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The expected number of real zeros E_n of a random polynomial of degree n if the coefficients are independent and distributed normally is given by E_n = ...

Kakutani's fixed point theorem is a result in functional analysis which establishes the existence of a common fixed point among a collection of maps defined on certain ...

The simplest interpretation of the Kronecker delta is as the discrete version of the delta function defined by delta_(ij)={0 for i!=j; 1 for i=j. (1) The Kronecker delta is ...

An attractive tiling of the square composed of two types of triangular tiles. It consists of 16 equilateral triangles and 32 15 degrees-15 degrees-150 degrees isosceles ...

Writing a Fourier series as f(theta)=1/2a_0+sum_(n=1)^(m-1)sinc((npi)/(2m))[a_ncos(ntheta)+b_nsin(ntheta)], where m is the last term, reduces the Gibbs phenomenon. The ...

The spherical harmonics form a complete orthogonal system, so an arbitrary real function f(theta,phi) can be expanded in terms of complex spherical harmonics by ...

An irregular dodecagonal cross in the shape of a dagger |. The six faces of a cube can be cut along seven edges and unfolded into a Latin cross (i.e., the Latin cross is the ...

To fit a functional form y=Ae^(Bx), (1) take the logarithm of both sides lny=lnA+Bx. (2) The best-fit values are then a = ...

The roots of a semisimple Lie algebra g are the Lie algebra weights occurring in its adjoint representation. The set of roots form the root system, and are completely ...

Consider a collection of diagonal matrices H_1,...,H_k, which span a subspace h. Then the ith eigenvalue, i.e., the ith entry along the diagonal, is a linear functional on h, ...