Finite Form of the Quintuple Product Identity

The celebrated quintuple product identity follows surprisingly from an almost-trivial algebraic identity, which is the limiting case of the terminating q-Dixon formula.Comment: 1 pag

Epidemic dynamics of respiratory syncytial virus in current and future climates.

A key question for infectious disease dynamics is the impact of the climate on future burden. Here, we evaluate the climate drivers of respiratory syncytial virus (RSV), an important determinant of disease in young children. We combine a dataset of county-level observations from the US with state-level observations from Mexico, spanning much of the global range of climatological conditions. Using a combination of nonlinear epidemic models with statistical techniques, we find consistent patterns of climate drivers at a continental scale explaining latitudinal differences in the dynamics and timing of local epidemics. Strikingly, estimated effects of precipitation and humidity on transmission mirror prior results for influenza. We couple our model with projections for future climate, to show that temperature-driven increases to humidity may lead to a northward shift in the dynamic patterns observed and that the likelihood of severe outbreaks of RSV hinges on projections for extreme rainfall

A multi-layer extension of the stochastic heat equation

Motivated by recent developments on solvable directed polymer models, we define a 'multi-layer' extension of the stochastic heat equation involving non-intersecting Brownian motions.Comment: v4: substantially extended and revised versio

Classification and selection of tenants in residential real estate: a constructivist approach

Choosing a tenant is a key issue in the housing rental market. Knowing, a priori, whether a tenant will pay the rent on time, be able to hold a good relationship with the neighbors or take care of the property (i.e. whether s/he will be a “good” tenant) is not a simple endeavor. It is crucial, however, as it can help save time, money and conflicts that can end up in court. This study aims to address this issue, through the integrated use of cognitive maps and the Decision EXpert (DEX) technique. Grounded on a constructivist logic, the study brought together a panel of experts with experience and knowledge in the residential rental market, in order to identify and articulate the criteria to be taken into account in the classification and selection of tenants. The results achieved show that the integration of these two methodologies (i.e. cognitive maps and DEX) can help increase our understanding of the decision problem at hand, and lead to more informed and potentially better tenant choices. Advantages and limitations of the framework are also discussed

Slip-Flow and Heat Transfer of a Non-Newtonian Nanofluid in a Microtube

The slip-flow and heat transfer of a non-Newtonian nanofluid in a microtube is theoretically studied. The power-law rheology is adopted to describe the non-Newtonian characteristics of the flow, in which the fluid consistency coefficient and the flow behavior index depend on the nanoparticle volume fraction. The velocity profile, volumetric flow rate and local Nusselt number are calculated for different values of nanoparticle volume fraction and slip length. The results show that the influence of nanoparticle volume fraction on the flow of the nanofluid depends on the pressure gradient, which is quite different from that of the Newtonian nanofluid. Increase of the nanoparticle volume fraction has the effect to impede the flow at a small pressure gradient, but it changes to facilitate the flow when the pressure gradient is large enough. This remarkable phenomenon is observed when the tube radius shrinks to micrometer scale. On the other hand, we find that increase of the slip length always results in larger flow rate of the nanofluid. Furthermore, the heat transfer rate of the nanofluid in the microtube can be enhanced due to the non-Newtonian rheology and slip boundary effects. The thermally fully developed heat transfer rate under constant wall temperature and constant heat flux boundary conditions is also compared

The Multisection method for triple products and identities of Rogers-Ramanujan type

AbstractBy applying the bisection and trisection method to Jacobi's triple product identity, we establish several identities factorizing sum and difference of infinite products, which lead, in turn, to new and elementary proofs for twenty identities of Rogers–Ramanujan type

On some classes of inverse series relations and their applications

AbstractThis paper gives a brief exposition of several recent results obtained by the authors concerning some classes of inverse relations, including the general binomial-type inversions and two kinds of general Stirling reciprocal transforms. Also described are some applications of the related inversion techniques to combinatorics (including new proofs of Rogers-Ramanujan identities and MacMahon's master theorem), interpolation methods and certain problems related to special polynomials and number sequences