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An operator A^~ such that A^~^2=A^~ or an element of an algebra x such that x^2=x.

Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

The symbol p^e∥n means, for p a prime, that p^e|n, but p^(e+1)n.

A reflexive relation.

Euclidean n-space is denoted R^n.

The robustness of a given outcome to small changes in initial conditions or small random fluctuations. Chaos is an example of a process which is not stable.

Some computations allow shortcuts which can be used to speed them up. Consider the operation of raising a number to a positive integer power. It is possible, for example, to ...

The interesting function defined by the definite integral G(x)=int_0^xsin(tsint)dt, illustrated above (Glasser 1990). The integral cannot be done in closed form, but has a ...

A wavelet used in multiresolution representation to analyze the information content of images. The wavelet is defined by ...

The Lorentzian function is the singly peaked function given by L(x)=1/pi(1/2Gamma)/((x-x_0)^2+(1/2Gamma)^2), (1) where x_0 is the center and Gamma is a parameter specifying ...