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In the case of a non-cyclic cubic field K this index formula can be combined with the conductor formula D = f 2 d to obtain a decomposition of the polynomial discriminant Δ = i(θ) 2 f 2 d into the square of the product i(θ)f and the discriminant d of the quadratic field k associated with the cubic field K, where d is squarefree up to a ...
A cyclic compound (or ring compound) is a term for a compound in the field of chemistry in which one or more series of atoms in the compound is connected to form a ring.
Suppose a function f(x, y, z) = 0, where x, y, and z are functions of each other. Write the total differentials of the variables = + = + Substitute dy into dx = [() + ()] + By using the chain rule one can show the coefficient of dx on the right hand side is equal to one, thus the coefficient of dz must be zero () + = Subtracting the second term and multiplying by its inverse gives the triple ...
The name octasulfur is the most commonly used for this chemical. It is systematically named cyclo-octasulfur (which is the preferred IUPAC name) and cyclooctasulfane.It is also the final member of the thiocane heterocylic series, where every carbon atom is substituted with a sulfur atom, thus this sulfur allotrope is systematically named octathiocane as well.
Heterocyclic organic chemistry is the branch of organic chemistry dealing with the synthesis, properties, and applications of organic heterocycles. [ 2 ] Examples of heterocyclic compounds include all of the nucleic acids , the majority of drugs, most biomass ( cellulose and related materials), and many natural and synthetic dyes.
In mathematics, the conductor-discriminant formula or Führerdiskriminantenproduktformel, introduced by Hasse (1926, 1930) for abelian extensions and by Artin () for ...
Cyclodextrins are a family of cyclic oligosaccharides, consisting of a macrocyclic ring of glucose subunits joined by α-1,4 glycosidic bonds. Cyclodextrins are produced from starch by enzymatic conversion. They are used in food, pharmaceutical, drug delivery, and chemical industries, as well as agriculture and environmental engineering. [1]
The cyclic form was identified in 2003 by N. Hansen and A. M. Wodtke using ultraviolet photolysis of chlorine azide. Although the reaction yielded mostly the linear form, about 20% of the molecules were cyclic. [4] [1] The ring has C 2v symmetry [1] —an isosceles triangle—in contrast to the linear form that has equal N–N bond-lengths.