Weighted Traces on Algebras of Pseudo-Differential Operators and Geometry of Loop Groups

Using {\it weighted traces} which are linear functionals of the type $$A\to tr^Q(A):=(tr(A Q^{-z})-z^{-1} tr(A Q^{-z}))_{z=0}$$ defined on the whole algebra of (classical) pseudo-differential operators (P.D.O.s) and where $Q$ is some positive invertible elliptic operator, we investigate the geometry of loop groups in the light of the cohomology of pseudo-differential operators. We set up a geometric framework to study a class of infinite dimensional manifolds in which we recover some results on the geometry of loop groups, using again weighted traces. Along the way, we investigate properties of extensions of the Radul and Schwinger cocycles defined with the help of weighted traces.Comment: 36 page

On vanishing theorems for Higgs bundles

We introduce the notion of Hermitian Higgs bundle as a natural generalization of the notion of Hermitian vector bundle and we study some vanishing theorems concerning Hermitian Higgs bundles when the base manifold is a compact complex manifold. We show that a first vanishing result, proved for these objects when the base manifold was K\"ahler, also holds when the manifold is compact complex. From this fact and some basic properties of Hermitian Higgs bundles, we conclude several results. In particular we show that, in analogy to the classical case, there are vanishing theorems for invariant sections of tensor products of Higgs bundles. Then, we prove that a Higgs bundle admits no nonzero invariant sections if there is a condition of negativity on the greatest eigenvalue of the Hitchin-Simpson mean curvature. Finally, we prove that invariant sections of certain tensor products of a weak Hermitian-Yang-Mills Higgs bundle are all parallel in the classical sense.Comment: 10 Pages, some typos corrected and minor change

Chirality distribution and transition energies of carbon nanotubes

From resonant Raman scattering on isolated nanotubes we obtained the optical transition energies, the radial breathing mode frequency and Raman intensity of both metallic and semiconducting tubes. We unambiguously assigned the chiral index (n_1,n_2) of approximately 50 nanotubes based solely on a third-neighbor tight-binding Kataura plot and find omega_RBM=214.4cm^-1nm/d+18.7cm^-1. In contrast to luminescence experiments we observe all chiralities including zig-zag tubes. The Raman intensities have a systematic chiral-angle dependence confirming recent ab-initio calculations.Comment: 4 pages, to be published in Phys. Rev. Let

Raman scattering study of electron-doped Prx_xCa1−x_{1-x}Fe2_2As2_2 superconductors

Temperature-dependent polarized Raman spectra of electron-doped superconducting Pr$_x$Ca$_{1-x}$Fe$_2$As$_2$ ($x \approx 0.12$) single crystals are reported. All four allowed by symmetry even-parity phonons are identified. Phonon mode of B$_{1g}$ symmetry at 222 cm$^{-1}$, which is associated with the c-axis motion of Fe ions, is found to exhibit an anomalous frequency hardening at low temperatures, that signals non-vanishing electron-phonon coupling in the superconducting state and implies that the superconducting gap magnitude $2\Delta_c < 27$meV.Comment: 4 pages, 3 figure

How host larval age, and nutrition and density of the parasitoid Dinarmus basalis (Hymenoptera: Pteromalidae) influence control of Acanthoscelides obtectus (Coleoptera: Bruchidae)

Choice of the targeted host developmental stage, regulation of parasitoid numbers released and introduction of food supplements are operational factors with a potential to influence the level of biological control. In a closed laboratory storage system maintained over two generations of the host, the impact of these three parameters on the control potential of the parasitoid Dinarmus basalis Rondani was investigated for high populations of larvae of Acanthoscelides obtectus (Say) feeding inside dry common bean seeds Phaseolus vulgaris. The beans were already infested with immature bruchids at the beginning of the storage period to simulate harvest conditions, characterized in a previous study. Treatments resulted in a reduction of 48-75% of the bruchid population within 16 weeks of storage. The best timing of parasitoid release was at the simulated harvest, as later releases reduced the bruchid population only by about half this percentage. Host feeding is postulated to be the key factor involved in the observed difference. The effect of increasing the number of parasitoids strongly depended on host age and food supplement. Addition of vials with honey had no direct effect on the bruchid population or on the parasitoid progeny. The ecological significance of these findings and implications for biological control are discusse

