A note on invariant imbedding and generalized semigroups

Generalized Invariant Imbedding Relation.

A Generalized Parameter Imbedding Method

The parameter imbedding method for the Fredholm equation converts it into an initial value problem in its parameter λ. We establish the method for general operator equations of the form [I + ˆ f (λ)]ψ = φ. It is particularly useful for studying spontaneous symmetry breaking problems, such as contained in the nonlinear Schwinger-Dyson equation.

Dissipation Functions and Invariant Imbedding, I.

A Note on Extending Semicharacters on Semigroups

The purpose of this note is to give a necessary and sufficient condition for a semicharacter on a subsemigroup of a commutative semigroup G to be extendable to a semicharacter on G. A bounded complex function x on a semigroup G is called a semicharacter of G if x(x)9^0 for some xEG and x(xy) = x(%)x(y) ior all x, yEG. Semicharacters were introduced by Hewitt and Zuckerman [l] and in a slightly ...

A Note on Artinianess of Certain Generalized

Let ?: R0?R be a ring homomorphism and suppose that a and a0, respectively, are ideals of R and R0 such that is an Artinian ring. Let M and N be two finitely generated R-modules and suppose that (R0,m0) is a local ring. In this note we prove that the R-modules and are Artinian for all integers i and j, whenever and . Also we will show that if a is principal, then the R-modules and ...