Diameter of Polyhedra: Limits of Abstraction

Connected Layer Families and Diameter of Polyhedra Semester Project

Given a polyhedron, its diameter is defined as the maximum distance between two of its vertices, where the distance between two vertices u and v is the number of edges contained in the shortest u− v path in the skeleton of the polyhedron. Bounding the diameter of a polyhedron with respect to its dimension d and the number n of its facets is one of the most important open problems in convex geom...

Recent Progress on the Diameter of Polyhedra and Simplicial Complexes

Some recent attempts of settling this question go by looking at the problem in the more general context of pure simplicial complexes: What is the maximum diameter of the dual graph of a simplicial (d − 1)sphere or (d− 1)-ball with n vertices? Here a simplicial (d − 1)-ball or sphere is a simplicial complex homeomorphic to the (d − 1)-ball or sphere. These complexes are necessarily pure (all the...

Jamie Tappenden on Kit Fine ’ S the Limits of Abstraction

the pathology of historical texts translation: a study of persian translations of 7th volume of cambridge history of iran

ترجمه با گسترش زبان آغاز شده و اهمیت آن روز به روز افزایش می یابد، و برای اولین بار به عنوان شاخه ای از دانش و روشی برای انتقال علوم، فرهنگ و تجربه در در دوره قاجار در ایران آغاز شد. در حقیقت متون تاریخی از اولین متونی هستند که در ایران ترجمه شدند چرا که به سیاستمداران آن دوره کمک می کردند تا به علل موفقیت جهان غرب و پیشرفت هایشان در طول تاریخ پی ببرند، بنابراین به تدریج ترجمه این گونه متون رون...

Limits in modified categories of interest

‎We firstly prove the completeness of the category of crossed modules in a modified category of interest‎. ‎Afterwards‎, ‎we define pullback crossed modules and pullback cat objects that are both obtained by pullback diagrams with extra structures on certain arrows‎. ‎These constructions unify many corresponding results for the cases of groups‎, ‎commutative algebras and can also be adapted to ...