Search Results for ""

Let ||f|| be the supremum of |f(x)|, a real-valued function f defined on (0,infty). If f is twice differentiable and both f and f^('') are bounded, Landau (1913) showed that ...

A means of describing how one state develops into another state over the course of time. Technically, a dynamical system is a smooth action of the reals or the integers on ...

A proof that is only based on visual elements, without any comments. An arithmetic identity can be demonstrated by a picture showing a self-evident equality between numerical ...

Suppose that f is an analytic function which is defined in the upper half-disk {|z|^2<1,I[z]>0}. Further suppose that f extends to a continuous function on the real axis, and ...

A real number that is b-normal for every base 2, 3, 4, ... is said to be absolutely normal. As proved by Borel (1922, p. 198), almost all real numbers in [0,1) are absolutely ...

B-trees were introduced by Bayer (1972) and McCreight. They are a special m-ary balanced tree used in databases because their structure allows records to be inserted, ...

There are four fully supported stellations of the rhombic dodecahedron including as usual the original solid in the count (Wells 1991; Webb). The three nontrivial ones ...

A ruled surface is a surface that can be swept out by moving a line in space. It therefore has a parameterization of the form x(u,v)=b(u)+vdelta(u), (1) where b is called the ...

The Löwenheim-Skolem theorem is a fundamental result in model theory which states that if a countable theory has a model, then it has a countable model. Furthermore, it has a ...

A root-finding algorithm which converges to a complex root from any starting position. To motivate the formula, consider an nth order polynomial and its derivatives, P_n(x) = ...