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A topology on a set X whose open sets are the unions of open balls B(X_0,r)={x in x|g(x_0,x)<r}, where g is a pseudometric on X, x_0 is any point of X, and r>0. There is a ...

A method to obtain a signal C_l(z) with a flat spectrum c(theta;z) (such as a pulse), but having a smaller amplitude than the pulse. ...

A set of five.

"The rationals" refers to the set of rational numbers and is commonly denoted Q.

The equivalence of manifolds under continuous deformation within the embedding space. Knots of opposite chirality have ambient isotopy, but not regular isotopy.

The divisibility test that an integer is divisible by 9 iff the sum of its digits is divisible by 9.

A root having multiplicity n=1 is called a simple root. For example, f(z)=(z-1)(z-2) has a simple root at z_0=1, but g=(z-1)^2 has a root of multiplicity 2 at z_0=1, which is ...

A smooth map f:S^1->R^3 whose image has singularities. In particular, in the theory of Vassiliev's knot invariants, singular knots with a finite number of ordinary double ...

Let H be a two-dimensional distribution function with marginal distribution functions F and G. Then there exists a copula C such that H(x,y)=C(F(x),G(y)). Conversely, for any ...

A smooth curve is a curve which is a smooth function, where the word "curve" is interpreted in the analytic geometry context. In particular, a smooth curve is a continuous ...