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Given an open subset U in n-dimensional space and two compact subsets C_0 and C_1 of U, where C_1 is derived from C_0 by a continuous motion, is it possible to move C_0 to ...

Let K be a number field and let O be an order in K. Then the set of equivalence classes of invertible fractional ideals of O forms a multiplicative Abelian group called the ...

Any entire analytic function whose range omits two points must be a constant function. Of course, an entire function that omits a single point from its range need not be a ...

Pickover's sequence gives the starting positions in the decimal expansion of pi (ignoring the leading 3) in which the first n digits of e occur (counting the leading 2). So, ...

Let f(x) be integrable in [-1,1], let (1-x^2)f(x) be of bounded variation in [-1,1], let M^' denote the least upper bound of |f(x)(1-x^2)| in [-1,1], and let V^' denote the ...

Polynomials P_k(x) which form the Sheffer sequence for g(t) = (2t)/(e^t-1) (1) f(t) = (e^t-1)/(e^t+1) (2) and have generating function ...

A chart made by plotting the numeric values of a set of quantities as a set of adjacent circular wedges with arc lengths proportional to the total amount. All wedges taken ...

A function is said to be piecewise constant if it is locally constant in connected regions separated by a possibly infinite number of lower-dimensional boundaries. The ...

A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value, |x|={-x for x<0; 0 for x=0; x for x>0. (1) Piecewise ...

A piecewise linear function is a function composed of some number of linear segments defined over an equal number of intervals, usually of equal size. For example, consider ...