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In probability and statistics, a moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both.
Conjecture Field Comments Eponym(s) Cites 1/3–2/3 conjecture: order theory: n/a: 70 abc conjecture: number theory: ⇔Granville–Langevin conjecture, Vojta's conjecture in dimension 1 ⇒Erdős–Woods conjecture, Fermat–Catalan conjecture Formulated by David Masser and Joseph Oesterlé. [1] Proof claimed in 2012 by Shinichi Mochizuki: n/a ...
Moreover, the act of "observing" or "measuring" an object is irreversible, and no truth can be attributed to an object except according to the results of its measurement (that is, the Copenhagen interpretation rejects counterfactual definiteness). Copenhagen-type interpretations hold that quantum descriptions are objective, in that they are ...
where is the Lebesgue measure on , is the canonical measure on the boundary of arising from its description as a moment polytope (if an edge of is given by a linear inequality () for some affine linear functional h on with integer coefficients, then =), and = (,) / (,). Additionally the norm of the test configuration can be given by
The Tamagawa measure does not depend on the choice of ω, nor on the choice of measures on the k v, because multiplying ω by an element of k* multiplies the Haar measure on G(A) by 1, using the product formula for valuations. The Tamagawa number τ(G) is defined to be the Tamagawa measure of G(A)/G(k).
electric dipole moment A measure of the separation of positive and negative electric charges within an electrical system, i.e. a measure of the system's overall electrical polarity. The SI unit for measuring electric dipole moment is the coulomb-metre (C⋅m), but the debye (D), a non-SI unit, is also widely used in chemistry and atomic physics.
In quantum mechanics, superdeterminism is a loophole in Bell's theorem.By postulating that all systems being measured are correlated with the choices of which measurements to make on them, the assumptions of the theorem are no longer fulfilled.
The telescope conjecture, which was fourth on the original list, remains of substantial interest because of its connection with the convergence of an Adams–Novikov spectral sequence. While opinion has been generally against the truth of the original statement, investigations of associated phenomena (for a triangulated category in general ...