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A confidence interval is an interval in which a measurement or trial falls corresponding to a given probability. Usually, the confidence interval of interest is symmetrically ...

An epsilon-delta definition is a mathematical definition in which a statement on a real function of one variable f having, for example, the form "for all neighborhoods U of ...

In real and functional analysis, equicontinuity is a concept which extends the notion of uniform continuity from a single function to collection of functions. Given ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), define the Hilbert function of M as the map ...

A linear ordinary differential equation of order n is said to be homogeneous if it is of the form a_n(x)y^((n))+a_(n-1)(x)y^((n-1))+...+a_1(x)y^'+a_0(x)y=0, (1) where ...

The intensity measure mu of a point process X relative to a Borel set B subset R^d is defined to be the expected number of points of X falling in B. Symbolically, ...

An equation proposed by Lambert (1758) and studied by Euler in 1779. x^alpha-x^beta=(alpha-beta)vx^(alpha+beta). (1) When alpha->beta, the equation becomes lnx=vx^beta, (2) ...

In practice, the vertical offsets from a line (polynomial, surface, hyperplane, etc.) are almost always minimized instead of the perpendicular offsets. This provides a ...

There are four fixed points (mod 1) of Minkowski's question mark function ?(x), namely x=0, 1/2, f and 1-f, where f<1/2 is a constant known as the Minkowski-Bower constant ...

An integer n is called a super unitary perfect number if sigma^*(sigma^*(n))=2n, where sigma^*(n) is the unitary divisor function. The first few are 2, 9, 165, 238, 1640, ... ...