In algebraic number theory, Minkowski's bound gives an upper bound of the norm of ideals to be checked in order to determine the class number of a number...

In mathematics, Minkowski's theorem is the statement that every convex set in R n {\displaystyle \mathbb {R} ^{n}} which is symmetric with respect to...

polytopes Minkowski's second theorem Minkowski space Minkowski's bound Minkowski's theorem in geometry of numbers Minkowski–Hlawka theorem Minkowski–Steiner...

class group of a quadratic field extension can be accomplished using Minkowski's bound and the Kronecker symbol because of the finiteness of the class group...

stated Minkowski's theorem in 1882, though the first proof was given by Hermann Minkowski in 1891. In the same year, Minkowski published his bound on the...

using Minkowski's bound. This result gives a bound, depending on the ring, such that every ideal class contains an ideal norm less than the bound. In general...

bodies Minkowski's question mark function Minkowski's second theorem Minkowski's theorem in geometry of numbers Minkowski–Bouligand dimension Minkowski cover...

{\textstyle \lambda _{1}(L)\lambda _{1}(L^{*})\leq n} follows from Minkowski's bound on the shortest vector; that is, λ 1 ( L ) ≤ n ( det ( L ) 1 / n )...

lower bound of S {\displaystyle S} , then b is less than or equal to the infimum of S {\displaystyle S} . Consequently, the term greatest lower bound (abbreviated...

In mathematics, Minkowski's second theorem is a result in the geometry of numbers about the values taken by a norm on a lattice and the volume of its...

forgotten for many years. It was rediscovered by H. Minkowski (1885), and an error in Minkowski's paper was found and corrected by C. L. Siegel (1935)...

Demonstrations Project. Minkowski's addition of convex shapes by Alexander Bogomolny: an applet Wikibooks:OpenSCAD User Manual/Transformations#minkowski by Marius Kintel:...

defined in terms of microscopic bound charges and bound currents respectively. The macroscopic bound charge density ρb and bound current density Jb in terms...

everywhere unramified extension of K, and it is abelian. Using the Minkowski bound, one can show that K has class number 2. Hence, its Hilbert class field...

In fractal geometry, the Minkowski–Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the fractal...

hull of a totally bounded subset of a topological vector space is again totally bounded. The Minkowski sum of two compact (totally bounded) sets is compact...

{\displaystyle K} is a convex centrally symmetric body. Minkowski's theorem, sometimes called Minkowski's first theorem, states that if vol ⁡ ( K ) > 2 n vol...

set in Rn, given as the image of a bounded set from Rm under a Lipschitz function, then the m-dimensional Minkowski content of A exists, and is equal to...

In mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures)...

method of visualizing four-dimensional objects with Schlegel diagrams. Minkowski's 1908 paper consolidating the role of time as the fourth dimension of...

inequality Melchior's inequality Milman's reverse Brunn–Minkowski inequality Milnor–Wood inequality Minkowski's first inequality for convex bodies Myers's theorem...

geometrical vector. A bound vector is defined as the combination of an ordinary vector quantity and a point of application or point of action. Bound vector quantities...

Hermann Minkowski; it has been called "Minkowski's theorem", although the same name has also been given to several unrelated results of Minkowski. The Minkowski...

called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include the set. A set that is not bounded is called...

Hermann Minkowski's Space–Time Formalism of Special Relativity". arXiv:1210.6929 [physics.hist-ph]. Galison, Peter Louis (1979). "Minkowski's space–time:...

triangle, while the perimeters of the successive stages increase without bound. Consequently, the snowflake encloses a finite area, but has an infinite...

case of scalar bound states through a scalar-particle exchange in the rainbow-ladder truncation, the Bethe—Salpeter equation in the Minkowski space can be...

lattice point. Although Minkowski's original proof was different, Blichfeldt's theorem can be used in a simple proof of Minkowski's theorem. Let X {\displaystyle...

proof by Hermann Minkowski (1911, pages 265–276) and proved by Edmund Hlawka (1943). The result is related to a linear lower bound for the Hermite constant...

Lebesgue measure and the + on the left-hand side denotes Minkowski addition. In general, no reverse bound is possible, since one can find convex bodies K and...