On the cotangent cohomology of rational surface singularities with almost reduced fundamental cycle

We prove dimension formulas for the cotangent spaces $T^{1}$ and $T^{2}$ for a class of rational surface singularities by calculating a correction term in the general dimension formulas. We get that it is zero if the dual graph of the rational surface singularity $X$ does not contain a particular type of configurations, and this generalizes a result of Theo de Jong stating that the correction term $c(X)$ is zero for rational determinantal surface singularities. In particular our result implies that $c(X)$ is zero for Riemenschneiders quasi-determinantal rational surface singularities, and this also generalise results for qoutient singularities.Comment: 11 pages, one figur

Lie-Rinehart cohomology and integrable connections on modules of rank one

Let $k$ be an algebraically closed field of characteristic 0, let $R$ be a commutative $k$-algebra, and let $M$ be a torsion free $R$-module of rank one with a connection $\nabla$. We consider the Lie-Rinehart cohomology with values in $End_{R}(M)$ with its induced connection, and give an interpretation of this cohomology in terms of the integrable connections on $M$. When $R$ is an isolated singularity of dimension $d\geq2$, we relate the Lie-Rinehart cohomology to the topological cohomology of the link of the singularity, and when $R$ is a quasi-homogenous hypersurface of dimension two, we give a complete computation of the cohomology.Comment: 13 page

Finite Approximations of Physical Models over Local Fields

We show that the Schr\"odinger operator associated with a physical system over a local field can be approximated in a very strong sense by finite Schr\"odinger operators. Some striking numerical results are included at the end of the article

Approximating cube roots of integers, after Heron's Metrica III.20

Heron, in Metrica III.20-22, is concerned with the the division of solid figures - pyramids, cones and frustra of cones - to which end there is a need to extract cube roots. We report here on some of our findings on the conjecture by Taisbak in C.M.Taisbak, Cube roots of integers. A conjecture about Heron's method in Metrika III.20. Historia Mathematica, 41 (2014), 103-104

The Effects of Internationalization on CEO Compensation

This study examines the relation between the internationalization of firms and CEO compensation. Starting from a sample of Norwegian and Swedish listed firms we analyze the effects of internationalization as manifest in the capital market (international cross-listing), the market for corporate control (foreign board membership), and the product and service market (export and foreign sales). We conclude that all three markets contribute positively to the compensation level of CEOs. We argue that part of the higher CEO compensation in internationally oriented firms - as compared to less internationalized firms within the same country - reflects a risk premium for reduction in job security.CEO Compensation; Internationalization; Corporate Governance; CEO Tenure; Cross-Listing; Foreign Board Membership

Phenotypic evolution studied by layered stochastic differential equations

Time series of cell size evolution in unicellular marine algae (division Haptophyta; Coccolithus lineage), covering 57 million years, are studied by a system of linear stochastic differential equations of hierarchical structure. The data consists of size measurements of fossilized calcite platelets (coccoliths) that cover the living cell, found in deep-sea sediment cores from six sites in the world oceans and dated to irregular points in time. To accommodate biological theory of populations tracking their fitness optima, and to allow potentially interpretable correlations in time and space, the model framework allows for an upper layer of partially observed site-specific population means, a layer of site-specific theoretical fitness optima and a bottom layer representing environmental and ecological processes. While the modeled process has many components, it is Gaussian and analytically tractable. A total of 710 model specifications within this framework are compared and inference is drawn with respect to model structure, evolutionary speed and the effect of global temperature.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS559 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Strategic Tax Competition; Implications of National Ownership

Two jurisdictions compete to capture the rents of a large multinational enterprise (MNE) which invests locally and which is partly owned by local investors. The MNE contributes to local welfare by tax payments and dividends, and it has private information about the efficiency of the operations in the two localisations. It is shown that the distortions in the MNE's real investment portfolio are determined by a trade-off between fiscal externalities and equity externalities, and that investments in the case of strategic tax competition may be lower than in the co-operative case. Ownership matters, and we show how the firm may reduce its overall tax payments by influencing the distribution of owner shares between investors in the two countries.Tax competition, mobility, common agency