On forking and definability of types in some dp-minimal theories

We prove in particular that, in a large class of dp-minimal theories including the p-adics, definable types are dense amongst non-forking types.Comment: Appeared previously as an appendix in arXiv:1210.447

Definability of restricted theta functions and families of abelian varieties

We consider some classical maps from the theory of abelian varieties and their moduli spaces and prove their definability, on restricted domains, in the o-minimal structure \Rae. In particular, we prove that the embedding of moduli space of principally polarized ableian varierty, Sp(2g,\Z)\backslash \CH_g, is definable in \Rae, when restricted to Siegel's fundamental set \fF_g. We also prove the definability, on appropriate domains, of embeddings of families of abelian varieties into projective space

Interparticle interaction and structure of deposits for competitive model in (2+1)- dimensions

A competitive (2+1)-dimensional model of deposit formation, based on the combination of random sequential absorption deposition (RSAD), ballistic deposition (BD) and random deposition (RD) models, is proposed. This model was named as RSAD$_{1-s}$(RD$_f$BD$_{1-f}$)$_s$. It allows to consider different cases of interparticle interactions from complete repulsion between near-neighbors in the RSAD model ($s=0$) to sticking interactions in the BD model ($s=1, f=0$) or absence of interactions in the RD model ($s=1$, $f=0$). The ideal checkerboard ordered structure was observed for the pure RSAD model ($s=0$) in the limit of $h \to \infty$. Defects in the ordered structure were observed at small $h$. The density of deposit $p$ versus system size $L$ dependencies were investigated and the scaling parameters and values of $p_\infty=p(L=\infty)$ were determined. Dependencies of $p$ versus parameters of the competitive model $s$ and $f$ were studied. We observed the anomalous behaviour of the eposit density $p_\infty$ with change of the inter-particle repulsion, which goes through minimum on change of the parameter $s$. For pure RSAD model, the concentration of defects decreases with $h$ increase in accordance with the critical law $\rho\propto h^{-\chi_{RSAD}}$, where $\chi_{RSAD} \approx 0.119 \pm 0.04$.Comment: 10 pages,4 figures, Latex, uses iopart.cl