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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 ...
The fourth central moment is a measure of the heaviness of the tail of the distribution. Since it is the expectation of a fourth power, the fourth central moment, where defined, is always nonnegative; and except for a point distribution, it is always strictly positive. The fourth central moment of a normal distribution is 3σ 4.
Let (,) be a closed symplectic manifold. A Hamiltonian diffeomorphism : is called nondegenerate if its graph intersects the diagonal of transversely. For nondegenerate Hamiltonian diffeomorphisms, one variant of the Arnold conjecture says that the number of fixed points is at least equal to the minimal number of critical points of a Morse function on , called the Morse number of .
In Bernoulli's own words, the "art of conjecture" is defined in Chapter II of Part IV of his Ars Conjectandi as: The art of measuring, as precisely as possible, probabilities of things, with the goal that we would be able always to choose or follow in our judgments and actions that course, which will have been determined to be better, more ...
In geometric measure theory, Falconer's conjecture, named after Kenneth Falconer, is an unsolved problem concerning the sets of Euclidean distances between points in compact-dimensional spaces. Intuitively, it states that a set of points that is large in its Hausdorff dimension must determine a set of distances that is large in measure .
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.
In probability and statistics, a factorial 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.