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In number theory, a branch of mathematics, Ramanujan's ternary quadratic form is the algebraic expression x 2 + y 2 + 10z 2 with integral values for x, y and z. [ 1 ] [ 2 ] Srinivasa Ramanujan considered this expression in a footnote in a paper [ 3 ] published in 1916 and briefly discussed the representability of integers in this form.
A mapping q : M → R : v ↦ b(v, v) is the associated quadratic form of b, and B : M × M → R : (u, v) ↦ q(u + v) − q(u) − q(v) is the polar form of q. A quadratic form q : M → R may be characterized in the following equivalent ways: There exists an R-bilinear form b : M × M → R such that q(v) is the associated quadratic form.
A ternary complex is a protein complex containing three different molecules that are bound together. In structural biology , ternary complex can also be used to describe a crystal containing a protein with two small molecules bound, such as a cofactor and a substrate ; or a complex formed between two proteins and a single substrate. [ 1 ]
In inorganic chemistry and materials chemistry, a ternary compound or ternary phase is a chemical compound containing three different elements. While some ternary compounds are molecular, e.g. chloroform (HCCl 3), more typically ternary phases refer to extended solids. Famous example are the perovskites. [1]
The catalecticant of a ternary quartic is the resultant of its 6 second partial derivatives. It vanishes when the ternary quartic can be written as a sum of five 4th powers of linear forms. See also
1. A contravariant of a ternary form, giving the equation of a dual curve. (Elliott 1895, p.400) reciprocity Exchanging the degree of a form with the degree of an invariant. For example, Hermite's law of reciprocity states that the degree p invariants of a form of degree n correspond to the degree n invariants of a form of degree p.
They have Brock Bowers and Jakobi Meyers to form a solid duo for their next passer. New York Jets Turn the page. The Aaron Rodgers experiment was a failure. The more the Jets leaned into it by ...
An integral quadratic form is a quadratic form on Z n, or equivalently a free Z-module of finite rank. Two such forms are in the same genus if they are equivalent over the local rings Z p for each prime p and also equivalent over R .