Mori dream spaces

We explore the circle of ideas connecting finite generation of the Cox ring, Mori dream spaces and invariant theory.     

Thermochemistry of Binding of Lead(II) and Cadmium(II) by Saccharides in Aqueous Solution

Solution calorimetry was used to determine enthalpies and stability constants for binding of lead(II) or cadmium(II) by galacturonic acid and several monosaccharides in aqueous solution. New values for enthalpies of solution in water are reported for galacturonic acid and maltose monohydrate. The interaction of water solvent with the reactants is the largest factor in the binding process.     

On the local behavior of certain homeomorphisms. II

In the previous paper by the authors, it is shown that a sense-preserving homeomorphism, absolutely continuous on lines (ACL), under certain integral conditions on the complex dilation is conformal at a point. This result includes the Teichmüller-Wittich-Belinski theorem. In the present paper, it is shown that under weakened conditions the local behavior of such a homeomorphism is similar to that of a quasiconformal mapping. Bibliography: 2 titles.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 237, 1997, pp. 11–20.Dedicated to the 90th anniversary of G. M. Goluzin's birth.     

Riemann-Roch-Grothendieck and torsion for foliations

In this article we prove a Riemann-Roch-Grothendieck theorem for the characteristic classes of a flat vector bundle over a foliation whose graph is Hausdorff. We assume that the strong foliation Novikov-Shubin invariants of the flat bundle are greater than three times the codimension of the foliation. Using transgression, we define a torsion form which in the odd acyclic case determines a Haefliger cohomology class which only depends on the foliation and the flat bundle. We construct examples where this torsion class is highly non-trivial.     

A uniqueness result concerning Schur ideals

A subset of the set of all positive semi-definite matrices of a given size which is invariant under Schur (componentwise) multiplication by an arbitrary positive semi-definite matrix is said to be a Schur ideal. A subset of -dimensional complex space is said to be if it arises as the set of possible values arising from restricting contractive elements from some uniform algebra to a finite set in the domain. When the uniform algebra is the disk algebra, the hyperconvex set is said to be a Pick body. Motivated by the classical Pick interpolation theorem, Paulsen has introduced a natural notion of duality between Schur ideals and hyperconvex sets. By using some recently developed results in operator algebras (matricial Schur ideals), we show that each Pick body has a unique affiliated Schur ideal.

     

The irreducibility of some level 1 Hecke polynomials

Let be the characteristic polynomial of the Hecke operator acting on the space of level 1 cusp forms . We show that is irreducible and has full Galois group over  for and ,  prime.

     

Application of an acoustic backscatter technique for characterizing the roughness of porous soil

An acoustic backscatter technique proposed by Oelze et al. [J. Acoust. Soc. Am. 109, 1826-1832 (2001)] was used to characterize the roughness of porous soil surfaces. Roughness estimation errors are minimized when the effective flow resistivity of the porous soil is high, e.g., above 300,000 mks Rayls/m. Four soil plots were constructed by roughening soil with farming implements. Three plots were sealed using Saran powder dissolved in methyl ethyl ketone (MEK) and then covered to prevent further weathering. A fourth plot was left in the open and exposed to rainfall, which also acted to seal the surface and further change the roughness. In sealing the surface the effective flow resistivity of the surface was increased above 300,000 mks Rayls/m, which is typical for weathered agricultural surfaces. The roughness power spectra of the soil surfaces were measured by acoustic backscatter and alternatively by a laser profiler. Regression analysis was used to approximate each roughness power spectrum versus roughness wave number with a best-fit line. The best-fit line was used to calculate the rms height and the correlation length of the rough surface by integrating the approximate roughness power spectrum over a range of roughness wave number values. The range of roughness wave number values defines the roughness length scales used in the statistical calculations. High-roughness wave numbers correspond to smaller length scales of roughness and low-roughness wave numbers correspond to larger length scales of roughness. Over certain ranges of roughness wave number values the statistics from the acoustic backscatter and laser profiler measurements is in good agreement. However, as the low-cutoff roughness wave number is decreased and the high-cutoff roughness wave number is increased, agreement between the laser and acoustic techniques diminishes.