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Let X be a set. Then a sigma-algebra F is a nonempty collection of subsets of X such that the following hold: 1. X is in F. 2. If A is in F, then so is the complement of A. ...

The distribution of a variable is a description of the relative numbers of times each possible outcome will occur in a number of trials. The function describing the ...

A left Hilbert Algebra A whose involution is an antilinear isometry is called a unimodular Hilbert algebra. The involution is usually denoted xi|->xi^*.

A 4-cusped hypocycloid which is sometimes also called a tetracuspid, cubocycloid, or paracycle. The parametric equations of the astroid can be obtained by plugging in n=a/b=4 ...

A branch cut is a curve (with ends possibly open, closed, or half-open) in the complex plane across which an analytic multivalued function is discontinuous. For convenience, ...

The natural logarithm lnx is the logarithm having base e, where e=2.718281828.... (1) This function can be defined lnx=int_1^x(dt)/t (2) for x>0. This definition means that e ...

The natural logarithm of 2 is a transcendental quantity that arises often in decay problems, especially when half-lives are being converted to decay constants. ln2 has ...

Let a particle travel a distance s(t) as a function of time t (here, s can be thought of as the arc length of the curve traced out by the particle). The speed (the scalar ...

The lines connecting the vertices and corresponding circle-circle intersections in Malfatti's problem coincide in a point X_(179) called the first Ajima-Malfatti point ...

Given a set of n+1 control points P_0, P_1, ..., P_n, the corresponding Bézier curve (or Bernstein-Bézier curve) is given by C(t)=sum_(i=0)^nP_iB_(i,n)(t), where B_(i,n)(t) ...