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t. e. Rouché's theorem, named after Eugène Rouché, states that for any two complex -valued functions f and g holomorphic inside some region with closed contour , if |g(z)| < |f(z)| on , then f and f + g have the same number of zeros inside , where each zero is counted as many times as its multiplicity. This theorem assumes that the contour ...
First stated in. 1929; 95 years ago (1929) In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials [1] —hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product: F irst ("first" terms of each binomial are multiplied together) O uter ("outside ...
For instance, the polynomial x 2 + 3x + 2 is an example of this type of trinomial with n = 1. The solution a 1 = −2 and a 2 = −1 of the above system gives the trinomial factorization: x 2 + 3x + 2 = (x + a 1)(x + a 2) = (x + 2)(x + 1). The same result can be provided by Ruffini's rule, but with a more complex and time-consuming process.
Trinomial expansion. In mathematics, a trinomial expansion is the expansion of a power of a sum of three terms into monomials. The expansion is given by. where n is a nonnegative integer and the sum is taken over all combinations of nonnegative indices i, j, and k such that i + j + k = n. [1] The trinomial coefficients are given by.
0.6. The Taft equation is a linear free energy relationship (LFER) used in physical organic chemistry in the study of reaction mechanisms and in the development of quantitative structure–activity relationships for organic compounds. It was developed by Robert W. Taft in 1952 [2][3][4] as a modification to the Hammett equation. [5]
Divergent synthesis. In chemistry a divergent synthesis is a strategy with the aim to improve the efficiency of chemical synthesis. It is often an alternative to convergent synthesis or linear synthesis. In one strategy divergent synthesis aims to generate a library of chemical compounds by first reacting a molecule with a set of reactants.
Factorization of polynomials. In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain. Polynomial factorization is one of the fundamental components of ...
S. N. 1 reaction. Substitution reaction with a carbocation intermediate. General reaction scheme for the S N 1 reaction. The leaving group is denoted "X", and the nucleophile is denoted "Nu–H". The unimolecular nucleophilic substitution (SN1) reaction is a substitution reaction in organic chemistry. The Hughes-Ingold symbol of the mechanism ...