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Mathematical chemistry [1] is the area of research engaged in novel applications of mathematics to chemistry; it concerns itself principally with the mathematical modeling of chemical phenomena. [2] Mathematical chemistry has also sometimes been called computer chemistry , but should not be confused with computational chemistry .
Also acid ionization constant or acidity constant. A quantitative measure of the strength of an acid in solution expressed as an equilibrium constant for a chemical dissociation reaction in the context of acid-base reactions. It is often given as its base-10 cologarithm, p K a. acid–base extraction A chemical reaction in which chemical species are separated from other acids and bases. acid ...
For example: "All humans are mortal, and Socrates is a human. ∴ Socrates is mortal." ∵ Abbreviation of "because" or "since". Placed between two assertions, it means that the first one is implied by the second one. For example: "11 is prime ∵ it has no positive integer factors other than itself and one." ∋ 1. Abbreviation of "such that".
Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
In a few cases, the semicolon (;) or even backslash (\) is used as a separator for arguments. This may confuse the translation to algorithmic languages. Superscripts may indicate not only a power (exponent), but some other modification of the function. Examples (particularly with trigonometric and hyperbolic functions) include:
The same term can also be used more informally to refer to something "standard" or "classic". For example, one might say that Euclid's proof is the "canonical proof" of the infinitude of primes. There are two canonical proofs that are always used to show non-mathematicians what a mathematical proof is like:
In mathematics, particularly in universal algebra and category theory, transport of structure refers to the process whereby a mathematical object acquires a new structure and its canonical definitions, as a result of being isomorphic to (or otherwise identified with) another object with a pre-existing structure. [1]
An affine (algebraic) variety is an affine algebraic set that is not the union of two proper affine algebraic subsets. Such an affine algebraic set is often said to be irreducible . If X is an affine algebraic set, and I is the ideal of all polynomials that are zero on X , then the quotient ring R = k [ x 1 , … , x n ] / I {\displaystyle R=k ...