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If p divides the numerator of the Bernoulli number B_(2k) for 0<2k<p-1, then (p,2k) is called an irregular pair. For p<30000, the irregular pairs of various forms are p=16843 ...

The repeated application of a transformation.

A Jensen disk is a disk in the complex plane whose diameter joins complex conjugate roots of a polynomial (Trott 2004, p. 22).

A joint distribution function is a distribution function D(x,y) in two variables defined by D(x,y) = P(X<=x,Y<=y) (1) D_x(x) = lim_(y->infty)D(x,y) (2) D_y(y) = ...

A primitive subgroup of the symmetric group S_n is equal to either the alternating group A_n or S_n whenever it contains at least one permutation which is a q-cycle for some ...

For any function f:A->B (where A and B are any sets), the kernel (also called the null space) is defined by Ker(f)={x:x in Asuch thatf(x)=0}, so the kernel gives the elements ...

Let the center B of a circle of radius a move along a line BA. Let O be a fixed point located a distance c away from AB. Draw a secant line through O and D, the midpoint of ...

The curve defined by the Cartesian equation f(x)=ln|(sinx)/x|=ln|sinc(x)|. The Kilroy curve arises in the study of spread spectra plotted on a logarithmic (decibel) scale, ...

A list of problems in low-dimensional topology maintained by Kirby (1995). The list currently runs about 380 pages.

The knot curve is a quartic curve with implicit Cartesian equation (x^2-1)^2=y^2(3+2y). (1) The x- and y-intercepts are (0,-1), (0,1/2), and (+/-1,0). It has horizontal ...