The rank of the semigroup of transformations stabilising a partition of a finite set

Let $\mathcal{P}$ be a partition of a finite set $X$. We say that a full transformation $f:X\to X$ preserves (or stabilizes) the partition $\mathcal{P}$ if for all $P\in \mathcal{P}$ there exists $Q\in \mathcal{P}$ such that $Pf\subseteq Q$. Let $T(X,\mathcal{P})$ denote the semigroup of all full transformations of $X$ that preserve the partition $\mathcal{P}$. In 2005 Huisheng found an upper bound for the minimum size of the generating sets of $T(X,\mathcal{P})$, when $\mathcal{P}$ is a partition in which all of its parts have the same size. In addition, Huisheng conjectured that his bound was exact. In 2009 the first and last authors used representation theory to completely solve Hisheng's conjecture. The goal of this paper is to solve the much more complex problem of finding the minimum size of the generating sets of $T(X,\mathcal{P})$, when $\mathcal{P}$ is an arbitrary partition. Again we use representation theory to find the minimum number of elements needed to generate the wreath product of finitely many symmetric groups, and then use this result to solve the problem. The paper ends with a number of problems for experts in group and semigroup theories

SIPS - Screening-Instrument für prämenstruelle Symptome*: Die deutsche Version des Premenstrual Symptoms Screening Tool zur Erfassung klinisch relevanter Beschwerden

Zusammenfassung: Hintergrund: Prämenstruelle dysphorische Störungen (PMDS) und schwere prämenstruelle Syndrome (PMS) treten häufig auf, bleiben jedoch oft unerkannt und unbehandelt. Begünstigt wird dies durch das Fehlen eines entsprechenden deutschsprachigen Screening-Instruments. Ziel dieser Studie war es, das englischsprachige Premenstrual Symptoms Screening Tool (PSST) ins Deutsche zu übertragen und seine Anwendung zu prüfen. Material und Methoden: Die deutschsprachige Version des PSST wurde als "Screening-Instrument für prämenstruelle Symptome" (SIPS) erstellt und ihre Güte an 47 Frauen mit und ohne PMDS/schwerem PMS internetbasiert mittels täglichen Symptomeinschätzungen bestimmt. Ergebnisse: Die Retest-Reliabilität des SIPS betrug r=0,69, das Cronbachsα 0,924. Als Validitätsmaß des SIPS zeigten sich signifikante Unterschiede zwischen Frauen mit und ohne PMDS/schwerem PMS, bestimmt durch das SIPS, bezüglich prospektiv erfasster prämenstrueller Symptomatik (F[2,44]=4,52, p<0,001) und Symptomveränderung (F[2,44]=25,23, p<0,001). Schlussfolgerung: Das SIPS ist reliabel und valide und kann helfen, Frauen mit behandlungsbedürftigen prämenstruellen Beschwerden zu identifiziere

SIPS - Screening-Instrument für prämenstruelle Symptome : Die deutsche Version des Premenstrual Symptoms Screening Tool zur Erfassung klinisch relevanter Beschwerden

Premenstrual Dysphoric Disorder (PMDD) and severe Premenstrual Syndrome (PMS) are common, yet often remain unrecognized and not adequately treated. One reason for this is the lack of a valid German screening instrument. The aim of the present study was to create a German version of the English "premenstrual symptoms screening tool (PSST)" and to verify its applicability. The German version of the PSST was created as "Screening- Instrument für Prämenstruelle Symptome (SIPS)" and its reliability and validity estimated based on data from 47 women with and without PMDD/severe PMS, using internet-based daily symptom-ratings. The retest-reliability of the SIPS was r=0.69, Cronbach`s Alpha was 0.924. As indicator of the convergent validity of the SIPS, there were significant differences between women with and without PMDD/severe PMS as identified by the SIPS, with regard to prospectively assessed premenstrual symptomatology (F(2,44)=4.52, p>0.001) and symptom change (F(2,44)=25.23, p>0.001). The SIPS is reliable and valid and may help improving the identification of women who require treatment for their premenstrual symptoms

Nucleate pool boiling in the long duration low gravity environment of the Space Shuttle

The results are presented of an experimental study of nucleate pool boiling performed in the low gravity environment of the space shuttle. Photographic observations of pool boiling in Freon 113 were obtained during the 'Tank Pressure Control Experiment,' flown on the Space Transportation System, STS-43 in August 1991. Nucleate boiling data from large (relative to bubble size) flat heating surfaces (0.1046 by 0.0742 m) was obtained at very low heat fluxes (0.22 to 1.19 kW/sq m). The system pressure and the bulk liquid subcooling varied in the range of 40 to 60 kPa and 3 to 5 C respectively. Thirty-eight boiling tests, each of 10-min duration for a given heat flux, were conducted. Measurements included the heater power, heater surface temperature, the liquid temperature and the system pressure as functions of heating time. Video data of the first 2 min of heating was recorded for each test. In some tests the video clearly shows the inception of boiling and the growth and departure of bubbles from the surface during the first 2 min of heating. In the absence of video data, the heater temperature variation during heating shows the inception of boiling and stable nucleate boiling. During the stable nucleate boiling, the wall superheat varied between 2.8 to 3.8 C for heat fluxes in the range of 0.95 to 1.19 kW/sq m. The wall superheat at the inception of boiling varied between 2 to 13 C

