Binary formBinary form is a musical form in 2 related sections, both of which are usually repeated. Binary is also a structure used to choreograph dance. In music this is usually performed as A-A-B-B. Binary form was popular during the Baroque period, often used to structure movements of keyboard sonatas. It was also used for short, one-movement works. Around the middle of the 18th century, the form largely fell from use as the principal design of entire movements as sonata form and organic development gained prominence.
Asymmetric inductionAsymmetric induction (also enantioinduction) describes the preferential formation in a chemical reaction of one enantiomer or diastereoisomer over the other as a result of the influence of a chiral feature present in the substrate, reagent, catalyst or environment. Asymmetric induction is a key element in asymmetric synthesis. Asymmetric induction was introduced by Hermann Emil Fischer based on his work on carbohydrates. Several types of induction exist.
Quadratic formIn mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, is a quadratic form in the variables x and y. The coefficients usually belong to a fixed field K, such as the real or complex numbers, and one speaks of a quadratic form over K. If , and the quadratic form equals zero only when all variables are simultaneously zero, then it is a definite quadratic form; otherwise it is an isotropic quadratic form.
Aldol condensationAn aldol condensation is a condensation reaction in organic chemistry in which two carbonyl moieties (of aldehydes or ketones) react to form a β-hydroxyaldehyde or β-hydroxyketone (an aldol reaction), and this is then followed by dehydration to give a conjugated enone. The overall reaction equation is as follows (where the Rs can be H) Aldol condensations are important in organic synthesis and biochemistry as ways to form carbon–carbon bonds.
Representable functorIn mathematics, particularly , a representable functor is a certain functor from an arbitrary into the . Such functors give representations of an abstract category in terms of known structures (i.e. sets and functions) allowing one to utilize, as much as possible, knowledge about the category of sets in other settings. From another point of view, representable functors for a category C are the functors given with C. Their theory is a vast generalisation of upper sets in posets, and of Cayley's theorem in group theory.
KetoneIn organic chemistry, a ketone ˈkiːtoʊn is a functional group with the structure , where R and R' can be a variety of carbon-containing substituents. Ketones contain a carbonyl group (which contains a carbon-oxygen double bond C=O). The simplest ketone is acetone (where R and R' is methyl), with the formula . Many ketones are of great importance in biology and in industry. Examples include many sugars (ketoses), many steroids (e.g., testosterone), and the solvent acetone.
Functor represented by a schemeIn algebraic geometry, a functor represented by a scheme X is a set-valued contravariant functor on the category of schemes such that the value of the functor at each scheme S is (up to natural bijections) the set of all morphisms . The scheme X is then said to represent the functor and that classify geometric objects over S given by F. The best known example is the Hilbert scheme of a scheme X (over some fixed base scheme), which, when it exists, represents a functor sending a scheme S to a flat family of closed subschemes of .
Α-Halo ketoneIn organic chemistry, an α-halo ketone is a functional group consisting of a ketone group or more generally a carbonyl group with an α-halogen substituent. α-Halo ketones are alkylating agents. Prominent α-halo ketones include phenacyl bromide and chloroacetone. The general structure is RR′C(X)C(=O)R where R is an alkyl or aryl residue and X any one of the halogens. The preferred conformation of a halo ketone is that of a cisoid with the halogen and carbonyl sharing the same plane as the steric hindrance with the carbonyl alkyl group is generally larger.
Tick-borne encephalitisTick-borne encephalitis (TBE) is a viral infectious disease involving the central nervous system. The disease most often manifests as meningitis, encephalitis or meningoencephalitis. Myelitis and spinal paralysis also occurs. In about one third of cases sequelae, predominantly cognitive dysfunction, persist for a year or more. The number of reported cases has been increasing in most countries. TBE is posing a concerning health challenge to Europe, as the number of reported human cases of TBE in all endemic regions of Europe have increased by almost 400% within the last three decades.
Ketone bodiesKetone bodies are water-soluble molecules or compounds that contain the ketone groups produced from fatty acids by the liver (ketogenesis). Ketone bodies are readily transported into tissues outside the liver, where they are converted into acetyl-CoA (acetyl-Coenzyme A)—which then enters the citric acid cycle (Krebs cycle) and is oxidized for energy. These liver-derived ketone groups include acetoacetic acid (acetoacetate), beta-hydroxybutyrate, and acetone, a spontaneous breakdown product of acetoacetate (see graphic).
