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A surface which can be interpreted as a self-intersecting rectangle in three dimensions. The Whitney umbrella is the only stable singularity of mappings from R^2 to R^3. It ...

If y has period 2pi, y^' is L^2, and int_0^(2pi)ydx=0, (1) then int_0^(2pi)y^2dx<int_0^(2pi)y^('2)dx (2) unless y=Acosx+Bsinx (3) (Hardy et al. 1988). Another inequality ...

A game played with two heaps of counters in which a player may take any number from either heap or the same number from both. The player taking the last counter wins. The rth ...

"The" Y-graph is another term used to refer to a claw graph. The term "Y-graph" is also used to refer to a graph expansion with the Y graph as its base (e.g., Horton and ...

Let points A^', B^', and C^' be marked off some fixed distance x along each of the sides BC, CA, and AB. Then the lines AA^', BB^', and CC^' concur in a point U known as the ...

Young's geometry is a finite geometry which satisfies the following five axioms: 1. There exists at least one line. 2. Every line of the geometry has exactly three points on ...

The d-analog of a complex number s is defined as [s]_d=1-(2^d)/(s^d) (1) (Flajolet et al. 1995). For integer n, [2]!=1 and [n]_d! = [3][4]...[n] (2) = ...

The constants C_n defined by C_n=[int_0^infty|d/(dt)((sint)/t)^n|dt]-1. (1) These constants can also be written as the sums C_n=2sum_(k=1)^infty(1+x_k^2)^(-n/2), (2) and ...

The h-statistic h_r is the unique symmetric unbiased estimator for a central moment of a distribution <h_r>=mu_r. (1) In addition, the variance var(h_r)=<(h_r-mu_r)^2> (2) is ...

There are several q-analogs of the cosine function. The two natural definitions of the q-cosine defined by Koekoek and Swarttouw (1998) are given by cos_q(z) = ...