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Expansion is an affine transformation (sometimes called an enlargement or dilation) in which the scale is increased. It is the opposite of a geometric contraction, and is ...

A function f(x) is logarithmically concave on the interval [a,b] if f>0 and lnf(x) is concave on [a,b]. The definition can also be extended to R^k->(0,infty) functions ...

The surface corresponding to the region of obscuration when a solid is illuminated from a point light source (located at the radiant point). A disk is the shadow of a sphere ...

In functional analysis, the Banach-Alaoglu theorem (also sometimes called Alaoglu's theorem) is a result which states that the norm unit ball of the continuous dual X^* of a ...

A number of attractive cube 6-compounds can be constructed. A first (left figures) is obtained by combining six cubes, each rotated by 1/6 of a turn about the line joining ...

Let f be a real-valued function defined on an interval [a,b] and let x_0 in (a,b). The four one-sided limits D^+f(x_0)=lim sup_(x->x_0+)(f(x)-f(x_0))/(x-x_0), (1) ...

The great ditrigonal dodecicosidodecahedron is the uniform polyhedron with Maeder index 42 (Maeder 1997), Wenninger index 81 (Wenninger 1989), Coxeter index 54 (Coxeter et ...

An interval is a connected portion of the real line. If the endpoints a and b are finite and are included, the interval is called closed and is denoted [a,b]. If the ...

There are a number of attractive compounds of two regular tetrahedra. The most symmetrical is the arrangement whose outer hull is the stella octangula (left figure), while ...

An equilateral triangle is a triangle with all three sides of equal length a, corresponding to what could also be known as a "regular" triangle. An equilateral triangle is ...