In this paper, we introduce and study quotients of fully nonlinear control systems. Our definition is inspired by categorical definitions of quotients as well as recent work on abstractions of affine control systems. We show that quotients exist under mild regularity assumptions and characterize the structure of the quotient state/input space. This allows one to understand how states and inputs...

We find two Fσδ ideals on N neither of which is Fσ whose quotient Boolean algebras are homogeneous but nonisomorphic. This solves a problem of Just and Krawczyk (1984). We consider Boolean algebras of the form P(N)/I, where I is an ideal on N containing the ideal Fin of finite sets. In [3] Just and Krawczyk formulated several conditions on the ideals I,J that guarantee their quotients P(N)/I an...

Abstract We prove the abelian–nonabelian correspondence for quasimap $I$-functions. That is, if $Z$ is an affine l.c.i. variety with action by a complex reductive group $G$, we explicit formula relating $I$-functions of geometric invariant theory quotients $Z\mathord{/\mkern -6mu/}_{\theta } G$ and T$ where $T$ maximal torus $G$. apply to compute $J$-functions some Grassmannian bundles on varie...

In this paper we will study artinian quotients A = R/I of the polynomial ring R = k[x1, ..., xr], where k is a field of characteristic zero, the xi’s all have degree 1 and I is a homogeneous ideal of R. These rings are often referred to as standard graded artinian algebras. Before explaining the main results of this work, we establish some of the notation we will use: the h-vector of A is h(A) ...

In this paper we devote to generalizing some results of componentwise linear modules over a polynomial ring to the ones over a Koszul algebra. Among other things, we show that the i-linear strand of the minimal free resolution of a componentwise linear module is the minimal free resolution of some module which is described explicitly for any i ∈ Z. In addition we present some theorems about whe...

A new C*-enlargement of a C*-algebra A nested between the local multiplier algebra Mloc(A) of A and its injective envelope I(A) is introduced. Various aspects of this maximal C*-algebra of quotients, Qmax(A), are studied, notably in the setting of AW*algebras. As a by-product we obtain a new example of a type I C*-algebra A such that Mloc(Mloc(A)) 6= Mloc(A).