Recovering S1S^1-invariant metrics on S2S^2 from the equivariant spectrum

We prove an inverse spectral result for $S^1$-invariant metrics on $S^2$ based on the so-called asymptotic equivariant spectrum. This is roughly the spectrum together with large weights of the $S^1$ action on the eigenspaces. Our result generalizes an inverse spectral result of the first and last named authors, together with Victor Guillemin, concerning $S^1$-invariant metrics on $S^2$ which are invariant under the antipodal map. We use higher order terms in the asymptotic expansion of a natural spectral measure associated with the Laplacian and the $S^1$ action.Comment: 16 pages; minor revisions throughout following comments from referee

Novel solid-state emissive polymers and polymeric blends from a T-Shaped benzodifuran scaffold: A comparative study

Two novel polyimines were synthesized from a benzodifuran based diamino monomer and two dialdehydes bearing bulky groups and a flexible spacer. The polymers display tuned luminescence performance according to the presence of half-salen groups. The effect of the intramolecular bond on the emission properties were examined. Two model compounds, replicating the same emissive Schiff base cores, were synthetized. From the models, dye-doped blends in the fluorophore/matrix ratio, resembling the polymers, were produced. Amorphous thin films of the covalent polymers and the polymeric blends were obtained by spin-coating technique. The Photoluminescent (PL) response of the different macromolecular systems were qualitatively and quantitatively examined and compared

Studying patterns of use of transport modes through data mining - Application to U.S. national household travel survey data set

Data collection activities related to travel require large amounts of financial and human resources to be conducted successfully. When available resources are scarce, the information hidden in these data sets needs to be exploited, both to increase their added value and to gain support among decision makers not to discontinue such efforts. This study assessed the use of a data mining technique, association analysis, to understand better the patterns of mode use from the 2009 U.S. National Household Travel Survey. Only variables related to self-reported levels of use of the different transportation means are considered, along with those useful to the socioeconomic characterization of the respondents. Association rules potentially showed a substitution effect between cars and public transportation, in economic terms but such an effect was not observed between public transportation and nonmotorized modes (e.g., bicycling and walking). This effect was a policy-relevant finding, because transit marketing should be targeted to car drivers rather than to bikers or walkers for real improvement in the environmental performance of any transportation system. Given the competitive advantage of private modes extensively discussed in the literature, modal diversion from car to transit is seldom observed in practice. However, after such a factor was controlled, the results suggest that modal diversion should mainly occur from cars to transit rather than from nonmotorized modes to transi

A novel DR/NIR T-shaped aiegen: Synthesis and x-ray crystal structure study

We developed a new benzodifuran derivative as the condensation product between 2,6-diamino-4-(4-nitrophenyl)benzo[1,2-b:4,5-b’]difuran-3,7-dicarboxylate and 3-hydroxy-2-naphthaldehyde. The intramolecular hydrogen-bond interactions in the terminal half-salen moieties produce a sterically encumbered highly conjugated main plane and a D-A-D (donor-acceptor-donor) T-shaped structure. The novel AIEgen (aggregation-induced enhanced emission generator) fulfils the requirement of RIR (restriction of intramolecular rotation) molecules. DR/NIR (deep red/near infrared) emission was recorded in solution and in the solid state, with a noteworthy photoluminescence quantum yield recorded on the neat crystals which undergo some mechanochromism. The crystal structure study of the probe from data collected at a synchrotron X-ray source shows a main aromatic plane π-stacked in a columnar arrangement

Defect-induced modification of low-lying excitons and valley selectivity in monolayer transition metal dichalcogenides

We study the effect of point-defect chalcogen vacancies on the optical properties of monolayer transition metal dichalcogenides using ab initio GW and Bethe-Salpeter equation calculations. We find that chalcogen vacancies introduce unoccupied in-gap states and occupied resonant defect states within the quasiparticle continuum of the valence band. These defect states give rise to a number of strongly-bound defect excitons and hybridize with excitons of the pristine system, reducing the valley-selective circular dichroism. Our results suggest a pathway to tune spin-valley polarization and other optical properties through defect engineering