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 generators of ...

drought stress, especially drought at terminal stages, plays an important role in reduction of yield in field crops such as common beans. 50 genotypes of common bean including 3 control genotypes (dehghan, bahman and naz) were used to evaluate and identify the tolerant genotypes. this experiment were performed in a randomized complete block design (rcbd) with three replications under two condit...

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...

pomegranate is an importantly popular fruit crop with iran the main center of its diversity throghout the world. the richest pomegranate genetic resources believed to exist in iran. the present investigation was carried out to study the genetic diversity of 15 genotypes of pomegranate in tarume zanjan making use of rapd markers. genomic dna was extracted from the plant,s leaf, and tested for th...