Asymptotics of relative heat traces and determinants on open surfaces of finite area

The goal of this paper is to prove that on surfaces with asymptotically cusp ends the relative determinant of pairs of Laplace operators is well defined. We consider a surface with cusps (M,g) and a metric h on the surface that is a conformal transformation of the initial metric g. We prove the existence of the relative determinant of the pair $(\Delta_{h},\Delta_{g})$ under suitable conditions on the conformal factor. The core of the paper is the proof of the existence of an asymptotic expansion of the relative heat trace for small times. We find the decay of the conformal factor at infinity for which this asymptotic expansion exists and the relative determinant is defined. Following the paper by B. Osgood, R. Phillips and P. Sarnak about extremal of determinants on compact surfaces, we prove Polyakov's formula for the relative determinant and discuss the extremal problem inside a conformal class. We discuss necessary conditions for the existence of a maximizer.Comment: This is the final version of the article before it gets published. 51 page

TB143: Reproductive Phenologies of Selected Flowering Plants in Eastern Maine Forests

This technical bulletin documents both flowering and fruiting patterns during the spring and summer of 1982 of plant species found in eastern Maine forests.https://digitalcommons.library.umaine.edu/aes_techbulletin/1201/thumbnail.jp

Achieving sub-diffraction imaging through bound surface states in negative-refracting photonic crystals at the near-infrared

We report the observation of imaging beyond the diffraction limit due to bound surface states in negative refraction photonic crystals. We achieve an effective negative index figure-of-merit [-Re(n)/Im(n)] of at least 380, ~125x improvement over recent efforts in the near-infrared, with a 0.4 THz bandwidth. Supported by numerical and theoretical analyses, the observed near-field resolution is 0.47 lambda, clearly smaller than the diffraction limit of 0.61 lambda. Importantly, we show this sub-diffraction imaging is due to the resonant excitation of surface slab modes, allowing refocusing of non-propagating evanescent waves

Intention of preserving forest remnants among landowners in the Atlantic Forest: The role of the ecological context via ecosystem services

Unravelling the psychological processes determining landowners' support towards forest conservation is crucial, particularly in rural areas of the tropics, where most forest remnants are within private lands. As human–nature connections are known to shape pro‐environmental behaviours, the intention of preserving forest remnants should ultimately be determined by the ecological context people live in. Here, we investigate the pathways through which the ecological context (forest cover), via direct contact with forests and ecosystem services and disservices, influence the psychological antecedents of conservation behaviour (beliefs, attitude and intention of preserving forest remnants). We conceptualized a model based on the Reasoned Action Approach, using the ecological context and these three forest experiences as background factors, and tested the model using Piecewise Structural Equation Modelling. Data were collected through an interview‐based protocol applied to 106 landowners across 13 landscapes varying in forest cover in a consolidated rural region in the Brazilian Atlantic Forest. Our results indicate that: (a) ecosystem services are more important than disservices for shaping intention of preserving forests, particularly non‐provisioning services; (b) contact with forest has an indirect effect on intention, by positively influencing the frequency of receiving ecosystem services; (c) people living in more forested ecological contexts have more contact with forests, receive ecosystem services more frequently and, ultimately, have stronger intention of preserving forests. Hence, our study suggests a dangerous positive feedback loop between deforestation, the extinction of forest experiences and impairment of human–nature connections. Local demands across the full range of ecosystem services, the balance between services and disservices and the ecological context people live in should be considered when developing conservation initiatives in tropical rural areas

A negative mass theorem for surfaces of positive genus

We define the "sum of squares of the wavelengths" of a Riemannian surface (M,g) to be the regularized trace of the inverse of the Laplacian. We normalize by scaling and adding a constant, to obtain a "mass", which is scale invariant and vanishes at the round sphere. This is an anlaog for closed surfaces of the ADM mass from general relativity. We show that if M has positive genus then on each conformal class, the mass attains a negative minimum. For the minimizing metric, there is a sharp logarithmic Hardy-Littlewood-Sobolev inequality and a Moser-Trudinger-Onofri type inequality.Comment: 8 page

Fast lemons and sour boulders:Testing crossmodal correspondences using an internet-based testing methodology

Abstract. According to a popular family of hypotheses, crossmodal matches between distinct features hold because they correspond to the same polarity on several conceptual dimensions (such as active–passive, good–bad, etc.) that can be identified using the semantic differential technique. The main problem here resides in turning this hypothesis into testable empirical predictions. In the present study, we outline a series of plausible consequences of the hypothesis and test a variety of well-established and previously untested crossmodal correspondences by means of a novel internet-based testing methodology. The results highlight that the semantic hypothesis cannot easily explain differences in the prevalence of crossmodal associations built on the same semantic pattern (fast lemons, slow prunes, sour boulders, heavy red); furthermore, the semantic hypothesis only minimally predicts what happens when the semantic dimensions and polarities that are supposed to drive such crossmodal associations are made more salient (e.g., by adding emotional cues that ought to make the good/bad dimension more salient); finally, the semantic hypothesis does not explain why reliable matches are no longer observed once intramodal dimensions with congruent connotations are presented (e.g., visually presented shapes and colour do not appear to correspond)

Local modes, phonons, and mass transport in solid 4^4He

We propose a model to treat the local motion of atoms in solid $^{4}$He as a local mode. In this model, the solid is assumed to be described by the Self Consistent Harmonic approximation, combined with an array of local modes. We show that in the bcc phase the atomic local motion is highly directional and correlated, while in the hcp phase there is no such correlation. The correlated motion in the bcc phase leads to a strong hybridization of the local modes with the T$_{1}(110)$ phonon branch, which becomes much softer than that obtained through a Self Consistent Harmonic calculation, in agreement with experiment. In addition we predict a high energy excitation branch which is important for self-diffusion. Both the hybridization and the presence of a high energy branch are a consequence of the correlation, and appear only in the bcc phase. We suggest that the local modes can play the role in mass transport usually attributed to point defects (vacancies). Our approach offers a more overall consistent picture than obtained using vacancies as the predominant point defect. In particular, we show that our approach resolves the long standing controversy regarding the contribution of point defects to the specific heat of solid $^{4}$He.Comment: 10 pages, 10 figure

Observations of zero-order bandgaps in negative-index photonic crystal superlattices at the near-infrared

We present the first observations of zero-n bandgaps in photonic crystal superlattices consisting of alternating stacks of negative index photonic crystals and positive index dielectric materials in the near-infrared. Guided by ab initio three-dimensional numerical simulations, the fabricated nanostructured superlattices demonstrate the presence of zero-order gaps in remarkable agreement with theoretical predictions across a range of different superlattice periods and unit cell variations. These volume-averaged zero-index superlattice structures present a new type of photonic band gap, with potential for complete wavefront control for arbitrary phase delay lines and open cavity resonances.Comment: 14 pages, 3 Figure