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A function f is said to be an entire modular form of weight k if it satisfies 1. f is analytic in the upper half-plane H, 2. f((atau+b)/(ctau+d))=(ctau+d)^kf(tau) whenever [a ...

A quaternion Kähler manifold is a Riemannian manifold of dimension 4n, n>=2, whose holonomy is, up to conjugacy, a subgroup of Sp(n)Sp(1)=Sp(n)×Sp(1)/Z_2, but is not a ...

A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...

The map x_(n+1)=2mux_n, (1) where x is computed modulo 1. A generalized Baker's map can be defined as x_(n+1) = {lambda_ax_n y_n<alpha ; (1-lambda_b)+lambda_bx_n y_n>alpha ...

A non-zero module which is not the direct sum of two of its proper submodules. The negation of indecomposable is, of course, decomposable. An abstract vector space is ...

A fractal curve created from the base curve and motif illustrated above (Lauwerier 1991, p. 37). As illustrated above, the number of segments after the nth iteration is ...

Tetrahedron picking is the process of picking tetrahedra at random within a given shape in 3 or higher dimensions. The most natural definition of a random tetrahedron is one ...

There are several versions of the Kaplan-Yorke conjecture, with many of the higher dimensional ones remaining unsettled. The original Kaplan-Yorke conjecture (Kaplan and ...

A collection of faces of an n-dimensional polytope or simplicial complex, one of each dimension 0, 1, ..., n-1, which all have a common nonempty intersection. In normal three ...

The robustness of a given outcome to small changes in initial conditions or small random fluctuations. Chaos is an example of a process which is not stable.