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The eigenvalues lambda satisfying P(lambda)=0, where P(lambda) is the characteristic polynomial, lie in the unions of the disks |z|<=1 |z+b_1|<=sum_(j=1)^n|b_j|.

A partial algebra is a pair A=(A,(f_i^A)_(i in I)), where for each i in I, there are an ordinal number alpha_i and a set X_i subset= A^(alpha_i) such that f_i^A is a function ...

The nth partial denominator in a generalized continued fraction b_0+K_(n=1)^infty(a_n)/(b_n) or simple continued fraction b_0+K_(n=1)^infty1/(b_n) is the expression b_n. For ...

A partial differential equation (PDE) is an equation involving functions and their partial derivatives; for example, the wave equation ...

The nth partial numerator in a generalized continued fraction b_0+K_(n=1)^infty(a_n)/(b_n) is the expression a_n. For a simple continued fraction b_0+K_(n=1)^infty1/(b_n), ...

An ideal I of a partial order P is a subset of the elements of P which satisfy the property that if y in I and x<y, then x in I. For k disjoint chains in which the ith chain ...

For a partial order, the size of the longest chain is called the length.

For a partial order, the size of the longest antichain is called the width.

Given a sequence {a_k}_(k=1)^n, a partial sum of the first N terms is given by S_N=sum_(k=1)^Na_k.

Each subsequent row of Pascal's triangle is obtained by adding the two entries diagonally above. This follows immediately from the binomial coefficient identity (n; r) = ...