Uniqueness of Gibbs Measure for Models With Uncountable Set of Spin Values on a Cayley Tree

We consider models with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k\geq 1$. It is known that the "splitting Gibbs measures" of the model can be described by solutions of a nonlinear integral equation. For arbitrary $k\geq 2$ we find a sufficient condition under which the integral equation has unique solution, hence under the condition the corresponding model has unique splitting Gibbs measure.Comment: 13 page

Historic buildings and the creation of experiencescapes: looking to the past for future success

Purpose: The purpose of this paper is to identify the role that the creative re-use of historic buildings can play in the future development of the experiences economy. The aesthetic attributes and the imbued historic connotation associated with the building help create unique and extraordinary “experiencescapes” within the contemporary tourism and hospitality industries. Design/methodology/approach: This paper provides a conceptual insight into the creative re-use of historic buildings in the tourism and hospitality sectors, the work draws on two examples of re-use in the UK. Findings: This work demonstrates how the creative re-use of historic buildings can help create experiences that are differentiated from the mainstream hospitality experiences. It also identifies that it adds an addition unquantifiable element that enables the shift to take place from servicescape to experiencescape. Originality/value: There has been an ongoing debate as to the significance of heritage in hospitality and tourism. However, this paper provides an insight into how the practical re-use of buildings can help companies both benefit from and contribute to the experiences economy

Topological expansion in the complex cubic log-gas model. One-cut case

We prove the topological expansion for the cubic log-gas partition function, with a complex parameter and defined on an unbounded contour on the complex plane. The complex cubic log-gas model exhibits two phase regions on the complex t-plane, with one cut and two cuts, separated by analytic critical arcs of the two types of phase transition: split of a cut and birth of a cut. The common point of the critical arcs is a tricritical point of the Painleve I type. In the present paper we prove the topological expansion for the partition function in the one-cut phase region. The proof is based on the Riemann-Hilbert approach to semiclassical asymptotic expansions for the associated orthogonal polynomials and the theory of S-curves and quadratic differentials

Open Problems and Conjectures Related to the Theory of Mathematical Quasicrystals

This list of problems arose as a collaborative effort among the participants of the Arbeitsgemeinschaft on Mathematical Quasicrystals, which was held at the Mathematisches Forschungsinstitut Oberwolfach in October 2015. The purpose of our meeting was to bring together researchers from a variety of disciplines, with a common goal of understanding different viewpoints and approaches surrounding the theory of mathematical quasicrystals. The problems below reflect this goal and this diversity and we hope that they will motivate further cross-disciplinary research and lead to new advances in our overall vision of this rapidly developing field

Species Richness and Trophic Diversity Increase Decomposition in a Co-Evolved Food Web

Ecological communities show great variation in species richness, composition and food web structure across similar and diverse ecosystems. Knowledge of how this biodiversity relates to ecosystem functioning is important for understanding the maintenance of diversity and the potential effects of species losses and gains on ecosystems. While research often focuses on how variation in species richness influences ecosystem processes, assessing species richness in a food web context can provide further insight into the relationship between diversity and ecosystem functioning and elucidate potential mechanisms underpinning this relationship. Here, we assessed how species richness and trophic diversity affect decomposition rates in a complete aquatic food web: the five trophic level web that occurs within water-filled leaves of the northern pitcher plant, Sarracenia purpurea. We identified a trophic cascade in which top-predators — larvae of the pitcher-plant mosquito — indirectly increased bacterial decomposition by preying on bactivorous protozoa. Our data also revealed a facultative relationship in which larvae of the pitcher-plant midge increased bacterial decomposition by shredding detritus. These important interactions occur only in food webs with high trophic diversity, which in turn only occur in food webs with high species richness. We show that species richness and trophic diversity underlie strong linkages between food web structure and dynamics that influence ecosystem functioning. The importance of trophic diversity and species interactions in determining how biodiversity relates to ecosystem functioning suggests that simply focusing on species richness does not give a complete picture as to how ecosystems may change with the loss or gain of species

Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman

In the introduction to this volume, we discuss some of the highlights of the research career of Chuck Newman. This introduction is divided into two main sections, the first covering Chuck's work in statistical mechanics and the second his work in percolation theory, continuum scaling limits, and related topics.Comment: 38 pages (including many references), introduction to Festschrift in honor of C.M. Newma