Lattices with many Borcherds products

We prove that there are only finitely many isometry classes of even lattices $L$ of signature $(2,n)$ for which the space of cusp forms of weight $1+n/2$ for the Weil representation of the discriminant group of $L$ is trivial. We compute the list of these lattices. They have the property that every Heegner divisor for the orthogonal group of $L$ can be realized as the divisor of a Borcherds product. We obtain similar classification results in greater generality for finite quadratic modules.Comment: 31 pages, 1 figur

Can hail and rain nucleate cloud droplets?

We present results from moist convection in a mixture of pressurized sulfur hexa-flouride (liquid and vapor) and helium (gas) to model the wet and dry components of the earth's atmosphere. To allow for homogeneous nucleation, we operate the experiment close to critical conditions. We report on the nucleation of microdroplets in the wake of large cold liquid drops falling through the supersaturated atmosphere and show that the homogeneous nucleation is caused by isobaric cooling of the saturated sulfur hexaflouride vapor. Our results carry over to atmospheric clouds: falling hail and cold rain drops may enhance the heterogeneous nucleation of microdroplets in their wake under supersaturated atmospheric conditions. We also observed that under appropriate conditions settling microdroplets form a rather stable horizontal cloud layer, which separates regions of super and sub critical saturation.Comment: 6 pages, 3 figure

Study of the Born-Oppenheimer Approximation for Mass-Scaling of Cold Collision Properties

Asymptotic levels of the A $^1\Sigma_u^+$ state of the two isotopomers $^{39}{\rm K}_2$ and $^{39}{\rm K}^{41}{\rm K}$ up to the dissociation limit are investigated with a Doppler-free high resolution laser-spectroscopic experiment in a molecular beam. The observed level structure can be reproduced correctly only if a mass dependent correction term is introduced for the interaction potential. The applied relative correction in the depth of the potential is $10^{-6}$, which is in the order of magnitude expected for corrections of the Born-Oppenheimer approximation. A similar change in ground state potentials might lead to significant changes of mass-scaled properties describing cold collisions like the s-wave scattering length.Comment: 8 pages, 6 figure

Lohnstruktur und Lohndifferenzierung in der DDR : Ergebnisse der Lohndatenerfassung vom September 1988

"In den Jahren 1984 und 1988 erfolgten in der DDR umfassende Lohndatenerhebungen, vorwiegend in der Industrie. Die Stichmonatserhebung vom September 1988 erfaßte personenbezogene Lohndaten und weitere damit korrespondierende Angaben von 2,4 Mio. Beschäftigten. Das Ziel bestand darin, für die zentrale Planwirtschaft nutzbare Aussagen zur Lohnhöhe und Lohnzusammensetzung der Produktionsarbeiter, Meister, Hoch- und Fachschulkader, technisch-ökonomischen Fachkräfte und anderer Beschäftigtengruppen zu gewinnen. Die Auswertung beschränkte sich auf die administrativen Gliederungen - die Ministerien. Untersuchungen zu regionalen Lohnverteilungen gab es nicht. Bis Ende 1989 waren in der DDR Veröffentlichungen zum Lohn verboten. Mit diesem Beitrag soll deshalb ein gestraffter Überblick über die Entlohnungssituation in der Industrie am Beispiel der wichtigsten Beschäftigtengruppen vermittelt werden. Soweit es trotz unterschiedlicher Strukturen und Zuordnungen vertretbar erscheint, werden Vergleiche zu den alten Bundesländern hergestellt, um auf wesentliche Unterschiede hinzuweisen. Die Lohnrelationen zwischen den Beschäftigtengruppen in der DDR waren stark nivelliert. Hoch- und Fachschulkader verdienten netto nur ca. 15 % mehr als Produktionsarbeiter, in den alten Bundesländern bis zu 70 %. Im Vergleich zu den alten Bundesländern waren die Verdienstunterschiede zwischen den Bereichen bzw. Branchen mit ca. 150 M/Monat gering. Erheblichen Einfluß auf die Lohnhöhe hatten mit einem Anteil bis zu 30 % am Bruttolohn die Schichtzuschläge für Schichtarbeiter in durchgehenden Schichtsystemen. Entgegen früheren offiziellen Darstellungen gab es auch in der DDR ein Lohngefälle zwischen Frauen und Männern. Die Frauen verdienten im Durchschnitt ca. 16 % weniger als die Männer, weil sie häufig die weniger qualifizierten Arbeiten ausführten. Ihre Position war allerdings besser als in den alten Bundesländern, wo das Lohnniveau der Frauen etwa 30 % unter dem der Männer liegt." (Autorenreferat)Lohnstruktur, Lohnunterschied, geschlechtsspezifische Faktoren, berufliche Qualifikation, Wirtschaftszweige, Stellung im Beruf, Schichtarbeit, DDR, Bundesrepublik Deutschland

