The Renormalization Group According to Balaban - I. Small fields

This is an expository account of Balaban's approach to the renormalization group. The method is illustrated with a treatment of the the ultraviolet problem for the scalar phi^4 model on a toroidal lattice in dimension d=3. This yields another proof of the stability bound. In this first paper we analyze the small field contribution to the partition function.Comment: 52 pages. Some corrections, additions, reorganizatio

Boundary value problems with Atiyah-Patodi-Singer type conditions and spectral triples

We study realizations of pseudodifferential operators acting on sections of vector-bundles on a smooth, compact manifold with boundary, subject to conditions of Atiyah-Patodi-Singer type. Ellipticity and Fredholm property, compositions, adjoints and self-adjointness of such realizations are discussed. We construct regular spectral triples $(\mathcal{A},\mathcal{H},\mathcal{D})$ for manifolds with boundary of arbitrary dimension, where $\mathcal{H}$ is the space of square integrable sections. Starting out from Dirac operators with APS-conditions, these triples are even in case of even dimensional manifolds; we show that the closure of $\mathcal{A}$ in $\mathscr{L}(\mathcal{H})$ coincides with the continuous functions on the manifold being constant on each connected component of the boundary.Comment: 27 pages, to appear in Journal of Noncommutative Geometr

Residential Real Estate Prices: A Room with a View

This article is the winner of the Real Estate Broker / Agency manuscript prize (sponsored by the Center for the Study of Real Estate Brokerage/ Agency at Cleveland State University) presented at the 2001 American Real Estate Society Annual Meeting. This study examines the effect that a view of Lake Erie has on the value of a home. Unlike previous studies, the current investigation is able to successfully control for view. That is, because of the unique building codes of lakefront homes in this sample, homes analyzed either do or do not have a view. Moreover, transaction-based home prices are used which is an improvement over previous studies that rely on appraisal-based data. The results indicate that square footage and lot size also significantly affect a home’s value. More importantly, having this very desirable view adds $256,544.72 (an 89.9% premium) to the value of the home.

Bounded Imaginary Powers of Differential Operators on Manifolds with Conical Singularities

We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted L^p-spaces over B, 1 < p < \infty. Under suitable ellipticity assumptions we can define a family of complex powers A^z. We also obtain sufficient information on the resolvent of A to show the boundedness of the purely imaginary powers. Examples concern unique solvability and maximal regularity for the solution of the Cauchy problem for the Laplacian on conical manifolds as well as certain quasilinear diffusion equations.Comment: 27 pages, 3 figures (revised version 23/04/'02

Regret Aversion and False Reference Points in Residential Real Estate

This study empirically exams the combination of regret aversion and false reference points in a residential real estate context. Survey respondents were put in a hypothetical situation, where they had purchased an investment property several years ago. Hindsight knowledge about a foregone all time high was introduced. As hypothesized, respondents on average expressed higher regret if they had actively failed to sell at the all time high (commission scenario) than if they had simply been unaware of the potential gain (omission scenario). Women were found to be more susceptible to regret aversion and false reference points than men.

Some new results on an old controversy: is perturbation theory the correct asymptotic expansion in nonabelian models?

Several years ago it was found that perturbation theory for two-dimensional O(N) models depends on boundary conditions even after the infinite volume limit has been taken termwise, provided $N>2$. There ensued a discussion whether the boundary conditions introduced to show this phenomenon were somehow anomalous and there was a class of `reasonable' boundary conditions not suffering from this ambiguity. Here we present the results of some computations that may be interpreted as giving some support for the correctness of perturbation theory with conventional boundary conditions; however the fundamental underlying question of the correctness of perturbation theory in these models and in particular the perturbative $\beta$ function remain challenging problems of mathematical physics.Comment: 4 pages, 3 figure