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A bounded operator T:V->W between two Banach spaces satisfies the inequality ||Tv||<=C||v||, (1) where C is a constant independent of the choice of v in V. The inequality is ...

A coordinate system obtained by inversion of the bicyclide coordinates. They are given by the transformation equations x = Lambda/(aUpsilon)snmudnnucospsi (1) y = ...

There are at least two theorems known as Chebyshev's theorem. The first is Bertrand's postulate, proposed by Bertrand in 1845 and proved by Chebyshev using elementary methods ...

A conical frustum is a frustum created by slicing the top off a cone (with the cut made parallel to the base). For a right circular cone, let s be the slant height and R_1 ...

Bezdek and Kuperberg (1991) have constructed packings of identical ellipsoids of densities arbitrarily close to ((24sqrt(2)-6sqrt(3)-2pi)pi)/(72)=0.753355... (OEIS A093824), ...

If f(x) is an even function, then b_n=0 and the Fourier series collapses to f(x)=1/2a_0+sum_(n=1)^inftya_ncos(nx), (1) where a_0 = 1/piint_(-pi)^pif(x)dx (2) = ...

For a power function f(x)=x^k with k>=0 on the interval [0,2L] and periodic with period 2L, the coefficients of the Fourier series are given by a_0 = (2^(k+1)L^k)/(k+1) (1) ...

Gelfond's theorem, also called the Gelfond-Schneider theorem, states that a^b is transcendental if 1. a is algebraic !=0,1 and 2. b is algebraic and irrational. This provides ...

The half-normal distribution is a normal distribution with mean 0 and parameter theta limited to the domain x in [0,infty). It has probability and distribution functions ...

A fair coin is tossed an even 2n number of times. Let D=|H-T| be the absolute difference in the number of heads and tails obtained. Then the probability distribution is given ...