Systematic Uncertainties in Black Hole Masses Determined from Single Epoch Spectra

We explore the nature of systematic errors that can arise in measurement of black hole masses from single-epoch spectra of active galactic nuclei (AGNs) by utilizing the many epochs available for NGC 5548 and PG1229+204 from reverberation mapping databases. In particular, we examine systematics due to AGN variability, contamination due to constant spectral components (i.e., narrow lines and host galaxy flux), data quality (i.e., signal-to-noise ratio, S/N), and blending of spectral features by comparing the precision and accuracy of single-epoch mass measurements to those of recent reverberation mapping studies. We calculate masses by characterizing the broad Hbeta emission line by both the full width at half maximum and the line dispersion and demonstrate the importance of removing narrow emission-line components and host starlight. We find that the reliability of line width measurements rapidly decreases for S/N lower than ~10 to 20 (per pixel) and that fitting the line profiles instead of direct measurement of the data does not mitigate this problem but can, in fact, introduce systematic errors. We also conclude that a full spectral decomposition to deblend the AGN and galaxy spectral features is unnecessary except to judge the contribution of the host galaxy to the luminosity and to deblend any emission lines that may inhibit accurate line width measurements. Finally, we present an error budget which summarizes the minimum observable uncertainties as well as the amount of additional scatter and/or systematic offset that can be expected from the individual sources of error investigated. In particular, we find that the minimum observable uncertainty in single-epoch mass estimates due to variability is ~ 20 per pixel) spectra.Comment: 60 pages, 20 figures, accepted for publication in Ap

The Lick AGN Monitoring Project: Reverberation Mapping of Optical Hydrogen and Helium Recombination Lines

We have recently completed a 64-night spectroscopic monitoring campaign at the Lick Observatory 3-m Shane telescope with the aim of measuring the masses of the black holes in 12 nearby (z < 0.05) Seyfert 1 galaxies with expected masses in the range ~10^6-10^7M_sun and also the well-studied nearby active galactic nucleus (AGN) NGC 5548. Nine of the objects in the sample (including NGC 5548) showed optical variability of sufficient strength during the monitoring campaign to allow for a time lag to be measured between the continuum fluctuations and the response to these fluctuations in the broad Hbeta emission, which we have previously reported. We present here the light curves for the Halpha, Hgamma, HeII 4686, and HeI 5876 emission lines and the time lags for the emission-line responses relative to changes in the continuum flux. Combining each emission-line time lag with the measured width of the line in the variable part of the spectrum, we determine a virial mass of the central supermassive black hole from several independent emission lines. We find that the masses are generally consistent within the uncertainties. The time-lag response as a function of velocity across the Balmer line profiles is examined for six of the AGNs. Finally we compare several trends seen in the dataset against the predictions from photoionization calculations as presented by Korista & Goad. We confirm several of their predictions, including an increase in responsivity and a decrease in the mean time lag as the excitation and ionization level for the species increases. Further confirmation of photoionization predictions for broad-line gas behavior will require additional monitoring programs for these AGNs while they are in different luminosity states. [abridged]Comment: 37 pages, 18 figures and 15 tables, accepted for publication in the Astrophysical Journa

Applying a biodeposition layer to increase the bond of a repair mortar on a mortar substrate

One of the major concerns in infrastructure repair is a sufficient bond between the substrate and the repair material, especially for the long-term performance and durability of the repaired structure. In this study, the bond of the repair material on the mortar substrate is promoted via the biodeposition of a calcium carbonate layer by a ureolytic bacterium. X-ray diffraction and scanning electron microscopy were used to examine the interfaces between the repair material and the substrate, as well as the polymorph of the deposited calcium carbonate. The approximately 50 mu m thick biodeposition film on the mortar surface mostly consisted of calcite and vaterite. Both the repair material and the substrate tended to show a good adherence to that layer. The bond, as assessed by slant shear specimen testing, was improved by the presence of the biodeposition layer. A further increase was found when engineering the substrate surface using a structured pattern layer of biodeposition. (C) 2017 Elsevier Ltd. All rights reserved

Reverberation Mapping Results from MDM Observatory

We present results from a multi-month reverberation mapping campaign undertaken primarily at MDM Observatory with supporting observations from around the world. We measure broad line region (BLR) radii and black hole masses for six objects. A velocity-resolved analysis of the H_beta response shows the presence of diverse kinematic signatures in the BLR.Comment: To appear in the Proceedings of the IAU Symposium No. 267: Co-Evolution of Central Black Holes and Galaxies, Rio de Janeiro, 200