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Any linear system of point-groups on a curve with only ordinary singularities may be cut by adjoint curves.

The kernel of a module homomorphism f:M-->N is the set of all elements of M which are mapped to zero. It is the kernel of f as a homomorphism of additive groups, and is a ...

A morphism f:Y->X in a category is a monomorphism if, for any two morphisms u,v:Z->Y, fu=fv implies that u=v. In the categories of sets, groups, modules, etc., a monomorphism ...

Polynomials s_k(x) which form the Sheffer sequence for f(t)=-(2t)/(1-t^2) (1) and have exponential generating function ...

A multiple root is a root with multiplicity n>=2, also called a multiple point or repeated root. For example, in the equation (x-1)^2=0, 1 is multiple (double) root. If a ...

A natural transformation Phi={Phi_C:F(C)->D(C)} between functors F,G:C->D of categories C and D is said to be a natural isomorphism if each of the components is an ...

A topology defined on a totally ordered set X whose open sets are all the finite intersections of subsets of the form {x in X|x>a} or {x in X|x<a}, where a in X. The order ...

A square matrix A such that the matrix power A^(k+1)=A for k a positive integer is called a periodic matrix. If k is the least such integer, then the matrix is said to have ...

Let f(z) be an analytic function in an angular domain W:|argz|<alphapi/2. Suppose there is a constant M such that for each epsilon>0, each finite boundary point has a ...

Let R be a commutative ring. A category C is called an R-category if the Hom-sets of C are R-modules.