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A subset E of a topological space S is said to be of second category in S if E cannot be written as the countable union of subsets which are nowhere dense in S, i.e., if ...

There are three types of cubic lattices corresponding to three types of cubic close packing, as summarized in the following table. Now that the Kepler conjecture has been ...

Eigenvectors are a special set of vectors associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic vectors, ...

A graph G is Hamilton-connected if every two vertices of G are connected by a Hamiltonian path (Bondy and Murty 1976, p. 61). In other words, a graph is Hamilton-connected if ...

Let a chess piece make a tour on an n×n chessboard whose squares are numbered from 1 to n^2 along the path of the chess piece. Then the tour is called a magic tour if the ...

The term metric signature refers to the signature of a metric tensor g=g_(ij) on a smooth manifold M, a tool which quantifies the numbers of positive, zero, and negative ...

An n×n complex matrix A is called positive definite if R[x^*Ax]>0 (1) for all nonzero complex vectors x in C^n, where x^* denotes the conjugate transpose of the vector x. In ...

The prime spiral, also known as Ulam's spiral, is a plot in which the positive integers are arranged in a spiral (left figure), with primes indicated in some way along the ...

The regular pentagon is the regular polygon with five sides, as illustrated above. A number of distance relationships between vertices of the regular pentagon can be derived ...

An ordinary differential equation (frequently called an "ODE," "diff eq," or "diffy Q") is an equality involving a function and its derivatives. An ODE of order n is an ...