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In the field of functional analysis, the Krein-Milman theorem is a result which characterizes all (nonempty) compact convex subsets K of "sufficiently nice" topological ...

Given the "peaks" of three equilateral triangles placed on the sides of a triangle T, construct T. The problem was proposed by Lemoine (1868) and solved for the general case ...

In n-dimensional Lorentzian space R^n=R^(1,n-1), the light cone C^(n-1) is defined to be the subset consisting of all vectors x=(x_0,x_1,...,x_(n-1)) (1) whose squared ...

There are no fewer than three distinct notions of the term local C^*-algebra used throughout functional analysis. A normed algebra A=(A,|·|_A) is said to be a local ...

The continuous distribution with parameters m and b>0 having probability and distribution functions P(x) = (e^(-(x-m)/b))/(b[1+e^(-(x-m)/b)]^2) (1) D(x) = 1/(1+e^(-(x-m)/b)) ...

A maximal ideal of a ring R is an ideal I, not equal to R, such that there are no ideals "in between" I and R. In other words, if J is an ideal which contains I as a subset, ...

Maximum likelihood, also called the maximum likelihood method, is the procedure of finding the value of one or more parameters for a given statistic which makes the known ...

The Maxwell (or Maxwell-Boltzmann) distribution gives the distribution of speeds of molecules in thermal equilibrium as given by statistical mechanics. Defining a=sqrt(kT/m), ...

A map projection given by the following transformation, x = lambda-lambda_0 (1) y = 5/4ln[tan(1/4pi+2/5phi)] (2) = 5/4sinh^(-1)[tan(4/5phi)]. (3) Here, x and y are the plane ...

Given a random variable x and a probability density function P(x), if there exists an h>0 such that M(t)=<e^(tx)> (1) for |t|<h, where <y> denotes the expectation value of y, ...