Leidenfrost pattern formation and boiling

We report on Leidenfrost patterns and boiling with compressed sulfur hexafluoride ( SF6). The experiments were carried out in a large aspect ratio Rayleigh–Bénard convection cell, where the distance between the horizontal plates is comparable with the capillary length of the working fluid. Pressures and temperatures were chosen such that the bottom plate was above and the top plate was below the liquid–vapor transition temperature of SF6. As a result, SF6 vapor condenses at the top plate and forms drops that grow in size. Leidenfrost patterns are formed as the drops do not fall but levitate by the vapor released in the gap between the hot bottom plate and the colder drops. When the size of these drops became too large, one or more vapor bubbles—chimneys—form inside them. We determine the critical size for the formation of a chimney as a function of the capillary length. For even larger drops and extended puddles many disconnected chimneys occur that can grow to sizes large enough for the formation of new drops inside them. By varying the temperatures and the pressure in the system, we observe various such patterns. When the area covered by a puddle becomes large it touches the hot bottom plate locally and boils off rapidly. This can be attributed to a local reduction of the bottom plate surface temperature below the Leidenfrost temperature

In-Silico Modeling of the Mitotic Spindle Assembly Checkpoint

The Mitotic Spindle Assembly Checkpoint ((M)SAC) is an evolutionary conserved mechanism that ensures the correct segregation of chromosomes by restraining cell cycle progression from entering anaphase until all chromosomes have made proper bipolar attachments to the mitotic spindle. Its malfunction can lead to cancer.We have constructed and validated for the human (M)SAC mechanism an in silico dynamical model, integrating 11 proteins and complexes. The model incorporates the perspectives of three central control pathways, namely Mad1/Mad2 induced Cdc20 sequestering based on the Template Model, MCC formation, and APC inhibition. Originating from the biochemical reactions for the underlying molecular processes, non-linear ordinary differential equations for the concentrations of 11 proteins and complexes of the (M)SAC are derived. Most of the kinetic constants are taken from literature, the remaining four unknown parameters are derived by an evolutionary optimization procedure for an objective function describing the dynamics of the APC:Cdc20 complex. MCC:APC dissociation is described by two alternatives, namely the "Dissociation" and the "Convey" model variants. The attachment of the kinetochore to microtubuli is simulated by a switching parameter silencing those reactions which are stopped by the attachment. For both, the Dissociation and the Convey variants, we compare two different scenarios concerning the microtubule attachment dependent control of the dissociation reaction. Our model is validated by simulation of ten perturbation experiments.Only in the controlled case, our models show (M)SAC behaviour at meta- to anaphase transition in agreement with experimental observations. Our simulations revealed that for (M)SAC activation, Cdc20 is not fully sequestered; instead APC is inhibited by MCC binding

Experimental perspectives on the matter-antimatter asymmetry puzzle: developments in electron EDM and antihydrogen experiments

In the search for clues to the matter-antimatter puzzle, experiments with atoms or molecules play a particular role. These systems allow measurements with very high precision, as demonstrated by the unprecedented limits down to $10^{-30}$ e.cm on electron EDM using molecular ions, and relative measurements at the level of $10^{-12}$ in spectroscopy of antihydrogen atoms. Building on these impressive measurements, new experimental directions offer potentials for drastic improvements. We review here some of the new perspectives in those fields and their associated prospects for new physics searches

Effects of 1,25(OH)2D3 on compensatory renal growth in the growing rat

Effects of 1,25(OH)2D3 on compensatory renal growth in the growing rat. Renal compensatory growth after uninephrectomy (UNX) was examined in vitamin D replete male 100g Sprague-Dawley rats. Five days after UNX, the contralateral kidney wet weight increased by 25% with the kidney weight/body weight ratio reaching a plateau by day 7 after UNX. The early weight increase was primarily due to an increased cell number, as evaluated by a stereological technique in perfusion-fixed kidneys. Twenty pmol 1,25(OH)2D3 by daily s.c. injection increased time-averaged 1,25(OH)2D3 concentrations 3.3-fold and reduced the increment in the kidney weight of UNX pairfed rats compared to solvent UNX controls. The number of mitoses (whole kidney and different nephron segments) were significantly reduced by giving 1,25(OH)2D3 to UNX animals at different levels of food intake. The effect was also demonstrable in PTX animals on a constant infusion of exogenous PTH (100 ng/kg/hr 1,34 bPTH by osmotic minipump). The data suggest that changes of 1,25(OH)2D3 concentration within a physiologically relevant range modulate compensatory (and possibly basal) growth of the kidney

Boundary Zonal Flow in Rotating Turbulent Rayleigh-Bénard Convection

For rapidly rotating turbulent Rayleigh–Bénard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of the BZF is cyclonic (in the rotating frame), the temperature is an anticyclonic traveling wave of mode one, whose signature is a bimodal temperature distribution near the radial boundary. The BZF width is found to scale like Ra1/4Ek2/3 where the Ekman number Ek decreases with increasing rotation rate