Lattices from Hermitian function fields

We consider the well-known Rosenbloom-Tsfasman function field lattices in the special case of Hermitian function fields. We show that in this case the resulting lattices are generated by their minimal vectors, provide an estimate on the total number of minimal vectors, and derive properties of the automorphism groups of these lattices. Our study continues previous investigations of lattices coming from elliptic curves and finite Abelian groups. The lattices we are faced with here are more subtle than those considered previously, and the proofs of the main results require the replacement of the existing linear algebra approaches by deep results of Gerhard Hiss on the factorization of functions with particular divisor support into lines and their inverses

Lattice Theory and Toeplitz Determinants

This is a survey of our recent joint investigations of lattices that are generated by finite Abelian groups. In the case of cyclic groups, the volume of a fundamental domain of such a lattice is a perturbed Toeplitz determinant with a simple Fisher-Hartwig symbol. For general groups, the situation is more complicated, but it can still be tackled by pure matrix theory. Our main result on the lattices under consideration states that they always have a basis of minimal vectors, while our results in the other direction concern exact and asymptotic formulas for perturbed Toeplitz determinants. The survey is a slightly modified version of the talk given by the first author at the Humboldt Kolleg and the IWOTA in Tbilisi in 2015. It is mainly for operator theorists and therefore also contains an introduction to the basics of lattice theory

On Lattices Generated by Finite Abelian Groups

This paper is devoted to the study of lattices generated by finite Abelian groups. Special species of such lattices arise in the exploration of elliptic curves over finite fields. In the case where the generating group is cyclic, they are also known as the Barnes lattices. It is shown that for every finite Abelian group with the exception of the cyclic group of order four these lattices have a basis of minimal vectors. Another result provides an improvement of a recent upper bound by M. Sha for the covering radius in the case of the Barnes lattices. Also discussed are properties of the automorphism groups of these lattices

Toeplitz determinants with perturbations in the corners

This paper is devoted to exact and asymptotic formulas for the determinants of Toeplitz matrices with perturbations by blocks of fixed size in the four corners. If the norms of the inverses of the unperturbed matrices remain bounded as the matrix dimension goes to infinity, then standard perturbation theory yields asymptotic expressions for the perturbed determinants. This premise is not satisfied for matrices generated by so-called Fisher-Hartwig symbols. In that case we establish formulas for pure single Fisher-Hartwig singularities and for the Hermitian matrices induced by general Fisher-Hartwig symbols

Spherical 2-Designs and Lattices from Abelian Groups

We consider lattices generated by finite Abelian groups. The main result says that such a lattice is strongly eutactic, which means the normalized minimal vectors of the lattice form a spherical 2-design, if and only if the group is of odd order or if it is a power of the group of order 2. This result also yields a criterion for the appropriately normalized minimal vectors to constitute a uniform normalized tight frame

Lattices from tight equiangular frames

We consider the set of all linear combinations with integer coefficients of the vectors of a unit tight equiangular (k,n) frame and are interested in the question whether this set is a lattice, that is, a discrete additive subgroup of the k-dimensional Euclidean space. We show that this is not the case if the cosine of the angle of the frame is irrational. We also prove that the set is a lattice for n = k + 1 and that there are infinitely many k such that a lattice emerges for n = 2k. We dispose of all cases in dimensions k at most 9. In particular, we show that a (7,28) frame generates a strongly eutactic lattice and give an alternative proof of Roland Bacher\u27s recent observation that this lattice is perfect

Fouling pathways in emulsion polymerization differentiated with a quartz crystal microbalance (QCM) integrated into the reactor wall

Emulsion polymerization fouling at hot interfaces is studied in situ, making use of a quartz crystal microbalance with dissipation monitoring (QCM-D). The resonator crystal is heated with a ring-shaped thermal pad from the back, turning it into a plate with elevated temperature. Configured to be one of the walls of a small reactor for emulsion polymerization, this resonator is prone to heat-transfer fouling, similar to regular heated parts of process equipment. The fouling kinetics is readily quantified with this QCM. During polymerization at constant temperature (80 °C), some deposition is always observed. However, a film with a thickness of less than 1 μm (determined gravimetrically with the QCM) is sometimes found, which stabilizes the surface against the deposition of much thicker layers. When reaction fouling proceeds directly to thick deposits, a small increase in resonance bandwidth often occurs a few minutes prior to the main transition, presumably caused by coagulum formed in the bulk making first contact with the surface. Furthermore, particle fouling is studied with temperature ramps on nonreactive dispersions. Fouling, if present, is readily observed

