The graded Betti numbers of the minimal free resolution (and also therefore the Hilbert function) of the ideal of a fat point subscheme Z of P are determined whenever Z is supported at any 6 or fewer distinct points. We also handle a broad range of cases in which the points can be infinitely near, related to the classification of normal cubic surfaces. All results hold over an arbitrary algebra...

We prove that, for each pair (m,n) of non-negative integers, there is a Banach space X for which K0(B(X)) ∼= Z m and K1(B(X)) ∼= Z . Along the way we compute the K-groups of all closed ideals of operators contained in the ideal of strictly singular operators, and we derive some results about the existence of splittings of certain short exact sequences.

Model Description • Actors: An infinite population of individuals indexed by ei, one’s ability to earn a secular income, and zi, one’s ideal level of doctrinal strictness. – ei ∼ g(e|θ), where θ captures human development and g(e|θ) satisfies the monotone likelihood ratio property (MLRP). – zi ∼ h(z|ρ), where ρ captures society’s overall preference for doctrinal strictness and h(z|ρ) satisfies ...

Abstract—In this paper we apply some results obtained for ”perturbed” Whittaker’s cardinal series, ∑ k∈Z ak sinc(t − λk), to problem of signal reconstruction in a Digital Audio Processes, where we consider ideal bandlimited interpolation and the variability of {λk}k∈Z models sampling clock jitter effects. Results applied in this work concern a stability theorem, by previous work, and a generali...

Let S be a standard N k-graded polynomial ring over a field K, let I be a multigraded homogeneous ideal of S, and let M be a finitely generated Z k-graded S-module. We prove that the resolution regularity, a multigraded variant of Castelnuovo-Mumford regularity, of I n M is asymptotically a linear function. This shows that the well known Z-graded phenomenon carries to multigraded situation.

There exists a feasible procedure to decide whether or not an arbitrary polynomial belongs to a given ideal in Z[x] if the ideal’s minimal basis is known. However, when this is not the case there is no feasible procedure to decide whether or not an arbitrary polynomial belongs to a given ideal. There already exists an effective procedure to find an ideal’s minimal basis, but it depends on solvi...

A Gabor system generated by a window function φ and a rectangular lattice aZ× Z/b is given by G(φ, aZ× Z/b) := {e−2πint/bφ(t−ma) : (m,n) ∈ Z× Z}. One of fundamental problems in Gabor analysis is to identify window functions φ and time-frequency shift lattices aZ × Z/b such that the corresponding Gabor system G(φ, aZ × Z/b) is a Gabor frame for L(R), the space of all square-integrable functions ...

Let S be a set of n ideals of a commutative ring A and let Geven (respectively Godd) denote the product of all the sums of even (respectively odd) number of ideals of S. If n ≤ 6 the product of Geven and the intersection of all ideals of S is included in Godd. In the case A is an Noetherian integral domain, this inclusion is replaced by equality if and only if A is a Dedekind domain.

The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

LetM =M(E) be a matroid on a linear ordered set E . The Orlik–Solomon Z-algebra OS(M) of M is the free exterior Z-algebra on E , modulo the ideal generated by the circuit boundaries. The Z-module OS(M) has a canonical basis called ‘no broken circuit basis’ and denoted nbc. Let eX = ∏ ei , ei ∈ X ⊂ E . We prove that when eX is expressed in the nbc basis, then all the coefficients are 0 or ±1. We...