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The extension of a, an ideal in commutative ring A, in a ring B, is the ideal generated by its image f(a) under a ring homomorphism f. Explicitly, it is any finite sum of the ...

Let P=p:q:r and U=u:v:w be points in trilinear coordinates, neither of which is on a side line of a reference triangle DeltaABC. Them the P-isoconjugate of U is the point ...

A right triangle with the two legs (and their corresponding angles) equal. An isosceles right triangle therefore has angles of 45 degrees, 45 degrees, and 90 degrees. For an ...

Let M be a bounded set in the plane, i.e., M is contained entirely within a rectangle. The outer Jordan measure of M is the greatest lower bound of the areas of the coverings ...

The kiss surface is the quintic surface of revolution given by the equation x^2+y^2=(1-z)z^4 (1) that is closely related to the ding-dong surface. It is so named because the ...

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)) ...