Analytic continuation of residue currents

Let $X$ be a complex manifold and f\colon X\to \C^p a holomorphic mapping defining a complete intersection. We prove that the iterated Mellin transform of the residue integral associated to $f$ has an analytic continuation to a neighborhood of the origin in \C^p

Basic Module Theory over Non-Commutative Rings with Computational Aspects of Operator Algebras

The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.Comment: To appear in the Proceedings of the AADIOS 2012 conference, to be published in Lecture Notes in Computer Scienc

A constructive study of the module structure of rings of partial differential operators

The purpose of this paper is to develop constructive versions of Stafford's theorems on the module structure of Weyl algebras A n (k) (i.e., the rings of partial differential operators with polynomial coefficients) over a base field k of characteristic zero. More generally, based on results of Stafford and Coutinho-Holland, we develop constructive versions of Stafford's theorems for very simple domains D. The algorithmization is based on the fact that certain inhomogeneous quadratic equations admit solutions in a very simple domain. We show how to explicitly compute a unimodular element of a finitely generated left D-module of rank at least two. This result is used to constructively decompose any finitely generated left D-module into a direct sum of a free left D-module and a left D-module of rank at most one. If the latter is torsion-free, then we explicitly show that it is isomorphic to a left ideal of D which can be generated by two elements. Then, we give an algorithm which reduces the number of generators of a finitely presented left D-module with module of relations of rank at least two. In particular, any finitely generated torsion left D-module can be generated by two elements and is the homomorphic image of a projective ideal whose construction is explicitly given. Moreover, a non-torsion but non-free left D-module of rank r can be generated by r+1 elements but no fewer. These results are implemented in the Stafford package for D=A n (k) and their system-theoretical interpretations are given within a D-module approach. Finally, we prove that the above results also hold for the ring of ordinary differential operators with either formal power series or locally convergent power series coefficients and, using a result of Caro-Levcovitz, also for the ring of partial differential operators with coefficients in the field of fractions of the ring of formal power series or of the ring of locally convergent power series. © 2014 Springer Science+Business Media

Global maps of soil temperature.

Research in global change ecology relies heavily on global climatic grids derived from estimates of air temperature in open areas at around 2 m above the ground. These climatic grids do not reflect conditions below vegetation canopies and near the ground surface, where critical ecosystem functions occur and most terrestrial species reside. Here, we provide global maps of soil temperature and bioclimatic variables at a 1-km <sup>2</sup> resolution for 0-5 and 5-15 cm soil depth. These maps were created by calculating the difference (i.e. offset) between in situ soil temperature measurements, based on time series from over 1200 1-km <sup>2</sup> pixels (summarized from 8519 unique temperature sensors) across all the world's major terrestrial biomes, and coarse-grained air temperature estimates from ERA5-Land (an atmospheric reanalysis by the European Centre for Medium-Range Weather Forecasts). We show that mean annual soil temperature differs markedly from the corresponding gridded air temperature, by up to 10°C (mean = 3.0 ± 2.1°C), with substantial variation across biomes and seasons. Over the year, soils in cold and/or dry biomes are substantially warmer (+3.6 ± 2.3°C) than gridded air temperature, whereas soils in warm and humid environments are on average slightly cooler (-0.7 ± 2.3°C). The observed substantial and biome-specific offsets emphasize that the projected impacts of climate and climate change on near-surface biodiversity and ecosystem functioning are inaccurately assessed when air rather than soil temperature is used, especially in cold environments. The global soil-related bioclimatic variables provided here are an important step forward for any application in ecology and related disciplines. Nevertheless, we highlight the need to fill remaining geographic gaps by collecting more in situ measurements of microclimate conditions to further enhance the spatiotemporal resolution of global soil temperature products for ecological applications

Evaluating and improving remembered sets in theHotSpot G1 garbage collector

In this master’s thesis project the remembered set implementation in Java HotSpot’s implementation of G1 is evaluated. It is verified by benchmarking that using Bloomfilters can reduce region scanning times when used as an intermediate data structure between card-precision bitmaps and region coarsening. It is shown that iterating the Bloomfilter is made faster by combining binary trees with the Bloom filters. It is also verified that using a more narrowinteger type, with an added bitmap to keep track of null entries, will decrease the memory footprint caused by remembered sets. Both modifications to the current implementation cause application through put regressions in SPECjbb2013.Utvärdering och förbättringar av remembered sets i Javamaskinen HotSpots skräpsamlare G1I det här examensarbetet undersöks implementationen av remembered sets i HotSpots implementation av skräpsamlingsalgoritmen G1. Det bekräftas genom prestandamätningar att användandet av Bloomfilter kan minska tidsåtgångenför regionsavsökning. Detta när Bloomfiltret används som en mellanliggande datastruktur mellan bitmappar på kortnivå och bitmappar på regionsnivå. Det bekräftas också genom prestandamätningar att iterering över Bloomfilter kan snabbas upp genom att kombinera filtret med ett binärt sökträd. Vidare visas det att användandet av en heltalstyp med mindre räckvidd, tillsammans med införandet av en bitmapp för att registrera nullvärden, kan minska minnesanvändningen som remembered sets medför. I den standardiserade prestandamätningen SPECjbb2013 medför båda förändringarna dock prestandaförsämringar

Averaging Residue Currents and the Stückrad–Vogel Algorithm

Trace formulas (Lagrange, Jacobi-Kronecker, Bergman-Weil) play a key role in division problems in analytic or algebraic geometry (including arithmetic aspects, see for example [10]). Unfortunately, they usually hold within the restricted frame of complete intersections. Besides the fact that it allows to carry local or semi global analytic problems to a global geometric setting (think about Crofton’s formula), averaging the Cauchy kernel (from C n \{z1... zn = 0} ⊂ P n (C)), in order to get the Bochner-Martinelli kernel (in C n+1 \ {0} ⊂ P n+1 (C) = C n+1 ∪ P n (C)), leads to the construction of explicit candidates for the realization of Grothendieck’s duality, namely BM residue currents ([27, 3, 6]), extending thus the cohomological incarnation of duality which appears in the complete intersection or Cohen-Macaulay cases. We will recall here such constructions and, in parallel, suggest how far one could take advantage of the multiplicative inductive construction introduced in [13] by N. Coleff and M. Herrera, by relating it to the Stückrad-Vogel algorithm developed in ([30],[31],[8]) towards improper intersection theory. Results presented here were initiated all along my long term collaboration with Carlos Berenstein. To both of us, the mathematical work of Leon Ehrenpreis certainly remained a constant and how much stimulating source of inspiration. This presentation relies also deeply on my collaboration with M. Andersson, H. Samuelsson and E. Wulcan in Göteborg, through the past years. 1 Coleff-Herrera residue currents for complete intersections and the Transformation Law Let X be a n-dimensional (ambient) complex manifold and V ⊂ X be