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A Lie algebra is nilpotent when its Lie algebra lower central series g_k vanishes for some k. Any nilpotent Lie algebra is also solvable. The basic example of a nilpotent Lie ...

A diagram lemma also known as 3×3 lemma. According to its most general statement, the commutative diagram illustrated above with exact rows and columns can be completed by ...

Given a smooth manifold M with an open cover U_i, a partition of unity subject to the cover U_i is a collection of smooth, nonnegative functions psi_i, such that the support ...

The Peters projection is a cylindrical equal-area projection that de-emphasizes the exaggeration of areas at high latitudes by shifting the standard latitude to phi_s=44.138 ...

A polyform of 30-60-90 triangles. The name was coined by Ed Pegg, Jr. because of the 30-60-90 triangle's use in mechanical drawing and drafting. The Eternity puzzle is based ...

A topological transformation in which a surface is made out of an infinitely elastic material which, however, may not be torn or cut. Using this simple prescription gives the ...

A pseudograph is a non-simple graph in which both graph loops and multiple edges are permitted (Zwillinger 2003, p. 220).

Quantization is a nonlinear process which generates additional frequency components (Thompson et al. 1986). This means that the signal is no longer band-limited, so the ...

A conjecture due to M. S. Robertson in 1936 which treats a univalent power series containing only odd powers within the unit disk. This conjecture implies the Bieberbach ...

A smooth manifold M=(M,g) is said to be semi-Riemannian if the indexMetric Tensor Index of g is nonzero. Alternatively, a smooth manifold is semi-Riemannian provided that it ...