was mixed with the flow of internal standard solution (In, 50 μg l⁻¹). Both methods have similar precision, however the behaviour of both studied elements was not the same. The chromatographic analysis itself was the main source of variability in the case of Cu. For Zn species analysis, the extraction process and the manipulation with the extract, played the significant role too. It was probably caused by lower stability of the present zinc chelates. The total amounts of Zn found in all chromatographic fractions represented 85–95% of Zn in sampled extract whereas those of Cu approached 100%. In case of small peaks the results of ID and EC were not the same. The EC results were lower then ID results. The great deal of results uncertainty accounts for the precision.