Resolvent Representation for Regular Differential Ideals

On the complexity of the resolvent representation of some prime differential ideals

We prove upper bounds on the order and degree of the polynomials involved in a resolvent representation of the prime differential ideal associated with a polynomial differential system for a particular class of ordinary first order algebraic-differential equations arising in control theory. We also exhibit a probabilistic algorithm which computes this resolvent representation within time polyno...

Most Complex Regular Ideals

A right ideal (left ideal, two-sided ideal) is a non-empty language L over an alphabet Σ such that L = LΣ∗ (L = Σ∗L, L = Σ∗LΣ∗). Let k = 3 for right ideals, 4 for left ideals and 5 for two-sided ideals. We show that there exist sequences (Ln | n > k) of right, left, and two-sided regular ideals, where Ln has quotient complexity (state complexity) n, such that Ln is most complex in its class und...

On unit-regular ideals

In this paper we introduce the notion of unit-regular ideals for unital rings, which is a natural generalization of unit-regular rings. It is shown that every square matrix over unit-regular ideals admits a diagonal reduction. We also prove that a regular ideal of a unital ring is unit-regular if and only if pseudo-similarity via the ideal is similarity. Let I be an ideal of a unital ring R. We...

Boundary Values of Regular Resolvent Families

We study properties of the boundary values (H ?i0) ?1 of the resolvent of a self-adjoint operator H for in a real open set on which H admits a locally strictly conjugate operator A (in the sense of E. Mourre, i.e. '(H) H; iA]'(H) aj'(H)j 2 for some real a > 0 if ' 2 C 1 0 (()). In particular, we determine the HH older-Zygmund class of the B(E; F)-valued maps 7 ! (H?i0) ?1 and 7 ! (H?i0)) ?1 in ...

Normal Ideals in Regular Rings