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It is thought that the totient valence function N_phi(m)>=2, i.e., if there is an n such that phi(n)=m, then there are at least two solutions n. This assertion is called ...

If a plane cuts the sides AB, BC, CD, and DA of a skew quadrilateral ABCD in points P, Q, R, and S, then (AP)/(PB)·(BQ)/(QC)·(CR)/(RD)·(DS)/(SA)=1 both in magnitude and sign ...

Given any triangle ABC, the signed sum of perpendicular distances from the circumcenter O to the sides (i.e., signed lengths of the pedal lines from O) is OO_A+OO_B+OO_C=R+r, ...

A fractal-like structure is produced for x<0 by superposing plots of Carotid-Kundalini functions ck_n of different orders n. the region -1<x<0 is called fractal land by ...

The function given by CK_n(x)=cos(nxcos^(-1)x), where n is an integer and -1<x<1.

The operating of shifting the leading digits of an addition into the next column to the left when the sum of that column exceeds a single digit (i.e., 9 in base 10).

The term "Cartan algebra" has two meanings in mathematics, so care is needed in determining from context which meaning is intended. One meaning is a "Cartan subalgebra," ...

A Cartan matrix is a square integer matrix who elements (A_(ij)) satisfy the following conditions. 1. A_(ij) is an integer, one of {-3,-2,-1,0,2}. 2. A_(ii)=2 the diagonal ...

The relationship Sq^i(x cup y)=Sigma_(j+k=i)Sq^j(x) cup Sq^k(y) encountered in the definition of the steenrod algebra.

Let g be a finite-dimensional Lie algebra over some field k. A subalgebra h of g is called a Cartan subalgebra if it is nilpotent and equal to its normalizer, which is the ...