On the structure theory of the Iwasawa algebra of a p-adic Lie group

This paper is motivated by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa algebra, i.e. the completed group algebra, Λ of a p-adic analytic group G. For G without any p-torsion element we prove that Λ is an Auslander regular ring. This result enables us to give a good definition of the notion of a pseudo-nullΛ-module. This is classical when G=ℤ ^k _p for some integer k≥1, but was previously unknown in the non-commutative case. Then the category of Λ-modules up to pseudo-isomorphisms is studied and we obtain a weak structure theorem for the ℤ _p -torsion part of a finitely generated Λ-module. We also prove a local duality theorem and a version of Auslander-Buchsbaum equality. The arithmetic applications to the Iwasawa theory of abelian varieties are published elsewhere. Received May 12, 2001 / final version received July 5, 2001?Published online September 3, 2001     

Occupational and consumer risk estimates for nanoparticles emitted by laser printers

Several studies have reported laser printers as significant sources of nanosized particles (<0.1 μm). Laser printers are used occupationally in office environments and by consumers in their homes. The current work combines existing epidemiological and toxicological evidence on particle-related health effects, measuring doses as mass, particle number and surface area, to estimate and compare the potential risks in occupational and consumer exposure scenarios related to the use of laser printers. The daily uptake of laser printer particles was estimated based on measured particle size distributions and lung deposition modelling. The obtained daily uptakes (particle mass 0.15–0.44 μg d⁻¹; particle number 1.1–3.1 × 10⁹ d⁻¹) were estimated to correspond to 4–13 (mass) or 12–34 (number) deaths per million persons exposed on the basis of epidemiological risk estimates for ambient particles. These risks are higher than the generally used definition of acceptable risk of 1 × 10⁻⁶, but substantially lower than the estimated risks due to ambient particles. Toxicological studies on ambient particles revealed consistent values for lowest observed effect levels (LOELs) which were converted into equivalent daily uptakes using allometric scaling. These LOEL uptakes were by a factor of about 330–1,000 (mass) and 1,000–2,500 (particle surface area) higher than estimated uptakes from printers. This toxicological assessment would indicate no significant health risks due to printer particles. Finally, our study suggests that particle number (not mass) and mass (not surface area) are the most conservative risk metrics for the epidemiological and toxicological risks presented here, respectively.     

A Range Condition for Polyconvex Variational Regularization

In the context of convex variational regularization, it is a known result that, under suitable differentiability assumptions, source conditions in the form of variational inequalities imply range conditions, while the converse implication only holds under an additional restriction on the operator. In this article, we prove the analogous result for polyconvex regularization. More precisely, we show that the variational inequality derived by the authors in 2017 implies that the derivative of the regularization functional must lie in the range of the dual-adjoint of the derivative of the operator. In addition, we show how to adapt the restriction on the operator in order to obtain the converse implication.     

Additivity of the two-dimensional Miller ideal

Let J (\mathbb M²){{\mathcal J}\,(\mathbb M^2)} denote the σ-ideal associated with two-dimensional Miller forcing. We show that it is relatively consistent with ZFC that the additivity of J (\mathbb M²){{\mathcal J}\,(\mathbb M^2)} is bigger than the covering number of the ideal of the meager subsets of ^ω ω. We also show that Martin’s Axiom implies that the additivity of J (\mathbb M²){{\mathcal J}\,(\mathbb M^2)} is 2 ^ω .Finally we prove that there are no analytic infinite maximal antichains in any finite product of \mathfrakP(w)/fin{\mathfrak{P}{(\omega)}/{\rm fin}} .     

Seasonal changes of Rubisco content and activity in Fagus sylvatica and Picea abies affected by elevated CO2 concentration

We studied Rubisco (ribulose-1,5-bisphosphate carboxylase/oxygenase) content and activity in juvenile tree species ?? broadleaved Fagus sylvatica L. and coniferous Picea abies (L.) Karsten exposed for three growing seasons to ambient (A = 385 ??mol mol^?1) and elevated (E = 700 ??mol mol^?1) CO₂ concentrations. Rubisco content was determined by the SDS-PAGE method, Rubisco activity was assayed spectrophotometrically. The highest content of Rubisco enzyme in F. sylvatica was measured immediately after full leaf development followed by a gradual decrease throughout the growing season. By contrast, Rubisco content in P. abies increased markedly during the growing season. In both tree species, down-regulation of Rubisco content in trees cultivated under elevated CO₂ concentration was observed. Rubisco activity was stimulated in F. sylvatica by E treatment but not in P. abies. Because no significant differences were found in Rubisco activation state between A and E, we assume that stimulation of Rubisco activity in E is not a consequence of higher carbamylation but could be caused by the release of inhibitors from active sites of Rubisco under elevated CO₂.     

