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Maximize the distance a Jeep can penetrate into the desert using a given quantity of fuel. The Jeep is allowed to go forward, unload some fuel, and then return to its base ...

The Johnson graph J(n,k) has vertices given by the k-subsets of {1,...,n}, with two vertices connected iff their intersection has size k-1. Special classes are summarized in ...

The Kakeya needle problems asks for the plane figure of least area in which a line segment of width 1 can be freely rotated (where translation of the segment is also ...

A lattice reduction algorithm, named after discoverers Lenstra, Lenstra, and Lovasz (1982), that produces a lattice basis of "short" vectors. It was noticed by Lenstra et al. ...

Let z=re^(itheta)=x+iy be a complex number, then inequality |(zexp(sqrt(1-z^2)))/(1+sqrt(1-z^2))|<=1 (1) holds in the lens-shaped region illustrated above. Written explicitly ...

There are two sets of constants that are commonly known as Lebesgue constants. The first is related to approximation of function via Fourier series, which the other arises in ...

Zygmund (1988, p. 192) noted that there exists a number alpha_0 in (0,1) such that for each alpha>=alpha_0, the partial sums of the series sum_(n=1)^(infty)n^(-alpha)cos(nx) ...

Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive ...

A matching, also called an independent edge set, on a graph G is a set of edges of G such that no two sets share a vertex in common. It is not possible for a matching on a ...

An independent edge set, also called a matching, of a graph G is a subset of the edges such that no two edges in the subset share a vertex in G. A maximum independent edge ...