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The Hochberg-O'Donnell fish graph is the unit-distance graph on 23 nodes and 42 edges illustrated above. It is triangle-free and is the smallest example of a unit-distance ...

Two mathematical objects are said to be homotopic if one can be continuously deformed into the other. For example, the real line is homotopic to a single point, as is any ...

The identity matrix is a the simplest nontrivial diagonal matrix, defined such that I(X)=X (1) for all vectors X. An identity matrix may be denoted 1, I, E (the latter being ...

An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length b and the remaining side has length a. This property ...

Laguerre-Gauss quadrature, also called Gauss-Laguerre quadrature or Laguerre quadrature, is a Gaussian quadrature over the interval [0,infty) with weighting function ...

In functional analysis, the Lax-Milgram theorem is a sort of representation theorem for bounded linear functionals on a Hilbert space H. The result is of tantamount ...

Intuitively, a d-dimensional discrete percolation model is said to be long-range if direct flow is possible between pairs of graph vertices or graph edges which are "very ...

Let there be three polynomials a(x), b(x), and c(x) with no common factors such that a(x)+b(x)=c(x). Then the number of distinct roots of the three polynomials is one or more ...

The product C of two matrices A and B is defined as c_(ik)=a_(ij)b_(jk), (1) where j is summed over for all possible values of i and k and the notation above uses the ...

If r is an algebraic number of degree n, then the totality of all expressions that can be constructed from r by repeated additions, subtractions, multiplications, and ...