Metabolome analysis of Arabidopsis thaliana roots identifies a key metabolic pathway for iron acquisition

Fe deficiency compromises both human health and plant productivity. Thus, it is important to understand plant Fe acquisition strategies for the development of crop plants which are more Fe-efficient under Fe-limited conditions, such as alkaline soils, and have higher Fe density in their edible tissues. Root secretion of phenolic compounds has long been hypothesized to be a component of the reduction strategy of Fe acquisition in non-graminaceous plants. We therefore subjected roots of Arabidopsis thaliana plants grown under Fe-replete and Fe-deplete conditions to comprehensive metabolome analysis by gas chromatography-mass spectrometry and ultra-pressure liquid chromatography electrospray ionization quadrupole time-of-flight mass spectrometry. Scopoletin and other coumarins were found among the metabolites showing the strongest response to two different Fe-limited conditions, the cultivation in Fe-free medium and in medium with an alkaline pH. A coumarin biosynthesis mutant defective in ortho-hydroxylation of cinnamic acids was unable to grow on alkaline soil in the absence of Fe fertilization. Co-cultivation with wild-type plants partially rescued the Fe deficiency phenotype indicating a contribution of extracellular coumarins to Fe solubilization. Indeed, coumarins were detected in root exudates of wild-type plants. Direct infusion mass spectrometry as well as UV/vis spectroscopy indicated that coumarins are acting both as reductants of Fe(III) and as ligands of Fe(II)

Dependence of the Martian radiation environment on atmospheric depth: Modeling and measurement

The energetic particle environment on the Martian surface is influenced by solar and heliospheric modulation and changes in the local atmospheric pressure (or column depth). The Radiation Assessment Detector (RAD) on board the Mars Science Laboratory rover Curiosity on the surface of Mars has been measuring this effect for over four Earth years (about two Martian years). The anticorrelation between the recorded surface Galactic Cosmic Ray-induced dose rates and pressure changes has been investigated by Rafkin et al. (2014) and the long-term solar modulation has also been empirically analyzed and modeled by Guo et al. (2015). This paper employs the newly updated HZETRN2015 code to model the Martian atmospheric shielding effect on the accumulated dose rates and the change of this effect under different solar modulation and atmospheric conditions. The modeled results are compared with the most up-to-date (from 14 August 2012 to 29 June 2016) observations of the RAD instrument on the surface of Mars. Both model and measurements agree reasonably well and show the atmospheric shielding effect under weak solar modulation conditions and the decline of this effect as solar modulation becomes stronger. This result is important for better risk estimations of future human explorations to Mars under different heliospheric and Martian atmospheric conditions

Zukunft der Produktivität von Dienstleistungssystemen

Das Thema 'Produktivität von Dienstleistungssystemen' besitzt eine hohe Relevanz für die Dienstleistungswirtschaft. Die Produktivitätsbetrachtung adressiert einen Bereich der Dienstleistungsdomäne, welcher bislang nur unzureichend betrachtet wurde. Darüber hinaus stellt die zunehmende Komplexität, wie sie in Dienstleistungssystemen zu diagnostizieren ist, besondere Herausforderungen an die Dienstleistungswirtschaft im Allgemeinen und die Produktivitätsbetrachtung im Speziellen. Aus diesem Grund wurde die strategische Partnerschaft „Produktivität von Dienstleistungen“ etabliert, in deren Rahmen verschiedene Arbeitskreise interdisziplinär vielfältige Aspekte von Produktivität bei Dienstleistungen bearbeiten. Innerhalb dieser gliedert sich der Arbeitskreis „Produktivität von Dienstleistungssystemen“ ein, welcher unter der Leitung der Universität Leipzig durchgeführt wurde. Innerhalb des Arbeitskreis „Produktivität von Dienstleistungssystemen“ wurden aktuelle Entwicklungen, zukünftige Herausforderungen, Best Practices sowie Forschungs- und Entwicklungsfragen aus der Sicht von Wirtschaft und Wissenschaft identifiziert und diskutiert. Die Ergebnisse sind in der vorliegenden Broschüre präsentiert