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Conway and Kochen, The Strong Free Will Theorem, published in Notices of the AMS. Volume 56, Number 2, February 2009. Rehmeyer, Julie (August 15, 2008). "Do Subatomic Particles Have Free Will?". Science News. Introduction to the Free Will Theorem, videos of six lectures given by J. H. Conway, Mar. 2009. Wüthrich, Christian (September 2011).
Because the sum of the reciprocals of the primes diverges, the Green–Tao theorem on arithmetic progressions is a special case of the conjecture. The weaker claim that A must contain infinitely many arithmetic progressions of length 3 is a consequence of an improved bound in Roth's theorem. A 2016 paper by Bloom [4] proved that if {,..
1974 The Gorenstein–Harada theorem classifying finite groups of sectional 2-rank at most 4 was 464 pages long. 1976 Eisenstein series. Langlands's proof of the functional equation for Eisenstein series was 337 pages long. 1983 Trichotomy theorem. Gorenstein and Lyons's proof for the case of rank at least 4 was 731 pages long, and Aschbacher's ...
The theorem of Du Bois-Reymond asserts that this weak form implies the strong form. If L {\displaystyle L} has continuous first and second derivatives with respect to all of its arguments, and if ∂ 2 L ∂ f ′ 2 ≠ 0 , {\displaystyle {\frac {\partial ^{2}L}{\partial f'^{2}}}\neq 0,} then f {\displaystyle f} has two continuous derivatives ...
Consider the autonomous Itō stochastic differential equation: = + with initial condition =, where denotes the Wiener process, and suppose that we wish to solve this SDE on some interval of time [,]. Then the Milstein approximation to the true solution X {\displaystyle X} is the Markov chain Y {\displaystyle Y} defined as follows:
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
They are called the strong law of large numbers and the weak law of large numbers. [16] [1] Stated for the case where X 1, X 2, ... is an infinite sequence of independent and identically distributed (i.i.d.) Lebesgue integrable random variables with expected value E(X 1) = E(X 2) = ... = μ, both versions of the law state that the sample average
Renewal theory is the branch of probability theory that generalizes the Poisson process for arbitrary holding times. Instead of exponentially distributed holding times, a renewal process may have any independent and identically distributed (IID) holding times that have finite mean. A renewal-reward process additionally has a random sequence of ...