AlkyneAcetylene Propyne 1-Butyne In organic chemistry, an alkyne is an unsaturated hydrocarbon containing at least one carbon—carbon triple bond. The simplest acyclic alkynes with only one triple bond and no other functional groups form a homologous series with the general chemical formula . Alkynes are traditionally known as acetylenes, although the name acetylene also refers specifically to , known formally as ethyne using IUPAC nomenclature. Like other hydrocarbons, alkynes are generally hydrophobic.
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.
Organolithium reagentIn organometallic chemistry, organolithium reagents are chemical compounds that contain carbon–lithium (C–Li) bonds. These reagents are important in organic synthesis, and are frequently used to transfer the organic group or the lithium atom to the substrates in synthetic steps, through nucleophilic addition or simple deprotonation. Organolithium reagents are used in industry as an initiator for anionic polymerization, which leads to the production of various elastomers.
AlkynylationIn organic chemistry, alkynylation is an addition reaction in which a terminal alkyne () is added to a carbonyl group () to form an α-alkynyl alcohol (). When the acetylide is formed from acetylene (), the reaction gives an α-ethynyl alcohol. This process is often referred to as ethynylation. Such processes often involve metal acetylide intermediates. The principal reaction of interest involves the addition of the acetylene () to a ketone () or aldehyde (): RR'C=O + HC#CR'' -> RR'C(OH)C#CR'' The reaction proceeds with retention of the triple bond.
AlkeneIn organic chemistry, an alkene is a hydrocarbon containing a carbon–carbon double bond. The double bond may be internal or in the terminal position. Terminal alkenes are also known as α-olefins. The International Union of Pure and Applied Chemistry (IUPAC) recommends using the name "alkene" only for acyclic hydrocarbons with just one double bond; alkadiene, alkatriene, etc., or polyene for acyclic hydrocarbons with two or more double bonds; cycloalkene, cycloalkadiene, etc.
AlkylationAlkylation is a chemical reaction that entails transfer of an alkyl group. The alkyl group may be transferred as an alkyl carbocation, a free radical, a carbanion, or a carbene (or their equivalents). Alkylating agents are reagents for effecting alkylation. Alkyl groups can also be removed in a process known as dealkylation. Alkylating agents are often classified according to their nucleophilic or electrophilic character. In oil refining contexts, alkylation refers to a particular alkylation of isobutane with olefins.
Transformation matrixIn linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.
Geometric transformationIn mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often both or both — such that the function is bijective so that its inverse exists. The study of geometry may be approached by the study of these transformations. Geometric transformations can be classified by the dimension of their operand sets (thus distinguishing between, say, planar transformations and spatial transformations).
Abelian varietyIn mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in algebraic geometry and indispensable tools for much research on other topics in algebraic geometry and number theory. An abelian variety can be defined by equations having coefficients in any field; the variety is then said to be defined over that field.
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.
