The number of nilpotent semigroups of degree 3

A semigroup is \emph{nilpotent} of degree 3 if it has a zero, every product of 3 elements equals the zero, and some product of 2 elements is non-zero. It is part of the folklore of semigroup theory that almost all finite semigroups are nilpotent of degree 3. We give formulae for the number of nilpotent semigroups of degree 3 with $n\in\N$ elements up to equality, isomorphism, and isomorphism or anti-isomorphism. Likewise, we give formulae for the number of nilpotent commutative semigroups with $n$ elements up to equality and up to isomorphism

Dilaton Contact Terms in the Bosonic and Heterotic Strings

Dilaton contact terms in the bosonic and heterotic strings are examined following the recent work of Distler and Nelson on the bosonic and semirigid strings. In the bosonic case dilaton two-point functions on the sphere are calculated as a stepping stone to constructing a `good' coordinate family for dilaton calculations on higher genus surfaces. It is found that dilaton-dilaton contact terms are improperly normalized, suggesting that the interpretation of the dilaton as the first variation of string coupling breaks down when other dilatons are present. It seems likely that this can be attributed to the tachyon divergence found in \TCCT. For the heterotic case, it is found that there is no tachyon divergence and that the dilaton contact terms are properly normalized. Thus, a dilaton equation analogous to the one in topological gravity is derived and the interpretation of the dilaton as the string coupling constant goes through.Comment: 44 pages, Figures now included. This replacement version includes the 7 figures as PostScript files appended to the end and the macros to insert them into the text. Also some typos in intermediate formulae were correcte

World-Sheet Supersymmetry Without Contact Terms

Green and Seiberg showed that, in simple treatments of fermionic string theory, it is necessary to introduce contact interactions when vertex operators collide. Otherwise, certain superconformal Ward identities would be violated. In this note, we show how these contact terms arise naturally when proper account is taken of the superconformal geometry involved when punctures collide. More precisely, we show that there is no contact term at all! Rather, corrections arise to the ``na\"\i ve" formula when the boundary of moduli space is described correctly.Comment: 14pp., 2 figures (included

Supergravity dressing of beta-functions in N=1 and N=2 supersymmetric models

We discuss the dressing of one-loop sigma-model beta-functions by induced supergravity, for both N=1 and N=2 supersymmetric theories. We obtain exact results by a superconformal gauge argument, and verify them in the semi-classical limit by explicit perturbative calculations in the light-cone gauge. We find that for N=2 theories there is no dressing of the one-loop beta-functions.Comment: 10 pages, latex, macros included, 2 figures in figures.u

Evidenzbasierte Therapie des Raynaud-Syndroms

Zusammenfassung: Das Raynaud-Syndrom ist mit einer Prävalenz von 3-5% ein häufiges klinisches Problem. Dennoch ist die Wirkung der meisten Therapiemöglichkeiten nur unzureichend durch kontrollierte Studien belegt. Zu den Therapien mit höherem Evidenzgrad gehört der Kalziumantagonist Nifedipin, für den in Metaanalysen sowohl bei primärem als auch bei sekundärem Raynaud-Syndrom eine verbesserte periphere Durchblutung sowie eine Abnahme der Frequenz und des Schweregrades der Raynaud-Attacken nachgewiesen werden konnte. Ähnliches gilt für intravenös appliziertes Iloprost in der Therapie des sekundären Raynaud-Syndroms bei systemischer Sklerose. Intravenös verabreichtes Iloprost verbessert darüber hinaus das Abheilen von Fingerkuppenulzera bei Patienten mit systemischer Sklerose. Vielversprechende Therapieansätze stellen Angiotensin-II-Rezeptor-1-Antagonisten (Losartan), die Kalziumantagonisten Felodipin und Amlodipin, Serotonin-Reuptake-Hemmer (Fluoxetin) und Phosphodiesterase-V-Hemmer (Sildenafil, Vardenafil) dar, die sich in kontrollierten Einzelstudien als wirksam erwiesen haben. Jedoch fehlen Erfahrungen mit größeren Patientenzahlen und längeren Anwendungszeiten, um diese Therapiemöglichkeiten abschließend zu beurteile

Deformed Quantum Cohomology and (0,2) Mirror Symmetry

We compute instanton corrections to correlators in the genus-zero topological subsector of a (0,2) supersymmetric gauged linear sigma model with target space P1xP1, whose left-moving fermions couple to a deformation of the tangent bundle. We then deduce the theory's chiral ring from these correlators, which reduces in the limit of zero deformation to the (2,2) ring. Finally, we compare our results with the computations carried out by Adams et al.[ABS04] and Katz and Sharpe[KS06]. We find immediate agreement with the latter and an interesting puzzle in completely matching the chiral ring of the former.Comment: AMSLatex, 30 pages, one eps figure. V4: typos corrected, final version appearing in JHE

Overview of pathogenesis of systemic sclerosis

The aetiology of SSc is subject to ongoing research, as the precise events that underlie the development of this disease remain unclear. The pathogenesis is known to involve endothelium, epithelium, fibroblasts, innate and adaptive immune systems and their component immunological mediators. Endothelial cell damage may be the initiating factor, but the precise triggering event(s) remain elusive. Angiogenesis also appears to be dysregulated. Vasculopathy shows similarities in different organs (e.g. pulmonary arterial hypertension, renal disease, digital tip ulcers). Endothelin-1 is a potent mediator of vasculopathy, and hence represents a highly relevant target for intervention of vascular features in SS

Continuum Annulus Amplitude from the Two-Matrix Model

An explicit expression for continuum annulus amplitudes having boundary lengths $\ell_{1}$ and $\ell_{2}$ is obtained from the two-matrix model for the case of the unitary series; $(p,q) = (m + 1, m)$. In the limit of vanishing cosmological constant, we find an integral representation of these amplitudes which is reproduced, for the cases of the $m = 2~(c=0)$ and the $m \rightarrow \infty~(c=1)$, by a continuum approach consisting of quantum mechanics of loops and a matter system integrated over the modular parameter of the annulus. We comment on a possible relation to the unconventional branch of the Liouville gravity.Comment: 9 pages, OU-HET 190, revised version. A part of the conclusions has been corrected. A new result on integral representation of the annulus amplitudes has been adde