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If all elements a_(ij) of an irreducible matrix A are nonnegative, then R=minM_lambda is an eigenvalue of A and all the eigenvalues of A lie on the disk |z|<=R, where, if ...

A^*(x)=sum_(lambda_n<=x)^'a_n=1/(2pii)int_(c-iinfty)^(c+iinfty)f(s)(e^(sx))/sds, where f(s)=suma_ne^(-lambda_ns).

An analog of the determinant for number triangles defined as a signed sum indexed by set partitions of {1,...,n} into pairs of elements. The Pfaffian is the square root of ...

An adjoint curve which bears a special relation to the base curve.

Let V be a variety, and write G(V) for the set of divisors, G_l(V) for the set of divisors linearly equivalent to 0, and G_a(V) for the group of divisors algebraically equal ...

Let x:p(x)->xp(x), then for any operator T, T^'=Tx-xT is called the Pincherle derivative of T. If T is a shift-invariant operator, then its Pincherle derivative is also a ...

The symbol "+" which is used to denote a positive number or to indicate addition.

The system of partial differential equations u_(xx)-u_(yy)+/-sinucosu+(cosu)/(sin^3u)(v_x^2-v_y^2)=0 (v_xcot^2u)_x=(v_ycot^2u)_y.

Every Lie algebra L is isomorphic to a subalgebra of some Lie algebra A^-, where the associative algebra A may be taken to be the linear operators over a vector space V.

A pointed space is a topological space X together with a choice of a basepoint x in X. The notation for a pointed space is (X,x). Maps between two pointed spaces must take ...