Enantioselective synthesisEnantioselective synthesis, also called asymmetric synthesis, is a form of chemical synthesis. It is defined by IUPAC as "a chemical reaction (or reaction sequence) in which one or more new elements of chirality are formed in a substrate molecule and which produces the stereoisomeric (enantiomeric or diastereomeric) products in unequal amounts." Put more simply: it is the synthesis of a compound by a method that favors the formation of a specific enantiomer or diastereomer.
Kinetic resolutionIn organic chemistry, kinetic resolution is a means of differentiating two enantiomers in a racemic mixture. In kinetic resolution, two enantiomers react with different reaction rates in a chemical reaction with a chiral catalyst or reagent, resulting in an enantioenriched sample of the less reactive enantiomer. As opposed to chiral resolution, kinetic resolution does not rely on different physical properties of diastereomeric products, but rather on the different chemical properties of the racemic starting materials.
Z-transformIn mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain (z-domain or z-plane) representation. It can be considered as a discrete-time equivalent of the Laplace transform (s-domain). This similarity is explored in the theory of time-scale calculus. Whereas the continuous-time Fourier transform is evaluated on the Laplace s-domain's imaginary line, the discrete-time Fourier transform is evaluated over the unit circle of the z-domain.
Building materialBuilding material is material used for construction. Many naturally occurring substances, such as clay, rocks, sand, wood, and even twigs and leaves, have been used to construct buildings. Apart from naturally occurring materials, many man-made products are in use, some more and some less synthetic. The manufacturing of building materials is an established industry in many countries and the use of these materials is typically segmented into specific specialty trades, such as carpentry, insulation, plumbing, and roofing work.
Cross productIn mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ), and is denoted by the symbol . Given two linearly independent vectors a and b, the cross product, a × b (read "a cross b"), is a vector that is perpendicular to both a and b, and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming.
Access networkAn access network is a type of telecommunications network which connects subscribers to their immediate service provider. It is contrasted with the core network, which connects local providers to one another. The access network may be further divided between feeder plant or distribution network, and drop plant or edge network. An access network, also referred to as an outside plant, refers to the series of wires, cables and equipment lying between a consumer/business telephone termination point (the point at which a telephone connection reaches the customer) and the local telephone exchange.
Internet accessInternet access is the ability of individuals and organizations to connect to the Internet using computer terminals, computers, and other devices; and to access services such as email and the World Wide Web. Internet access is sold by Internet service providers (ISPs) delivering connectivity at a wide range of data transfer rates via various networking technologies. Many organizations, including a growing number of municipal entities, also provide cost-free wireless access and landlines.
Infinite productIn mathematics, for a sequence of complex numbers a1, a2, a3, ... the infinite product is defined to be the limit of the partial products a1a2...an as n increases without bound. The product is said to converge when the limit exists and is not zero. Otherwise the product is said to diverge. A limit of zero is treated specially in order to obtain results analogous to those for infinite sums. Some sources allow convergence to 0 if there are only a finite number of zero factors and the product of the non-zero factors is non-zero, but for simplicity we will not allow that here.
Wallis productIn mathematics, the Wallis product for pi, published in 1656 by John Wallis, states that Wallis derived this infinite product using interpolation, though his method is not regarded as rigorous. A modern derivation can be found by examining for even and odd values of , and noting that for large , increasing by 1 results in a change that becomes ever smaller as increases. Let (This is a form of Wallis' integrals.) Integrate by parts: Now, we make two variable substitutions for convenience to obtain: We obtain values for and for later use.
Triple productIn geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors. The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product. The scalar triple product (also called the mixed product, box product, or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two.
