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 ³ 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.

Introduction: Academic faculty members need to emphasize ethical principles in order to improve higher education, with the understanding of this importance, the current research was conducted with the aim of designing the ethical model of academic faculty members in Iran's higher education. Material & Methods: This research is a type of qualitative study that uses foundational data theory. The participants, including experts and faculty members of the country's public universities, who were responsible for the promotion of academic members, were selected as key informants through a targeted sampling method of 45 people. Data were collected through semi-structured interviews. The reliability and validity of the data were obtained from the two methods of reviewing the participants and recoding by experts. Data were analyzed by open, central and selective coding. Results: The results showed that the moral model of faculty members in Iran's higher education is explained in 10 main categories and 27 subcategories. Major and core categories in the form of 6 dimensions of causal conditions including (individual factors, organizational factors), core (cultural-educational, educational ethics, research ethics, scientific-executive), background conditions (higher education policies, moral activism), intervening conditions (environmental factors), strategies (micro level-university, macro level-higher education) and consequences (individual and organizational) were elevated to a higher abstract level and finally the research paradigm model was presented. Conclusion: The regulations for the promotion of academic staff members in Iran require a detailed revision of the content with an ethical and qualitative approach in order to make the indicators of the promotion regulations efficient and effective.

In this article we introduce the notion of Fractal w-operad emerging from a natural  w-operad associated to any coglobular object in the category of higher operads in Batanin’s sense, which in fact is a coendomorphism. w-operads. We have in mind coglobular object of higher operads which algebras are kind of higher transformations. It follows that this natural w-operad acts on the globular object associated to these higher transformations. To construct the natural w-operad we introduce some general technology and give meaning to saying an w-operad possesses the fractal property. If an w-operad B0P has this property then one can define a globular object of all higherB0P-transformations and show that the globular object has aB0P-algebra structure.

In this article we discuss examples of fractal w-operads. Thus we show that there is an w-operadic approach to explain existence of the globular set of globular sets1, the reflexive globular set of reflexive globular sets, the w-magma of w-magmas, and also the reflexive w-magma of reflexive.w-magmas. Thus, even though the existence of the globular set of globular sets is intuitively evident, many other higher structures which fractality are less evident, could be described with the same technology, using fractal w-operads. We have in mind the non-trivial question of the existence of the weak w-category of the weak w-categories in the globular setting, which is described in [9] with the same technology up to a contractibility hypothesis.

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 cluster algebras. From quiver representations, we proceed to the cluster category, which yields a complete categorification of the cluster algebra and its combinatorial underpinnings.

When studying Russian morphology, one can distinguish two categories. These categories are "grammatical" and "lexico-grammatical". Grammatical categories can be specified through a series of grammatical features of words. Considering different criteria, Russian grammarians and linguists divide grammatical categories of their language into different types. In determining lexico-grammatical types, in addition to a series of grammatical features, they also consider a series of lexico-semantic features as well. The lexica-grammatical type is determined in the different forms of parts of speech.