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More formally, proposition B is a corollary of proposition A, if B can be readily deduced from A or is self-evident from its proof. In many cases, a corollary corresponds to a special case of a larger theorem, [4] which makes the theorem easier to use and apply, [5] even though its importance is generally considered to be secondary to that of ...
Kawasaki's theorem (mathematics of paper folding) Kelvin's circulation theorem ; Kempf–Ness theorem (algebraic geometry) Kepler conjecture (discrete geometry) Kharitonov's theorem (control theory) Khinchin's theorem (probability) Killing–Hopf theorem (Riemannian geometry) Kinoshita–Lee–Nauenberg theorem (quantum field theory)
Artin reciprocity law is a general theorem in number theory that forms a central part of global class field theory. Named after Emil Artin. Ashby's law of requisite variety, that the number of states in a control mechanism must be greater than or equal to the number of states in the system it controls.
Corollary 1: the ground-state density uniquely determines the potential and thus all properties of the system, including the many-body wavefunction. In particular, the HK functional, defined as F [ n ] = T [ n ] + U [ n ] {\displaystyle F[n]=T[n]+U[n]} , is a universal functional of the density (not depending explicitly on the external potential).
Ptolemy's Theorem yields as a corollary a pretty theorem [2] regarding an equilateral triangle inscribed in a circle. Given An equilateral triangle inscribed on a circle and a point on the circle. The distance from the point to the most distant vertex of the triangle is the sum of the distances from the point to the two nearer vertices.
A representation of Hess's law (where H represents enthalpy) Hess's law of constant heat summation, also known simply as Hess's law, is a relationship in physical chemistry and thermodynamics [1] named after Germain Hess, a Swiss-born Russian chemist and physician who published it in 1840.
According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews (MR) database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The ...
This theorem is of central importance in model theory, where the words "by compactness" are commonplace. [5] Another cornerstone of first-order model theory is the Löwenheim–Skolem theorem. According to the theorem, every infinite structure in a countable signature has a countable elementary substructure.