Diazonium compoundDiazonium compounds or diazonium salts are a group of organic compounds sharing a common functional group where R can be any organic group, such as an alkyl or an aryl, and X is an inorganic or organic anion, such as a halide. According to X-ray crystallography the linkage is linear in typical diazonium salts. The bond distance in benzenediazonium tetrafluoroborate is 1.083(3) Å, which is almost identical to that for dinitrogen molecule (N≡N). The linear free energy constants σm and σp indicate that the diazonium group is strongly electron-withdrawing.
Hydrogen storageSeveral methods exist for storing hydrogen. These include mechanical approaches such as using high pressures and low temperatures, or employing chemical compounds that release H2 upon demand. While large amounts of hydrogen are produced by various industries, it is mostly consumed at the site of production, notably for the synthesis of ammonia. For many years hydrogen has been stored as compressed gas or cryogenic liquid, and transported as such in cylinders, tubes, and cryogenic tanks for use in industry or as propellant in space programs.
Unitary groupIn mathematics, the unitary group of degree n, denoted U(n), is the group of n × n unitary matrices, with the group operation of matrix multiplication. The unitary group is a subgroup of the general linear group GL(n, C). Hyperorthogonal group is an archaic name for the unitary group, especially over finite fields. For the group of unitary matrices with determinant 1, see Special unitary group. In the simple case n = 1, the group U(1) corresponds to the circle group, consisting of all complex numbers with absolute value 1, under multiplication.
Automorphism groupIn mathematics, the automorphism group of an object X is the group consisting of automorphisms of X under composition of morphisms. For example, if X is a finite-dimensional vector space, then the automorphism group of X is the group of invertible linear transformations from X to itself (the general linear group of X). If instead X is a group, then its automorphism group is the group consisting of all group automorphisms of X. Especially in geometric contexts, an automorphism group is also called a symmetry group.
R33-class airshipThe R.33 class of British rigid airships were built for the Royal Naval Air Service during the First World War, but were not completed until after the end of hostilities, by which time the RNAS had become part of the Royal Air Force. The lead ship, R.33, served successfully for ten years and survived one of the most alarming and heroic incidents in airship history when she was torn from her mooring mast in a gale. She was called a "Pulham Pig" by the locals, as the blimps based there had been, and is immortalised in the village sign for Pulham St Mary.
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.
Alkyl groupIn organic chemistry, an alkyl group is an alkane missing one hydrogen. The term alkyl is intentionally unspecific to include many possible substitutions. An acyclic alkyl has the general formula of . A cycloalkyl group is derived from a cycloalkane by removal of a hydrogen atom from a ring and has the general formula . Typically an alkyl is a part of a larger molecule. In structural formulae, the symbol R is used to designate a generic (unspecified) alkyl group. The smallest alkyl group is methyl, with the formula .
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.
Group (mathematics)In mathematics, a group is a non-empty set with an operation that satisfies the following constraints: the operation is associative, has an identity element, and every element of the set has an inverse element. Many mathematical structures are groups endowed with other properties. For example, the integers with the addition operation is an infinite group, which is generated by a single element called 1 (these properties characterize the integers in a unique way).
Linear independenceIn the theory of vector spaces, a set of vectors is said to be if there exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear combination exists, then the vectors are said to be . These concepts are central to the definition of dimension. A vector space can be of finite dimension or infinite dimension depending on the maximum number of linearly independent vectors. The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space.
