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In algebra and number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers less than n is one less than a multiple of n.
Descartes's theorem (plane geometry) Descartes's theorem on total angular defect ; Diaconescu's theorem (mathematical logic) Diller–Dress theorem (field theory) Dilworth's theorem (combinatorics, order theory) Dinostratus' theorem (geometry, analysis) Dimension theorem for vector spaces (vector spaces, linear algebra) Dini's theorem
Three spin-off games accompany the main series: Geometry Dash Meltdown, Geometry Dash World and Geometry Dash SubZero. Geometry Dash Lite is a free version of the main game that includes fewer levels, displays advertisements, and lacks the level editor and most online features, along with various unlockable characters.
The modularity theorem is a special case of more general conjectures due to Robert Langlands. The Langlands program seeks to attach an automorphic form or automorphic representation (a suitable generalization of a modular form) to more general objects of arithmetic algebraic geometry, such as to every elliptic curve over a number field. Most ...
For example, let G be the graph Z 2 and let R be a random walk starting from the point (0,0). Let T be the time when R first hits the circle of radius 100 (we mean here of course a discretized circle). LE(R) is called the loop-erased random walk starting at (0,0) and stopped at the circle.
Layer cake representation. In mathematics, the layer cake representation of a non-negative, real-valued measurable function defined on a measure space (,,) is the formula = (,) (),
An example of a Riemannian submersion arises when a Lie group acts isometrically, freely and properly on a Riemannian manifold (,). The projection π : M → N {\displaystyle \pi :M\rightarrow N} to the quotient space N = M / G {\displaystyle N=M/G} equipped with the quotient metric is a Riemannian submersion.
The theorem generalizes the Riemann mapping theorem from conformal to quasiconformal homeomorphisms, and is stated as follows. Suppose that D is a simply connected domain in C that is not equal to C , and suppose that μ : D → C is Lebesgue measurable and satisfies ‖ μ ‖ ∞ < 1 {\displaystyle \|\mu \|_{\infty }<1} .