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A quadratic form with integer coefficients is called an integral binary quadratic form, often abbreviated to binary quadratic form. This article is entirely devoted to integral binary quadratic forms. This choice is motivated by their status as the driving force behind the development of algebraic number theory.
Jones et al. utilized the CBS reduction in the total synthesis of MK-0417, a water-soluble carbonic anhydrase inhibitor which has been used therapeutically to reduce intraocular pressure. [14] Asymmetric reduction of a key bicyclic sulfone intermediate was accomplished with the CBS oxazaborolidine catalyst containing Me as the R’ group.
Note that there is a close relation between reducing binary quadratic forms and continued fraction expansion; one step in the continued fraction expansion of a certain quadratic irrationality gives a unary operation on the set of reduced forms, which cycles through all reduced forms in one equivalence class.
The parameters may be derived from various experimental data such as the osmotic coefficient, mixed ion activity coefficients, and salt solubility. They can be used to calculate mixed ion activity coefficients and water activities in solutions of high ionic strength for which the Debye–Hückel theory is no longer adequate.
The following chart shows the solubility of various ionic compounds in water at 1 atm pressure and room temperature (approx. 25 °C, 298.15 K). "Soluble" means the ionic compound doesn't precipitate, while "slightly soluble" and "insoluble" mean that a solid will precipitate; "slightly soluble" compounds like calcium sulfate may require heat to precipitate.
Squaric acid, also called quadratic acid because its four carbon atoms approximately form a square, is a diprotic organic acid with the chemical formula C 4 O 2 (OH) 2. [4]The conjugate base of squaric acid is the hydrogensquarate anion HC 4 O − 4; and the conjugate base of the hydrogensquarate anion is the divalent squarate anion C 4 O 2− 4.
Deprotonation of acetic acid by a hydroxide ion. Deprotonation (or dehydronation) is the removal (transfer) of a proton (or hydron, or hydrogen cation), (H +) from a Brønsted–Lowry acid in an acid–base reaction. [1] [2] The species formed is the conjugate base of that acid.
The iterations are continued until no significant reduction in U is achieved, that is, until a convergence criterion is satisfied. If, however, the updated parameters do not result in a decrease of the objective function, that is, if divergence occurs, the increment calculation must be modified.