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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.
In the toric setting many of the complicated definitions of K-stability simplify to be given by data on the moment polytope of the polarised toric variety (,). First it is known that to test K-stability, it is enough to consider toric test configurations , where the total space of the test configuration is also a toric variety.
The conjecture was also independently proven by Danny Calegari and David Gabai, and implies the Ahlfors measure conjecture. [6] In 2012, he announced a proof of the virtually Haken conjecture, which was published a year later. [7] The conjecture (now theorem) states that every aspherical 3-manifold is finitely covered by a Haken manifold.
The conjectures in following list were not necessarily generally accepted as true before being disproved. Atiyah conjecture (not a conjecture to start with) Borsuk's conjecture; Chinese hypothesis (not a conjecture to start with) Doomsday conjecture; Euler's sum of powers conjecture; Ganea conjecture; Generalized Smith conjecture; Hauptvermutung
In mathematics, the Ahlfors conjecture, now a theorem, states that the limit set of a finitely-generated Kleinian group is either the whole Riemann sphere, or has measure 0. The conjecture was introduced by Ahlfors ( 1966 ), who proved it in the case that the Kleinian group has a fundamental domain with a finite number of sides.
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 1929 Ahlfors published the first proof of this conjecture, now known as the Denjoy–Carleman–Ahlfors theorem. [3] It states that the number of asymptotic values approached by an entire function of order ρ along curves in the complex plane going toward infinity is less than or equal to 2ρ.
The history of scientific method considers changes in the methodology of scientific inquiry, not the history of science itself. The development of rules for scientific reasoning has not been straightforward; scientific method has been the subject of intense and recurring debate throughout the history of science, and eminent natural philosophers and scientists have argued for the primacy of ...