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 ...

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...

small and medium enterprises development policy by  cluster approach  program is a new method to attempt to industrial development goals in developed and developing country in the world. in the last decades in some of country such as iran concentrate that programmed. industrial development program by cluster approach need some measurable factor for control and assessment. program’s control must...

the local solid flow structure of gas-solid bubbling fluidized bed was investigated to identify and characterize the particle clusters. extensive mathematical calculations were carried out using the energy-minimization multi-scale (emms) approach for evaluating cluster properties including the velocity, the size and the void fraction of clusters in the dense phase of the bed. the results showed...

The study relates to the problem of cluster management in the conditions of sustainable development. Against the background of the assumptions and conditions for sustainable development, the specificity of the cluster activity in the conditions of the Polish economy has been presented. The objective of the paper is to characterize the cluster management standards in Poland. Such standards have ...

In this survey, we give an overview over some aspects of the set of tilting objects in an $m-$cluster category, with focus on those properties which are valid for all $m geq 1$. We focus on the following three combinatorial aspects: modeling the set of tilting objects using arcs in certain polygons, the generalized assicahedra of Fomin and Reading, and colored quiver mutation.

background: alkaptonuria is a rare genetic disease leading to the accumulation of homogentesic acid in joint and ear cartilage, sclera and some other tissues causing significant morbidity in these patients. in this paper, we report three cases of alkaptonuria among the family or household members. case presentation: a 51-year-old man with mechanical low back and knee pain was referred to rheuma...

in this survey, we give an overview over some aspects of the set of tilting objects in an $m-$cluster category, with focus on those properties which are valid for all $m geq 1$. we focus on the following three combinatorial aspects: modeling the set of tilting objects using arcs in certain polygons, the generalized assicahedra of fomin and reading, and colored quiver mutation.