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If the domain of the functions is a topological space and the codomain is a uniform space, local uniform convergence (i.e. uniform convergence on a neighborhood of each point) and compact (uniform) convergence (i.e. uniform convergence on all compact subsets) may be defined. "Compact convergence" is always short for "compact uniform convergence ...
A sequence (a 1, a 2, a 3, ...) of real numbers is said to be equidistributed modulo 1 or uniformly distributed modulo 1 if the sequence of the fractional parts of a n, denoted by (a n) or by a n − ⌊a n ⌋, is equidistributed in the interval [0, 1].
The Bates distribution is the average of n i.i.d. U(0,1) distributions. The standard uniform distribution is a special case of the beta distribution, with parameters (1,1). The sum of two independent uniform distributions U 1 (a,b)+U 2 (c,d) yields a trapezoidal distribution, symmetric about its mean, on
The earliest numbering systems were significantly different from the modern variation. Until the 1920s, when the NFL limited its rosters to 22 players, it was rare to see player numbers much higher than 25 (Red Grange was a notable exception, wearing 77 with the Chicago Bears while playing halfback, which would not be allowed under current NFL rules), and numbers had little correlation with ...
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theory also studies the natural, or whole, numbers.
Illustration of filling the unit interval (horizontal axis) with the first n terms using the equidistribution theorem with four common irrational numbers, for n from 0 to 999 (vertical axis). The 113 distinct bands for π are due to the closeness of its value to the rational number 355/113.
In mathematics, the Weierstrass M-test is a test for determining whether an infinite series of functions converges uniformly and absolutely.It applies to series whose terms are bounded functions with real or complex values, and is analogous to the comparison test for determining the convergence of series of real or complex numbers.
Starting with the real numbers, the corresponding projective "line" is geometrically a circle, and then the extra point / gives the shape that is the source of the term "wheel". Or starting with the complex numbers instead, the corresponding projective "line" is a sphere (the Riemann sphere ), and then the extra point gives a 3-dimensional ...