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The spectrum of a ring is the set of proper prime ideals, Spec(R)={p:p is a prime ideal in R}. (1) The classical example is the spectrum of polynomial rings. For instance, ...

The combination of a central dilation and a rotation about the same center. However, the combination of a central dilation and a rotation whose centers are distinct is also a ...

A Steiner system S(t,k,v) is a set X of v points, and a collection of subsets of X of size k (called blocks), such that any t points of X are in exactly one of the blocks. ...

A subset of an algebraic variety which is itself a variety. Every variety is a subvariety of itself; other subvarieties are called proper subvarieties. A sphere of the ...

Every convex body B in the Euclidean plane with area A can be inscribed in a triangle of area at most equal to 2A (Gross 1918, Eggleston 1957). The worst possible fit ...

The dimension of an object is a topological measure of the size of its covering properties. Roughly speaking, it is the number of coordinates needed to specify a point on the ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a modular Hilbert algebra if A has an inner product <··> and a ...

A projection matrix P is an n×n square matrix that gives a vector space projection from R^n to a subspace W. The columns of P are the projections of the standard basis ...

There are a couple of versions of this theorem. Basically, it says that any bounded linear functional T on the space of compactly supported continuous functions on X is the ...

The Dedekind eta function is defined over the upper half-plane H={tau:I[tau]>0} by eta(tau) = q^_^(1/24)(q^_)_infty (1) = q^_^(1/24)product_(k=1)^(infty)(1-q^_^k) (2) = ...