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A Cartan matrix is a square integer matrix who elements (A_(ij)) satisfy the following conditions. 1. A_(ij) is an integer, one of {-3,-2,-1,0,2}. 2. A_(ii)=2 the diagonal ...

A state diagram is a labeled directed graph together with state information that can be used to indicate that certain paths on in a system may be traversed only in a certain ...

When discussing a rotation, there are two possible conventions: rotation of the axes, and rotation of the object relative to fixed axes. In R^2, consider the matrix that ...

Quantifier elimination is the removal of all quantifiers (the universal quantifier forall and existential quantifier exists ) from a quantified system. A first-order theory ...

A spectral sequence is a tool of homological algebra that has many applications in algebra, algebraic geometry, and algebraic topology. Roughly speaking, a spectral sequence ...

Turmites, also called turning machines, are 2-dimensional Turing machines in which the "tape" consists of a grid of spaces that can be written and erased by an active ...

Let A_1, A_2, A_3, and A_4 be four points on a circle, and H_1, H_2, H_3, H_4 the orthocenters of triangles DeltaA_2A_3A_4, etc. If, from the eight points, four with ...

The spherical harmonics form a complete orthogonal system, so an arbitrary real function f(theta,phi) can be expanded in terms of complex spherical harmonics by ...

If a function has a Fourier series given by f(x)=1/2a_0+sum_(n=1)^inftya_ncos(nx)+sum_(n=1)^inftyb_nsin(nx), (1) then Bessel's inequality becomes an equality known as ...

Pogson's ratio is the constant 100^(1/5)=10^(2/5)=2.511886431... (OEIS A189824) appearing in the definition of the astronomical magnitude (brightness) scale. This scale is ...