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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.
It is a common observation that when oil and water are poured into the same container, they separate into two phases or layers, because they are immiscible.In general, aqueous (or water-based) solutions, being polar, are immiscible with non-polar organic solvents (cooking oil, chloroform, toluene, hexane etc.) and form a two-phase system.
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.
These water-soluble form, bile acids e.g., deoxycholic and lithocholic are adsorbed to dietary fiber and an increased fecal loss of sterols, dependent in part on the amount and type of fiber. A further factor is an increase in the bacterial mass and activity of the ileum as some fibers e.g., pectin are digested by bacteria.
Another form to synthesize formazans is by the reaction of active methylene compounds with diazonium salts. Diazonium salts add to active methylene compounds to form an intermediate azo compound, followed by the addition of a second diazonium salt (under more alkaline conditions), yielding tetrazene, which then forms a 3-substituted formazan.
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.
Polydextrose is a form of soluble fiber and has shown healthful prebiotic benefits when tested in animals. It contains only 1 kcal per gram and, therefore, is able to help reduce calories. It contains only 1 kcal per gram and, therefore, is able to help reduce calories.
Pages in category "Quadratic forms" The following 61 pages are in this category, out of 61 total. ... Binary quadratic form; Brauer–Wall group; Büchi's problem; C.