Affine varietyIn algebraic geometry, an affine algebraic set is the set of the common zeros over an algebraically closed field k of some family of polynomials in the polynomial ring An affine variety or affine algebraic variety, is an affine algebraic set such that the ideal generated by the defining polynomials is prime. Some texts call variety any algebraic set, and irreducible variety an algebraic set whose defining ideal is prime (affine variety in the above sense).
Ring (chemistry)In chemistry, a ring is an ambiguous term referring either to a simple cycle of atoms and bonds in a molecule or to a connected set of atoms and bonds in which every atom and bond is a member of a cycle (also called a ring system). A ring system that is a simple cycle is called a monocycle or simple ring, and one that is not a simple cycle is called a polycycle or polycyclic ring system. A simple ring contains the same number of sigma bonds as atoms, and a polycyclic ring system contains more sigma bonds than atoms.
Blowing upIn mathematics, blowing up or blowup is a type of geometric transformation which replaces a subspace of a given space with all the directions pointing out of that subspace. For example, the blowup of a point in a plane replaces the point with the projectivized tangent space at that point. The metaphor is that of zooming in on a photograph to enlarge part of the picture, rather than referring to an explosion. Blowups are the most fundamental transformation in birational geometry, because every birational morphism between projective varieties is a blowup.
Cyclic compoundA cyclic compound (or ring compound) is a term for a compound in the field of chemistry in which one or more series of atoms in the compound is connected to form a ring. Rings may vary in size from three to many atoms, and include examples where all the atoms are carbon (i.e., are carbocycles), none of the atoms are carbon (inorganic cyclic compounds), or where both carbon and non-carbon atoms are present (heterocyclic compounds with rings containing both carbon and non-carbon).
Yield (chemistry)In chemistry, yield, also referred to as reaction yield, is a measure of the quantity of moles of a product formed in relation to the reactant consumed, obtained in a chemical reaction, usually expressed as a percentage. Yield is one of the primary factors that scientists must consider in organic and inorganic chemical synthesis processes. In chemical reaction engineering, "yield", "conversion" and "selectivity" are terms used to describe ratios of how much of a reactant was consumed (conversion), how much desired product was formed (yield) in relation to the undesired product (selectivity), represented as X, Y, and S.
CarbeneIn organic chemistry, a carbene is a molecule containing a neutral carbon atom with a valence of two and two unshared valence electrons. The general formula is or where the R represents substituents or hydrogen atoms. The term "carbene" may also refer to the specific compound , also called methylene, the parent hydride from which all other carbene compounds are formally derived. Carbenes are classified as either singlets or triplets, depending upon their electronic structure.
CyclopropanationIn organic chemistry, cyclopropanation refers to any chemical process which generates cyclopropane () rings. It is an important process in modern chemistry as many useful compounds bear this motif; for example pyrethroid insecticides and a number of quinolone antibiotics (ciprofloxacin, sparfloxacin, etc.). However, the high ring strain present in cyclopropanes makes them challenging to produce and generally requires the use of highly reactive species, such as carbenes, ylids and carbanions.