Quinolizidine alkaloids and phomopsins in lupin seeds and lupin containing food

In recent years there has been growing interest in replacing (genetically modified) soya by lupin. Lupin seeds, flours and lupin containing food have been analyzed in order to assess the relevance of a potential health hazard given by mycotoxins and/or naturally occurring alkaloids. Since not all important alkaloids used for quantitation were commercially available, isolation of lupanine, 13alpha-hydroxylupanine and angustifoline from lupin flours of high alkaloid contents was performed. Alkaloids were analyzed by GC-MS/GC-FID in parallel, while the phomopsin mycotoxins were analyzed by ELISA, since chromatographic methods were not sensitive enough and required time-consuming sample cleanup. The analyzed lupin containing foods were free of phomopsins. In foods where lupin was only a minor constituent the alkaloid content was of no concern. However, roasted lupin beans intended as coffee surrogate had alkaloid contents close to the Australian intervention limit of 200 microg/g.     

Case studies of CSEARCH supported structure elucidation strategies: lupeol and a new germacrane derivative

The NMR based structure elucidation of secondary natural products can be supported by the CSEARCH database system. In the case of the triterpene lupeol the correct identification was performed without further experiments. The structure proposal for the new germacrane derivate hydroxygermacrene-D was proven by isomer generation and subsequent ranking of the eight isomers obtained by weighted spectrum estimation.     

The GL2 Main Conjecture for Elliptic Curves without Complex Multiplication

Let G be a compact p-adic Lie group, with no element of order p, and having a closed normal subgroup H such that G/H is isomorphic to Z_p. We prove the existence of a canonical Ore set S^* of non-zero divisors in the Iwasawa algebra Λ(G) of G, which seems to be particularly relevant for arithmetic applications. Using localization with respect to S^*, we are able to define a characteristic element for every finitely generated Λ(G)-module M which has the property that the quotient of M by its p-primary submodule is finitely generated over the Iwasawa algebra of H. We discuss the evaluation of this characteristic element at Artin representations of G, and its relation to the G-Euler characteristics of the twists of M by such representations. Finally, we illustrate the arithmetic applications of these ideas by formulating a precise version of the main conjecture of Iwasawa theory for an elliptic curve E over Q, without complex multiplication, over the field F generated by the coordinates of all its p-power division points; here p is a prime at least 5 where E has good ordinary reduction, and G is the Galois group of F over Q.     

Ramsey and Freeness Properties of Polish Planes

Suppose that X is a Polish space which is not -compact. We provethat for every Borel colouring of X² by countably many colours,there exists a monochromatic rectangle with both sides closedand not -compact. Moreover, every Borel colouring of [X]² byfinitely many colours has a homogeneous set which is closedand not -compact. We also show that every Borel measurable functionf:X² X has a free set which is closed and not -compact. Ascorollaries of the proofs we obtain two results: firstly, theproduct forcing of two copies of superperfect tree forcing doesnot add a Cohen real, and, secondly, it is consistent with ZFCto have a closed subset of the Baire space which is not -compactand has the property that, for any three of its elements, noneof them is constructible from the other two. A similar proofshows that it is consistent to have a Laver tree such that noneof its branches is constructible from any other branch. Thelast four results answer questions of Goldstern and Brendle.2000 Mathematics Subject Classification: 03E15, 26B99, 54H05.     

Symbolic Computation for Moments and Filter Coefficients of Scaling Functions

Algebraic relations between discrete and continuous moments of scaling functions are investigated based on the construction of Bell polynomials. We introduce families of scaling functions which are parametrized by moments. Filter coefficients of scaling functions and wavelets are computed with computer algebra methods (in particular Gröbner bases) using relations between moments. Moreover, we propose a novel concept for data compression based on parametrized wavelets.Received December 15, 2003