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.
Radical initiatorIn chemistry, radical initiators are substances that can produce radical species under mild conditions and promote radical reactions. These substances generally possess weak bonds—bonds that have small bond dissociation energies. Radical initiators are utilized in industrial processes such as polymer synthesis. Typical examples are molecules with a nitrogen-halogen bond, azo compounds, and organic and inorganic peroxides. Halogens undergo homolytic fission relatively easily.
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.
DiazoIn organic chemistry, the diazo group is an organic moiety consisting of two linked nitrogen atoms (azo, ) at the terminal position. Overall charge-neutral organic compounds containing the diazo group bound to a carbon atom are called diazo compounds or diazoalkanes and are described by the general structural formula . The simplest example of a diazo compound is diazomethane, . Diazo compounds () should not be confused with azo compounds () or with diazonium compounds ().
CalixareneA calixarene is a macrocycle or cyclic oligomer based on a methylene-linked phenols. With hydrophobic cavities that can hold smaller molecules or ions, calixarenes belong to the class of cavitands known in host–guest chemistry. Calixarene nomenclature is straightforward and involves counting the number of repeating units in the ring and including it in the name. A calix[4]arene has 4 units in the ring and a calix[6]arene has 6.
Momentum exchange tetherA momentum exchange tether is a kind of space tether that could theoretically be used as a launch system, or to change spacecraft orbits. Momentum exchange tethers create a controlled force on the end-masses of the system due to the pseudo-force known as centrifugal force. While the tether system rotates, the objects on either end of the tether will experience continuous acceleration; the magnitude of the acceleration depends on the length of the tether and the rotation rate.
