Algebraic varietyAlgebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition. Conventions regarding the definition of an algebraic variety differ slightly.
Projective varietyIn algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space over k that is the zero-locus of some finite family of homogeneous polynomials of n + 1 variables with coefficients in k, that generate a prime ideal, the defining ideal of the variety. Equivalently, an algebraic variety is projective if it can be embedded as a Zariski closed subvariety of .
AcetylideIn organometallic chemistry, acetylide refers to chemical compounds with the chemical formulas and , where M is a metal. The term is used loosely and can refer to substituted acetylides having the general structure (where R is an organic side chain). Acetylides are reagents in organic synthesis. The calcium acetylide commonly called calcium carbide is a major compound of commerce. Alkali metal and alkaline earth metal acetylides of the general formula MC≡CM are salt-like Zintl phase compounds, containing C22− ions.
Chow varietyIn mathematics, particularly in the field of algebraic geometry, a Chow variety is an algebraic variety whose points correspond to effective algebraic cycles of fixed dimension and degree on a given projective space. More precisely, the Chow variety is the fine moduli variety parametrizing all effective algebraic cycles of dimension and degree in . The Chow variety may be constructed via a Chow embedding into a sufficiently large projective space.
Organosodium chemistryOrganosodium chemistry is the chemistry of organometallic compounds containing a carbon to sodium chemical bond. The application of organosodium compounds in chemistry is limited in part due to competition from organolithium compounds, which are commercially available and exhibit more convenient reactivity. The principal organosodium compound of commercial importance is sodium cyclopentadienide. Sodium tetraphenylborate can also be classified as an organosodium compound since in the solid state sodium is bound to the aryl groups.
Michael addition reactionIn organic chemistry, the Michael reaction or Michael 1,4 addition is a reaction between a Michael donor (an enolate or other nucleophile) and a Michael acceptor (usually an α,β-unsaturated carbonyl) to produce a Michael adduct by creating a carbon-carbon bond at the acceptor's β-carbon. It belongs to the larger class of conjugate additions and is widely used for the mild formation of carbon-carbon bonds.
CarbanionIn organic chemistry, a carbanion is an anion in which carbon is negatively charged. Formally, a carbanion is the conjugate base of a carbon acid: where B stands for the base. The carbanions formed from deprotonation of alkanes (at an sp3 carbon), alkenes (at an sp2 carbon), arenes (at an sp2 carbon), and alkynes (at an sp carbon) are known as alkyl, alkenyl (vinyl), aryl, and alkynyl (acetylide) anions, respectively.
Grignard reactionThe Grignard reaction (ɡʁiɲaʁ) is an organometallic chemical reaction in which carbon alkyl, allyl, vinyl, or aryl magnesium halides (Grignard reagent) are added to the carbonyl groups of either an aldehyde or ketone. This reaction is important for the formation of carbon–carbon bonds. (R2 could also be a hydrogen)Grignard reactions and reagents were discovered by and are named after the French chemist François Auguste Victor Grignard (University of Nancy, France), who published it in 1900 and was awarded the 1912 Nobel Prize in Chemistry for this work.
Generalized flag varietyIn mathematics, a generalized flag variety (or simply flag variety) is a homogeneous space whose points are flags in a finite-dimensional vector space V over a field F. When F is the real or complex numbers, a generalized flag variety is a smooth or complex manifold, called a real or complex flag manifold. Flag varieties are naturally projective varieties. Flag varieties can be defined in various degrees of generality. A prototype is the variety of complete flags in a vector space V over a field F, which is a flag variety for the special linear group over F.
ProcessA process is a series or set of activities that interact to produce a result; it may occur once-only or be recurrent or periodic. Things called a process include: Business process, activities that produce a specific service or product for customers Business process modeling, activity of representing processes of an enterprise in order to deliver improvements Manufacturing process management, a collection of technologies and methods used to define how products are to be manufactured. Process architecture, s
