Homology of homogeneous divisors

This work deals with arbitrary reduced free divisors in a polynomial ring over a field of characteristic zero, by stressing the ideal theoretic and homological behavior of the corresponding singular locus. A particular emphasis is given to both weighted homogeneous and homogeneous polynomials, allowing to introduce new families of free divisors not coming from either hyperplane arrangements or discriminants in singularity theory.     

The equations of almost complete intersections

In this paper we inject four Hilbert functions in the determination of the defining equations of the Rees algebra of almost complete intersections of finite co-length. Because three of the corresponding modules are Artinian, some of these relationships are very effective, with the novel approach opening up tracks to the determination of the equations and also to processes of going from homologically defined sets of equations to higher degrees ones. While not specifically directed towards the extraction of elimination equations, it will show how some of these arise naturally.     

Smooth Surjections Without Surjective Restrictions

Let f:E→F be a surjective mapping between two real or complex Banach spaces, with f having some strong differentiability properties. We investigate when there is a smaller Banach space G?E such that the restriction of f to G remains surjective.     

Use of central-field potentials for describing H2(D2) elastic scattering by other molecules

Differential elastic scattering cross sections have been measured for the systems H₂ + O₂, SF₆, NH₃, CO and CH₄ and for D₂ + O₂, SF₆, and NH₃ using crossed molecular beams. These experiments represent a wide variation in the size, anisotropy and initial relative collision energy E of the scattering partners, and of the corresponding de Broglie wavelengths. In all cases, rapid quantum oscillations have been resolved. From these differential cross sections, central-field potentials have been obtained which were independent of the energy and the isotopic composition of the hydrogen molecule used, as required for such potentials to be physically meaningful. Therefore, anisotropy effects do not seem important in describing the differential elastic scattering of these H₂(D₂) systems.     

A potential tool for high-resolution monitoring of ocean acidification

Current anthropogenic carbon dioxide emissions generate besides global warming unprecedented acidification rates of the oceans. Recent evidence indicates the possibility that ocean acidification and low oceanic pH may be a major reason for several mass extinctions in the past. However, a major bottleneck for research on ocean acidification is long-term monitoring and the collection of consistent high-resolution pH measurements. This study presents a low-power (<1 W) small sample volume (25 μL) semiconductor based fluorescence method for real-time ship-board pH measurements at high temporal and spatial resolution (approximately 15 s and 100 m between samples). A 405 nm light emitting diode and the blue and green channels from a digital camera was used for swift detection of fluorescence from the pH sensitive dye 6,8-Dihydroxypyrene-1,3-disulfonic acid in real-time. Main principles were demonstrated by automated continuous measurements of pH in the surface water across the Baltic Sea and the Kattegat region with a large range in salinity (∼3–30) and temperature (∼0–25 °C). Ship-board precision of salinity and temperature adjusted pH measurements were estimated as low as 0.0001 pH units.     

ChemInform Abstract: Polymorph Engineering of TiO2: Demonstrating How Absolute Reference Potentials Are Determined by Local Coordination.

A multiscale quantum‐chemical approach is used for examining the electronic structure of eight known TiO₂ polymorphs and aligning their ionization potential and electron affinity relative to an absolute energy reference.