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A Lindenmayer system, also known as an L-system, is a string rewriting system that can be used to generate fractals with dimension between 1 and 2. Several example fractals ...

A random closed set (RACS) in R^d is a measurable function from a probability space (Omega,A,P) into (F,Sigma) where F is the collection of all closed subsets of R^d and ...

Rosser's rule states that every Gram block contains the expected number of roots, which appears to be true for computable Gram blocks. Rosser et al. (1969) expressed a belief ...

Consider a formula in prenex normal form, Q_1x_1...Q_nx_nN. If Q_i is the existential quantifier (1<=i<=n) and x_k, ..., x_m are all the universal quantifier variables such ...

Consider the sample standard deviation s=sqrt(1/Nsum_(i=1)^N(x_i-x^_)^2) (1) for n samples taken from a population with a normal distribution. The distribution of s is then ...

If f:M->N, then the tangent map Tf associated to f is a vector bundle homeomorphism Tf:TM->TN (i.e., a map between the tangent bundles of M and N respectively). The tangent ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. This partitions graphs into ...

Linear Algebra

LCF notation is a concise and convenient notation devised by Joshua Lederberg (winner of the 1958 Nobel Prize in Physiology and Medicine) for the representation of cubic ...

Cauchy's integral formula states that f(z_0)=1/(2pii)∮_gamma(f(z)dz)/(z-z_0), (1) where the integral is a contour integral along the contour gamma enclosing the point z_0. It ...