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Calculus I

A connected bipartite graph is called Hamilton-laceable, a term apparently introduced in Simmons (1978), if it has a u-v Hamiltonian path for all pairs of vertices u and v, ...

A game played on a board of a given shape consisting of a number of holes of which all but one are initially filled with pegs. The goal is to remove all pegs but one by ...

A contingency table, sometimes called a two-way frequency table, is a tabular mechanism with at least two rows and two columns used in statistics to present categorical data ...

There exists an integer N such that every string in the look and say sequence "decays" in at most N days to a compound of "common" and "transuranic elements." The table below ...

Probability and Statistics

An acyclic digraph is a directed graph containing no directed cycles, also known as a directed acyclic graph or a "DAG." Every finite acyclic digraph has at least one node of ...

Let F be the set of complex analytic functions f defined on an open region containing the set closure of the unit disk D={z:|z|<1} satisfying f(0)=0 and df/dz(0)=1. For each ...

A bounded lattice is an algebraic structure L=(L, ^ , v ,0,1), such that (L, ^ , v ) is a lattice, and the constants 0,1 in L satisfy the following: 1. for all x in L, x ^ ...

Let f:M|->N be a map between two compact, connected, oriented n-dimensional manifolds without boundary. Then f induces a homomorphism f_* from the homology groups H_n(M) to ...