Generating functionIn mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a formal power series. This series is called the generating function of the sequence. Unlike an ordinary series, the formal power series is not required to converge: in fact, the generating function is not actually regarded as a function, and the "variable" remains an indeterminate. Generating functions were first introduced by Abraham de Moivre in 1730, in order to solve the general linear recurrence problem.
Heterocyclic compoundA heterocyclic compound or ring structure is a cyclic compound that has atoms of at least two different elements as members of its ring(s). Heterocyclic organic chemistry is the branch of organic chemistry dealing with the synthesis, properties, and applications of organic heterocycles. Examples of heterocyclic compounds include all of the nucleic acids, the majority of drugs, most biomass (cellulose and related materials), and many natural and synthetic dyes. More than half of known compounds are heterocycles.
Forced conversionForced conversion is the adoption of a different religion or the adoption of irreligion under duress. Someone who has been forced to convert to a different religion or irreligion may continue, covertly, to adhere to the beliefs and practices which were originally held, while outwardly behaving as a convert. Crypto-Jews, crypto-Christians, crypto-Muslims and crypto-Pagans are historical examples of the latter. In general, anthropologists have shown that the relationship between religion and politics is complex, especially when it is viewed over the expanse of human history.
Sigmatropic reactionA sigmatropic reaction in organic chemistry is a pericyclic reaction wherein the net result is one σ-bond is changed to another σ-bond in an uncatalyzed intramolecular reaction. The name sigmatropic is the result of a compounding of the long-established sigma designation from single carbon–carbon bonds and the Greek word tropos, meaning turn. In this type of rearrangement reaction, a substituent moves from one part of a π-bonded system to another part in an intramolecular reaction with simultaneous rearrangement of the π system.
Religious conversionReligious conversion is the adoption of a set of beliefs identified with one particular religious denomination to the exclusion of others. Thus "religious conversion" would describe the abandoning of adherence to one denomination and affiliating with another. This might be from one to another denomination within the same religion, for example, from Protestant Christianity to Roman Catholicism or from Sunnī Islam to Shīʿa Islam. In some cases, religious conversion "marks a transformation of religious identity and is symbolized by special rituals".
Conversion to JudaismConversion to Judaism (גיור, giyur) is the process by which non-Jews adopt the Jewish religion and become members of the Jewish ethnoreligious community. It thus resembles both conversion to other religions and naturalization. The procedure and requirements for conversion depend on the sponsoring denomination. Furthermore, a conversion done in accordance with one Jewish denomination is not a guarantee of recognition by another denomination.
Ethylene oxideEthylene oxide is an organic compound with the formula . It is a cyclic ether and the simplest epoxide: a three-membered ring consisting of one oxygen atom and two carbon atoms. Ethylene oxide is a colorless and flammable gas with a faintly sweet odor. Because it is a strained ring, ethylene oxide easily participates in a number of addition reactions that result in ring-opening. Ethylene oxide is isomeric with acetaldehyde and with vinyl alcohol. Ethylene oxide is industrially produced by oxidation of ethylene in the presence of a silver catalyst.
