Multicanonical Spin Glass Simulations

We report a Monte Carlo simulation of the $2D$ Edwards-Anderson spin glass model within the recently introduced multicanonical ensemble. Replica on lattices of size $L^2$ up to $L=48$ are investigated. Once a true groundstate is found, we are able to give a lower bound on the number of statistically independent groundstates sampled. Temperature dependence of the energy, entropy and other quantities of interest are easily calculable. In particular we report the groundstate results. Computations involving the spin glass order parameter are more tedious. Our data indicate that the large $L$ increase of the ergodicity time is reduced to an approximately $V^3$ power law. Altogether the results suggest that the multicanonical ensemble improves the situation of simulations for spin glasses and other systems which have to cope with similar problems of conflicting constraints.Comment: 24 page

Smoothness of the Green Function for a Special Domain

Cataloged from PDF version of article.We consider a compact set K ⊂ ℝ in the form of the union of a sequence of segments. By means of nearly Chebyshev polynomials for K, the modulus of continuity of the Green functions gℂ\K is estimated. Markov's constants of the corresponding set are evaluated. © Instytut Matematyczny PAN, 2012

Flora planine Aydogdu (Denizli / Turska)

The floristic characteristics of Mt Aydogdu (Denizli, Turkey) are presented and the vascular plant species growing in the area are documented. The study was carried out between 2000– 2003, and 1112 vascular plant samples were collected. At the end of the study, 586 taxa (at specific and infraspecific ranks) belonging to 82 families and 314 genera were identified. Asteraceae (76 species), Fabaceae (65 species) and Brassicaceae (43 species) are the largest families and Trifolium L. (13 species), Ornithogalum L. (9 species) and Veronica L. (9 species) are the largest genera in the area. The phytogeographic elements and their proportion represented in the study area are as follows: Mediterranean 180 (30.7%), Irano-Turanian 43 (7.3%), Euro-Siberian 24 (4.0%) and multiregional or of unknown phytogeographic origin 339 (58.0%). The endemism rate of the area is 9.7%, less then one third of the mean endemism rate in Turkey.U radu su prikazane florističke osobine planine Aydogdu (Denizli, Turska) i zabilježene su vrste vaskularnih biljaka koje rastu na tom području. Istraživanje je provedeno između 2000. i 2003., a prikupljeno je 1112 uzoraka vaskularnih biljaka. Na kraju istraživanja determinirano je sveukupno 586 svojti (na razini vrste i podvrste) iz 82 porodice i 314 rodova. Najzastupljenije porodice su Asteraceae (76 vrsta), Fabaceae (65 vrsta) i Brassicaceae (43 vrste), te rodovi Trifolium L. (13 vrsta), Ornithogalum L. (9 vrsta) i Veronica L. (9 vrsta). Fitogeografski elementi i njihov omjer je sljedeći: Mediteranski 180 (30.7%), Irano-Turanski 43 (7.3%), Eurosibirski 24 (4.0%) i multiregionalni ili nepoznatog fitogeografskog porijekla 339 (58.0%). Stupanj endemizma ovog područja je 9.7%, manje od jedne trećine srednje vrijednosti endemizma za Tursku