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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 ...

An odd composite number N is called a Somer-Lucas d-pseudoprime (with d>=1) if there exists a nondegenerate Lucas sequence U(P,Q) with U_0=0, U_1=1, D=P^2-4Q, such that ...

Let X and Y be topological spaces. Then their join is the factor space X*Y=(X×Y×I)/∼, (1) where ∼ is the equivalence relation (x,y,t)∼(x^',y^',t^')<=>{t=t^'=0 and x=x^'; or ; ...

F(x) = Li_2(1-x) (1) = int_(1-x)^0(ln(1-t))/tdt, (2) where Li_2(x) is the dilogarithm.

The placement of n points on a sphere so as to minimize the maximum distance of any point on the sphere from the closest one of the n points.

A square grid is a grid formed by tiling the plane regularly with squares.

Defined for samples x_i, i=1, ..., N by alpha_r=1/Nsum_(i=1)^Nz_i^r=(mu_r)/(sigma^r), (1) where z_i=(x_i-x^_)/(s_x). (2) The first few are alpha_1 = 0 (3) alpha_2 = 1 (4) ...

The exploration of three-dimensional space from two-dimensional sections of projections of solid bodies.