Let M be a Hilbert module of holomorphic functions over a natural function algebra A (Ω), where Ω ⊆Cm is a bounded domain. Let M0 ⊆M be the submodule of functions vanishing to order k on a hypersurface Z ⊆ Ω. We describe a method, which in principle may be used, to construct a set of complete unitary invariants for quotient modules Q = M ⊖M0. The invariants are given explicitly in the particula...

We consider the following problem: For a system consisting of two submodules, the behavior of one submodule is known as well as the desired behavior S of the global system. What should be the behavior of the second submodule such that the behavior of the composition of the two submodules conforms to S ?-This problem has also been called "equation solving", and in the context of supervisory cont...

A method for solving CCS equations of type (AIX)\L ~ B, where X is unknown, is presented. The method is useful in a top-down design methodology: if a system (B) and some of its submodules (.4) axe specified, solving such an equation amounts to constructing the missing submodules. The method works by successively transforming equations into simpler equations, in parallel with generation of a sol...

The full-bridge submodule (FBSM)-based modular multilevel converter (FBSM-MMC) offers promising performance due to its ability output negative FBSM voltage. This paper studies this of the FBSM-MMC under zero-sequence voltage injection (ZSVI) and second-order harmonic current (SHCI). focus research is redistribute powers by injecting an additional power degree freedom, resulting in a smaller cap...

let $m$ be a module over a commutative ring $r$ and let $n$ be a proper submodule of $m$. the total graph of $m$ over $r$ with respect to $n$, denoted by $t(gamma_{n}(m))$, have been introduced and studied in [2]. in this paper, a generalization of the total graph $t(gamma_{n}(m))$, denoted by $t(gamma_{n,i}(m))$ is presented, where $i$ is an ideal of $r$. it is the graph with all elements of $...

Let An(k) be the Weyl algebra, with k a field of characteristic zero. It is known that every projective finitely generated left module is free or isomorphic to a left ideal. Let M be a left submodule of a free module. In this paper we give an algorithm to compute the projective dimension of M . If M is projective and rank(M) ≥ 2 we give a procedure to find a basis. © 2003 Elsevier Ltd. All righ...

Corollary 1.2 Let G be an almost simple classical group with natural module V of dimension n. If G is linear, assume that G does not contain a graph automorphism. Let 2 ≤ k < n − 1, and let K be the stabilizer of a nondegenerate or totally singular k-space of V . Let P be the stabilizer of a singular 1-space of V . Then the permutation module 1P is a submodule of 1 G K unless one of the followi...

Recently, Douglas and Wang proved that for each polynomial q, the submodule [q] of the Bergman module generated by q is essentially normal [9]. Using improved techniques, we show that the Hardy-space analogue of this result holds, and more.