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A fixed point for which the stability matrix has one zero eigenvector with positive eigenvalue lambda>0.

The upper-trimmed subsequence of x={x_n} is the sequence lambda(x) obtained by dropping the first occurrence of n for each n. If x is a fractal sequence, then lambda(x)=x.

The unit upper half-disk is the portion of the complex plane satisfying {|z|<=1,I[z]>0}.

The limit of an upper sum, when it exists, as the mesh size approaches 0.

Let the greatest term H of a sequence be a term which is greater than all but a finite number of the terms which are equal to H. Then H is called the upper limit of the ...

For every topological T1-space X, the following conditions are equivalent. 1. X is regular and second countable, 2. X is separable and metrizable. 3. X is homeomorphic to a ...

Let (K,|·|) be a valuated field. The valuation group G is defined to be the set G={|x|:x in K,x!=0}, with the group operation being multiplication. It is a subgroup of the ...

Let (K,|·|) be a non-Archimedean field. Its valuation ring R is defined to be R={x in K:|x|<=1}. The valuation ring has maximal ideal M={x in K:|x|<1}, and the field R/M is ...

Let p be an irregular prime, and let P=rp+1 be a prime with P<p^2-p. Also let t be an integer such that t^3≢1 (mod P). For an irregular pair (p,2k), form the product ...

A quantity which takes on the value zero is said to vanish identically, or sometimes simply to vanish. The term "vanish identically" is preferred when emphasis is needed that ...