These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generator...

Generalising Nachbin's theory of ``topology and order'', in this paper we   continue the study of quantale-enriched categories equipped with a compact   Hausdorff topology. We compare these $V$-categorical compact Hausdorff spaces   with ultrafilter-quantale-enriched categories, and show that the presence of a   compact Hausdorff topology guarantees Cauchy completeness and (suitably   defined) ...

We present the results of a systematical analysis of the intrinsic optical afterglow light curves for a complete sample of gamma-ray bursts (GRBs) observed in the period from Feb. 1997 to Aug. 2005. These light curves are generally well-sampled, with at least four detections in the R band. The redshifts of all the bursts in the sample are available. We derive the intrinsic R band afterglow ligh...

Photometric observations of 20 Tc-deficient and 24 Tc-rich S stars in the near infrared are presented in this paper. With the IRAS data, infrared two color diagrams, IRAS low-resolution spectra and energy distributions are discussed to summarize the way to segregate Tc-rich stars from Tc-deficient ones.