The K-theory of toric varieties in positive characteristic

We show that if X is a toric scheme over a regular ring containing a field then the direct limit of the K-groups of X taken over any infinite sequence of nontrivial dilations is homotopy invariant. This theorem was known in characteristic 0. The affine case of our result was conjectured by Gubeladze.Comment: Companion paper to arXiv:1106.138

Toric varieties, monoid schemes and cdhcdh descent

We give conditions for the Mayer-Vietoris property to hold for the algebraic K-theory of blow-up squares of toric varieties in any characteristic, using the theory of monoid schemes. These conditions are used to relate algebraic K-theory to topological cyclic homology in characteristic p. To achieve our goals, we develop for monoid schemes many notions from classical algebraic geometry, such as separated and proper maps.Comment: v2 changes: field of positive characteristic replaced by regular ring containing such a field at appropriate places. Minor changes in expositio

The Artinian Berger Conjecture

We propose an Artinian version of Berger's Conjecture for curves, concerning the module of K\"ahler differentials of an algebra. Our version implies Berger's Conjecture in characteristic 0. We establish our Artinian Berger Conjecture in a number of cases, and prove that Berger's Conjecture holds for curve singularities whose conductor ideal contains the cube of a maximal ideal.Departamento de Matemátic

Isotopic composition of stratospheric ozone

We present a kinetic calculation for the isotopic composition of stratospheric ozone. The calculated enrichments of ^(49)O_3 and ^(50)O_3 are in agreement with atmospheric measurements made at midlatitudes. Integrating the kinetic fractionation processes in the formation and photolysis of ozone, we obtain enrichments of ∼7.5–10.5 and ∼7.5–12.5% (referenced to atmospheric O_2) for δ^(49)O_3 and δ^(50)O_3, respectively, at altitudes between 20 and 35 km; the photolysis in the Hartley band of ozone is responsible for the observed altitude variation. The overall magnitude of the ozone enrichments (∼10%) is large compared with that commonly known in atmospheric chemistry and geochemistry. The heavy oxygen atom in ozone is therefore useful as a tracer of chemical species and pathways that involve ozone or its derived products. For example, the mass anomalies of oxygen in two greenhouse gases, CO_2 and N_2O, are likely the consequences of the transfer of heavy oxygen atoms from ozone

Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation

A novel multiscale mathematical and computational model of the pulmonary circulation is presented and used to analyse both arterial and venous pressure and flow. This work is a major advance over previous studies by Olufsen et al. (Ann Biomed Eng 28:1281–1299, 2012) which only considered the arterial circulation. For the first three generations of vessels within the pulmonary circulation, geometry is specified from patient-specific measurements obtained using magnetic resonance imaging (MRI). Blood flow and pressure in the larger arteries and veins are predicted using a nonlinear, cross-sectional-area-averaged system of equations for a Newtonian fluid in an elastic tube. Inflow into the main pulmonary artery is obtained from MRI measurements, while pressure entering the left atrium from the main pulmonary vein is kept constant at the normal mean value of 2 mmHg. Each terminal vessel in the network of ‘large’ arteries is connected to its corresponding terminal vein via a network of vessels representing the vascular bed of smaller arteries and veins. We develop and implement an algorithm to calculate the admittance of each vascular bed, using bifurcating structured trees and recursion. The structured-tree models take into account the geometry and material properties of the ‘smaller’ arteries and veins of radii ≥ 50 μ m. We study the effects on flow and pressure associated with three classes of pulmonary hypertension expressed via stiffening of larger and smaller vessels, and vascular rarefaction. The results of simulating these pathological conditions are in agreement with clinical observations, showing that the model has potential for assisting with diagnosis and treatment for circulatory diseases within the lung