Electron-phonon renormalization of the absorption edge of the cuprous halides

Compared to most tetrahedral semiconductors, the temperature dependence of the absorption edges of the cuprous halides (CuCl, CuBr, CuI) is very small. CuCl and CuBr show a small increase of the gap $E_0$ with increasing temperature, with a change in the slope of $E_0$ vs. $T$ at around 150 K: above this temperature, the variation of $E_0$ with $T$ becomes even smaller. This unusual behavior has been clarified for CuCl by measurements of the low temperature gap vs. the isotopic masses of both constituents, yielding an anomalous negative shift with increasing copper mass. Here we report the isotope effects of Cu and Br on the gap of CuBr, and that of Cu on the gap of CuI. The measured isotope effects allow us to understand the corresponding temperature dependences, which we also report, to our knowledge for the first time, in the case of CuI. These results enable us to develop a more quantitative understanding of the phenomena mentioned for the three halides, and to interpret other anomalies reported for the temperature dependence of the absorption gap in copper and silver chalcogenides; similarities to the behavior observed for the copper chalcopyrites are also pointed out.Comment: 14 pages, 5 figures, submitted to Phys. Rev.

Field Infestation of Phaseolus vulgaris by Acanthoscelides obtectus (Coleoptera: Bruchidae), Parasitoid Abundance, and Consequences for Storage Pest Control

Over a period of 3 yr we collected 19 samples (1 kg each) of recently harvested beans (Phaseolus vulgaris L.) from eight small-scale farms in Restrepo, Valle de Cauca, Colombia. Initial infestation by Acanthoscelides obtectus (Say) was low, but frequent. At harvest, 90% of the bean samples were infested by the weevil. The average level of infestation was 16 weevils per 1,000 beans, with a maximum of 55 weevils. Infested beans usually carried multiple larvae with a maximum of 13 larvae per bean. Emergence data indicate that oviposition by A. obtectus in the field is confined to a very short period before harvest. This relatively narrow time window can be exploited for proper timing of control measures. Only one species of parasitoid, Horismenus ashmeadii (Dalla Torre) (Hymenoptera: Eulophidae), was recorded, emerging from 21% of the samples. Samples with parasitoids had an average of five parasitoids per 1,000 beans, with a maximum of 12 parasitoids. This represented a parasitization level of 18%. During the 16 wk of storage, two weevil generations emerged, which caused visible damage in 0.5 and 34% of the beans (average of 14%). Although H. ashmeadii was successful in attacking the first generation of A. obtectus in the field, it failed to attack or develop under storage conditions. This indivates H. ashmeadii cannot serve as a postharvest control agen

Predictive validity of the CriSTAL tool for short-term mortality in older people presenting at Emergency Departments: a prospective study

