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

Kidney Stones and Energy Drinks: A Literature Review

Kidney stones are common, painful, and expensive to treat. Several factors play a role in the development of stones, particularly the consumption of sugars such as fructose. As such, the consumption of sugary energy drinks contributes to the development of kidney stones. However, there is a lack of understanding behind the mechanism of kidney stone development and the role energy drinks play in stone development. This review analyzes the mechanism of kidney stone development and the effect energy drink consumption has on stone development. Here, we also detail the dietary roles calcium, oxalate, ascorbic acid, and animal protein have on stone development

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

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