24 Übersetzungen
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Anwendungsbeispiele Englisch
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- Via Lebesgue's decomposition theorem, every σ-finite measure can be decomposed into the sum of an absolutely continuous measure and a singular measure with respect to another σ-finite measure.
- Paul Seymour's decomposition theorem for regular matroids (1980) was the most significant and influential work of the late 1970s and the 1980s.
- Per the polar decomposition theorem, the deformation produced by such shearing force is equivalent to rotation of the rock combined with shortening in one direction and extension in another.
- This "decomposition theorem" is a by-product of the stationary case of electrodynamics.
- The concept of normal surface is due to Hellmuth Kneser, who utilized it in his proof of the prime decomposition theorem for 3-manifolds.
- This consequence of the Hahn decomposition theorem is called the "Jordan decomposition".
- Its existence follows from the Doob–Meyer decomposition theorem and, for continuous local martingales, it is the same as the quadratic variation.
- Some important basic results about the cohomology of Lie algebras include Whitehead's lemmas, Weyl's theorem, and the Levi decomposition theorem.
- One of the main theorems of von Neumann and Murray in their original series of papers is a proof of the decomposition theorem: Any von Neumann algebra is a direct integral of factors.
- In the case of finite groups, this is Mackey's decomposition theorem.
- This dual object is suitable for formulating a Fourier transform and a Plancherel theorem for unimodular separable locally compact groups of type I and a decomposition theorem for arbitrary representations of separable locally compact groups of type I.
- Since this is not true of R3, the Hodge decomposition theorem is not strictly a generalization of the Helmholtz theorem.
- In 1952 Georges de Rham proved the "de Rham decomposition theorem", a principle for splitting a Riemannian manifold into a Cartesian product of Riemannian manifolds by splitting the tangent bundle into irreducible spaces under the action of the local holonomy groups.
- By the Helmholtz decomposition theorem however, all vector fields can be describable in terms of a scalar potential and corresponding vector potential.
- This result, now known as the "de Rham decomposition theorem", has become a fundamental textbook result in Riemannian geometry.
- So this Hodge decomposition theorem connects topology and complex geometry for compact Kähler manifolds.
- The Jordan normal form is named after Camille Jordan, who first stated the Jordan decomposition theorem in 1870.
- Many other proofs exist which apply similar methods but which avoid the need to use the Doob–Meyer decomposition theorem, such as the use of the quadratic variation [...] in the Itô isometry, the use of the Doléans measure for submartingales, or the use of the Burkholder–Davis–Gundy inequalities instead of the Itô isometry.
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