Stack (mathematics)In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets. Stacks are used to formalise some of the main constructions of descent theory, and to construct fine moduli stacks when fine moduli spaces do not exist. Descent theory is concerned with generalisations of situations where isomorphic, compatible geometrical objects (such as vector bundles on topological spaces) can be "glued together" within a restriction of the topological basis.
Ring strainIn organic chemistry, ring strain is a type of instability that exists when bonds in a molecule form angles that are abnormal. Strain is most commonly discussed for small rings such as cyclopropanes and cyclobutanes, whose internal angles are substantially smaller than the idealized value of approximately 109°. Because of their high strain, the heat of combustion for these small rings is elevated. Ring strain results from a combination of angle strain, conformational strain or Pitzer strain (torsional eclipsing interactions), and transannular strain, also known as van der Waals strain or Prelog strain.
AllenesIn organic chemistry, allenes are organic compounds in which one carbon atom has double bonds with each of its two adjacent carbon atoms (, where R is H or some organyl group). Allenes are classified as cumulated dienes. The parent compound of this class is propadiene (), which is itself also called allene. An group of the structure is called allenyl, where R is H or some alkyl group. Compounds with an allene-type structure but with more than three carbon atoms are members of a larger class of compounds called cumulenes with bonding.
AtropisomerAtropisomers are stereoisomers arising because of hindered rotation about a single bond, where energy differences due to steric strain or other contributors create a barrier to rotation that is high enough to allow for isolation of individual conformers. They occur naturally and are important in pharmaceutical design. When the substituents are achiral, these conformers are enantiomers (atropoenantiomers), showing axial chirality; otherwise they are diastereomers (atropodiastereomers).
