The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

Perfect graphs were defined by Claude Berge in the 1960s. They are important objects for graph theory, linear programming and combinatorial optimization. Claude Berge made a conjecture about them, that was proved by Chudnovsky, Robertson, Seymour and Thomas in 2002, and is now called the strong perfect graph theorem. This is a survey about perfect graphs, mostly focused on the strong perfect gr...

this paper has three parts. in the first part, we bring to the fore an ancient vedic concept of mesocosm and discuss its religious and cosmic significance within indian religion. this part also brings an initial approach towards philosophy of spirituality by focusing on the role of breath within the very concept of mesocosm. in the second part, based on our preliminary analysis, we present an o...

For a not empty perfect subset of the unit circle C there is a perfect subset of C measure zero which being rotated to every position intersects the first set on a nonempty perfect set. This result may be stated in terms of set of distances between pairs of points from these two sets. A generalization of this result to a product of tori is suggested. 2000 Mathematics Subject Classification: 26-...

The need for a reconsideration of human-nature relationships has been widely recognized in the Anthropocene. It is difficult to rethink, however, because there crisis imagination that deeply entrenched within fundamental premises modernity. This article explores how ‘critical animism’ developed by Miyazaki Hayao Studio Ghibli can address this paucity providing alternative ways knowing and being...