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The index associated to a metric tensor g on a smooth manifold M is a nonnegative integer I for which index(gx)=I for all x in M. Here, the notation index(gx) denotes the ...

In many cases, the Hausdorff dimension correctly describes the correction term for a resonator with fractal perimeter in Lorentz's conjecture. However, in general, the proper ...

The Mordell conjecture states that Diophantine equations that give rise to surfaces with two or more holes have only finite many solutions in Gaussian integers with no common ...

The upside-down capital delta symbol del , also called "del," used to denote the gradient and other vector derivatives. The following table summarizes the names and notations ...

Let two disks of radius r intersect one another perpendicularly and have a diameter in common. If the distance between the centers of the disks is sqrt(2) times their radius, ...

In elementary geometry, orthogonal is the same as perpendicular. Two lines or curves are orthogonal if they are perpendicular at their point of intersection. Two vectors v ...

Following the work of Fuchs in classifying first-order ordinary differential equations, Painlevé studied second-order ordinary differential equation of the form ...

The pathwidth of a graph G, also called the interval thickness, vertex separation number, and node searching number, is one less than the size of the largest set in a path ...

An m×n matrix which gives the possible outcome of a two-person zero-sum game when player A has m possible moves and player B n moves. The analysis of the matrix in order to ...

A figurate number corresponding to a pentagonal pyramid. The first few are 1, 6, 18, 40, 75, ... (OEIS A002411). The generating function for the pentagonal pyramidal numbers ...