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The function z=f(x)=ln(x/(1-x)). (1) This function has an inflection point at x=1/2, where f^('')(x)=(2x-1)/(x^2(x-1)^2)=0. (2) Applying the logit transformation to values ...

The fitting subgroup is the subgroup generated by all normal nilpotent subgroups of a group H, denoted F(H). In the case of a finite group, the subgroup generated will itself ...

Let lambda be (possibly complex) eigenvalues of a set of random n×n real matrices with entries independent and taken from a standard normal distribution. Then as n->infty, ...

The socle of a group G is the subgroup generated by its minimal normal subgroups. For example, the symmetric group S_4 has two nontrivial normal subgroups: A_4 and ...

For a group G and a normal subgroup N of G, the quotient group of N in G, written G/N and read "G modulo N", is the set of cosets of N in G. Quotient groups are also called ...

A Tychonoff plank is a topological space that is an example of a normal space which has a non-normal subset, thus showing that normality is not a hereditary property. Let ...

Ball point picking is the selection of points randomly placed inside a ball. n random points can be picked in a unit ball in the Wolfram Language using the function ...

The contrapedal curve, also called a normal pedal curve, is defined analogously to a usual pedal curve with "tangent" replaced by "normal." In particular, the contrapedal ...

The polynomials in the diagonal of the Smith normal form or rational canonical form of a matrix are called its invariant factors.

A Pólya plot is a plot of the vector field of (R[f(z)],-I[f(z)]) of a complex function f(z). Several examples are shown above. Pólya plots can be created in the Wolfram ...