Ground state representation of the infinite one-dimensional Heisenberg ferromagnet. IV. A completely integrable quantum system

The purpose of this article is to show that the ground state representation of the infinite one-dimensional spin $\text{1}\text{2}$ Heisenberg chain, with isotropic nearest neighbor interactions, provides an example of a completely integrable quantum system.     

A Simple and Effective Component Procurement Policy for Stochastic Assembly Systems

We examine the component procurement problem in a single-item, make-to-stock assembly system. The suppliers are uncapacitated and have independent but non-identically distributed stochastic delivery lead times. Assembly is instantaneous, product demand follows a Poisson process and unsatisfied demand is backordered. The objective is to minimize the sum of steady-state holding and backorder costs over a pre-specified class of replenishment policies. To keep the analysis tractable, we impose a synchronization assumption that no mixing occurs between sets of component orders. Combining existing results from queueing theory with original results concerning distributions that are closed under maximization and translation, we derive a simple approximate solution to the problem when lead time variances are identical. In simulations, our derived policy is within 2% of optimal and significantly outperforms policies that ignore either component dependence or lead time stochasticity. It is also quite robust with respect to various model assumptions, except the synchronization one.     

Solution of the Truncated Parabolic Moment Problem

Given real numbers with ₀₀ >0 , the truncated parabolic moment problem for entails finding necessary and sufficient conditions for the existence of a positive Borel measure , supported in the parabola p(x, y) = 0, such that We prove that admits a representing measure (as above) if and only if the associated moment matrix is positive semidefinite, recursively generated and has a column relation p(X, Y) = 0, and the algebraic variety () associated to satisfies card In this case, admits a rank -atomic (minimal) representing measure.Submitted: August 25, 2003     

Unbounded Disjointness Preserving Linear Functionals

Let X be a locally compact Hausdorff space and C ₀(X) the Banach space of continuous functions on X vanishing at infinity. In this paper, we shall study unbounded disjointness preserving linear functionals on C ₀(X). They arise from prime ideals of C ₀(X), and we translate it into the cozero set ideal setting. In particular, every unbounded disjointness preserving linear functional of c ₀ can be constructed explicitly through an ultrafilter on complementary to a cozero set ideal. This ultrafilter method can be extended to produce many, but in general not all, such functionals on C ₀(X) for arbitrary X. We also make some remarks where C ₀(X) is replaced by a non-commutative C*-algebra.     

Reform Teaching Strategies Used by Student Teachers

The purposes of this study were to observe the teaching practices occurring in student teachers' science and mathematics K‐12 classrooms, compare the student teachers' perceptions of their teaching with what was actually occurring in their classrooms, and determine which college faculty members and courses these student teachers felt contributed to the teaching methods they used. Data on each student teacher were gathered via field notes of three classes, an observation protocol completed after each lesson, and an interview. Composites were written for each of the students. The total data set of all composites was examined to see if any patterns generalizable to the whole were evident. Differences between and among grade levels and content areas surfaced and are discussed.     

Linear Independence of Gabor Systems in Finite Dimensional Vector Spaces

We discuss the linear independence of systems ofmvectors in n-dimensional complex vector spaces where the m vectors are time-frequency shifts of one generating vector. Such systems are called Gabor systems. When n is prime, we show that there exists an open, dense subset with full-measure of such generating vectors with the property that any subset of n vectors in the corresponding full Gabor system of n² vectors is linearly independent. We derive consequences relevant to coding, operator identification and time-frequency analysis in general.     

Monoidal Categories and Multiextensions

We associate to a group-like monoidal grupoid a principal bundle E satisfying most of the axioms defining a biextension. The obstruction to the existence of a genuine biextension structure on E is exhibited. When this obstruction vanishes, the biextension E is alternating and a trivialization of E induces a trivialization of . The analogous theory for monoidal n-categories is also examined, as well as the appropriate generalization of these constructions in a sheaf-theoretic context. In the n-categorial situation, this produces a higher commutator calculus, in which some interesting generalizations of the notion of an alternating biextension occur. For n=2, the corresponding cocycles are constructed explicitly, by a partial symmetrization process, from the cocycle describing the n-category.