© 2018, The Author(s). Abstract: To determine the validity of the Australian clinical prediction tool Criteria for Screening and Triaging to Appropriate aLternative care (CRISTAL) based on objective clinical criteria to accurately identify risk of death within 3 months of admission among older patients. Methods: Prospective study of ≥ 65 year-olds presenting at emergency departments in five Australian (Aus) and four Danish (DK) hospitals. Logistic regression analysis was used to model factors for death prediction; Sensitivity, specificity, area under the ROC curve and calibration with bootstrapping techniques were used to describe predictive accuracy. Results: 2493 patients, with median age 78–80 years (DK–Aus). The deceased had significantly higher mean CriSTAL with Australian mean of 8.1 (95% CI 7.7–8.6 vs. 5.8 95% CI 5.6–5.9) and Danish mean 7.1 (95% CI 6.6–7.5 vs. 5.5 95% CI 5.4–5.6). The model with Fried Frailty score was optimal for the Australian cohort but prediction with the Clinical Frailty Scale (CFS) was also good (AUROC 0.825 and 0.81, respectively). Values for the Danish cohort were AUROC 0.764 with Fried and 0.794 using CFS. The most significant independent predictors of short-term death in both cohorts were advanced malignancy, frailty, male gender and advanced age. CriSTAL’s accuracy was only modest for in-hospital death prediction in either setting. Conclusions: The modified CriSTAL tool (with CFS instead of Fried’s frailty instrument) has good discriminant power to improve prognostic certainty of short-term mortality for ED physicians in both health systems. This shows promise in enhancing clinician’s confidence in initiating earlier end-of-life discussions

Electroreflectance spectroscopy in self-assembled quantum dots: lens symmetry

Modulated electroreflectance spectroscopy $\Delta R/R$ of semiconductor self-assembled quantum dots is investigated. The structure is modeled as dots with lens shape geometry and circular cross section. A microscopic description of the electroreflectance spectrum and optical response in terms of an external electric field (${\bf F}$) and lens geometry have been considered. The field and lens symmetry dependence of all experimental parameters involved in the $\Delta R/R$ spectrum have been considered. Using the effective mass formalism the energies and the electronic states as a function of ${\bf F}$ and dot parameters are calculated. Also, in the framework of the strongly confined regime general expressions for the excitonic binding energies are reported. Optical selection rules are derived in the cases of the light wave vector perpendicular and parallel to $$. Detailed calculation of the Seraphin coefficients and electroreflectance spectrum are performed for the InAs and CdSe nanostructures. Calculations show good agreement with measurements recently performed on CdSe/ZnSe when statistical distribution on size is considered, explaining the main observed characteristic in the electroreflectance spectra

Manifestation of geometric frustration on magnetic and thermodynamic properties of pyrochlores Sm2X2O7Sm_2X_2O_7 (X=Ti, Zr)

We present here magnetization, specific heat and Raman studies on single-crystalline specimens of the first pyrochlore member $Sm_2Ti_2O_7$ of the rare-earth titanate series. Its analogous compound $Sm_2Zr_2O_7$ in the rare-earth zirconate series is also investigated in the polycrystalline form. The Sm spins in $Sm_2Ti_2O_7$ remain unordered down to at least T = 0.5 K. The absence of magnetic ordering is attributed to very small values of exchange ($\theta_{cw} ~ -0.26 K$) and dipolar interaction ($\mu_{eff} ~ 0.15 \mu_B$) between the $Sm^{3+}$ spins in this pyrochlore. In contrast, the pyrochlore $Sm_2Zr_2O_7$ is characterized by a relatively large value of Sm-Sm spin exchange ($\theta_{cw} ~ - 10 K$); however, long-range ordering of the $Sm^{3+}$ spins is not established at least down to T = 0.67 K, due to frustration of the $Sm^{3+}$ spins on the pyrochlore lattice. The ground state of $Sm^{3+}$ ions in both pyrochlores is a well-isolated Kramer's doublet. The higher-lying crystal field excitations are observed in the low-frequency region of the Raman spectra of the two compounds recorded at T = 10 K. At higher temperatures, the magnetic susceptibility of $Sm_2Ti_2O_7$ shows a broad maximum at T = 140 K while that of $Sm_2Zr_2O_7$ changes monotonically. Whereas $Sm_2Ti_2O_7$ is a promising candidate for investigating spin-fluctuations on a frustrated lattice as indicated by our data, the properties of $Sm_2Zr_2O_7$ seem to conform to a conventional scenario where geometrical frustration of the spin exclude their long-range ordering.Comment: 24 pages, 6 figures, Accepted for publication in Phys. Rev.