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In chemistry, the haloform reaction (also referred to as the Lieben haloform reaction) is a chemical reaction in which a haloform (CHX 3, where X is a halogen) is produced by the exhaustive halogenation of an acetyl group (R−C(=O)CH 3, where R can be either a hydrogen atom, an alkyl or an aryl group), in the presence of a base.
Trihalomethanes with all the same halogen atoms are called haloforms. Many trihalomethanes find uses in industry as solvents or refrigerants . Some THMs are also environmental pollutants , and a few are considered carcinogenic .
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities.
Bromoform was discovered in 1832 by Löwig who distilled a mixture of bromal and potassium hydroxide, as analogous to preparation of chloroform from chloral. [5]Bromoform can be prepared by the haloform reaction using acetone and sodium hypobromite, by the electrolysis of potassium bromide in ethanol, or by treating chloroform with aluminium bromide.
A matrix effect value of less than 100 indicates suppression, while a value larger than 100 is a sign of matrix enhancement. An alternative definition of matrix effect utilizes the formula: M E = 100 ( A ( e x t r a c t ) A ( s t a n d a r d ) ) − 100 {\displaystyle ME=100\left({\frac {A(extract)}{A(standard)}}\right)-100}
In complex analysis of one and several complex variables, Wirtinger derivatives (sometimes also called Wirtinger operators [1]), named after Wilhelm Wirtinger who introduced them in 1927 in the course of his studies on the theory of functions of several complex variables, are partial differential operators of the first order which behave in a very similar manner to the ordinary derivatives ...
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced / ʃ ə ˈ l ɛ s k i / shə-LES-kee) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations.
A matrix () is called a fundamental matrix solution if the columns form a basis of the solution set. A matrix () is called a principal fundamental matrix solution if all columns are linearly independent solutions and there exists such that () is the identity.