Eisenstein type series for Calabi–Yau varieties

In this article we introduce an ordinary differential equation associated to the one parameter family of Calabi–Yau varieties which is mirror dual to the universal family of smooth quintic three folds. It is satisfied by seven functions written in the q-expansion form and the Yukawa coupling turns out to be rational in these functions. We prove that these functions are algebraically independent over the field of complex numbers, and hence, the algebra generated by such functions can be interpreted as the theory of (quasi) modular forms attached to the one parameter family of Calabi–Yau varieties. Our result is a reformulation and realization of a problem of Griffiths around seventies on the existence of automorphic functions for the moduli of polarized Hodge structures. It is a generalization of the Ramanujan differential equation satisfied by three Eisenstein series.     

天然丰度的N-磷酰化氨基酸的15N NMR 研究

采用¹⁵N-¹H的2D HSQC、HMBC实验方法,测定了天然丰度的N-磷酰化氨基酸样品在溶液中的¹⁵N化学位移δ_N及偶合常数J_N-P,J_N-H. 实验表明：对于¹⁵N天然丰度样品,这是一种快速有效的实验方法. 研究发现：N-酰化后的氨基酸,其δ_N以及与氮原子直接相连的质子¹H的化学位移均发生十分明显的高场位移,而偶合常数¹J_N-P,¹J_N-H的变化与化合物构型相关联 .     

Effects of in situ thermal annealing on the structural, optical, and electrical properties in Hg0.7Cd0.3Te epilayers grown on CdTe buffer layers

Scanning electron microscopy (SEM), Fourier transform infrared (FTIR) transmission, and Hall effect measurements were performed to investigate the structural, optical, and electrical properties of as-grown and in situ-annealed Hg_0.7Cd_0.3Te epilayers grown on CdTe buffer layers by using molecular beam epitaxy. After the Hg_0.7Cd_0.3Te epilayers had been annealed in a Hg-cell flux atmosphere, the SEM images showed that the surface morphologies of the Hg_0.7Cd_0.3Te thin films were mirror-like with no indication of pinholes or defects, and the FTIR spectra showed that the transmission intensities had increased in comparison to that of the as-grown Hg_0.7Cd_0.3Te epilayer. Hall-effect measurements showed that n-Hg_0.7Cd_0.3Te epilayers were converted to p-Hg_0.7Cd_0.3Te epilayers. These results indicate that the surface, optical, and electrical properties of the Hg_1 − xCd_xTe epilayers are improved by annealing and that as-grown n-Hg_1 − xCd_xTe epilayers can be converted to p-Hg_1 − xCd_xTe epilayers by in situ annealing.     

The AB2-XA1 electronic transition of NO2: A rovibronic survey covering 14 300-18 000 cm

More than 250 rotationally resolved vibrational bands of the A²B₂-X²A₁ electronic transition of ¹⁵NO₂ have been observed in the 14 300-18 000 cm⁻¹ range. The bands have been recorded in a recently constructed setup designed for high resolution spectroscopy of jet cooled molecules by combining time gated fluorescence spectroscopy and molecular beam techniques. The majority of the observed bands has been rotationally assigned and can be identified as transitions starting from the vibrational ground state or from vibrationally excited (hot band) states. An exceptionally strong band is located at 14 851 cm⁻¹ and studied in more detail as a typical benchmark transition to monitor ¹⁵NO₂ in atmospheric remote sensing experiments. Standard rotational fit routines provide band origins, rotational and spin rotation constants. A subset of 177 vibronic levels of ²B₂ vibronic symmetry has been analyzed in the energy range between 14 300 and 17 250 cm⁻¹, in terms of integrated density and using Next Neighbor Distribution. It is found that the overall statistical properties and polyad structure of ¹⁵NO₂ are comparable to those of ¹⁴NO₂ but that the internal structures of the polyads are completely different. This is a direct consequence of the X²A₁-A²B₂ vibronic mixing.     

The ν5 and 2ν9 bands of the N isotopic species of nitric acid (H15NO3): Line positions and intensities

Nitric acid (HNO₃) plays an important role in the Earth’s atmosphere as a reservoir molecule of NO_x species. It has a strong infrared signature at 11 μm which is one of the most commonly used for the infrared retrieval of this species in the atmosphere since this spectral region coincides with an atmospheric window. It is therefore essential to have high quality spectral parameters in this spectral region. For the H¹⁴NO₃ (main) isotopic species, the 11 μm bands were already the subject of numerous extensive studies which involve not only the ν₅ and 2ν₉ cold bands but also the first hot bands. The present work is the first high resolution Fourier transform analysis of the 11 μm bands for H¹⁵NO₃, which is the second most abundant isotopomer of nitric acid [a ≅ 0.00365(7)]. In this way, the analysis of the ν₅ and 2ν₉ cold bands centered at 871.0955 and 893.4518 cm⁻¹ was performed, and as for H¹⁴NO₃, these bands are significantly perturbed since rather strong resonances couple the 5¹ and 9² rotational levels. The theoretical model that we used to compute the line positions and line intensities is directly issued from the one which we used recently for H¹⁴NO₃ [A. Perrin, J. Orphal, J.-M. Flaud, S. Klee, G. Mellau, H. Mäder, D. Walbrodt, M. Winnewisser, J. Mol. Spectrosc. 228 (2004) 375-391]. Actually, for the H¹⁵NO₃ line positions, the Hamiltonian matrix accounts for the rather strong Fermi and the weaker Coriolis interactions linking the 5¹⇔9² rotational levels. Using this model which accounts correctly for the strong mixing of the 5¹ and 9² upper state energy levels, the ν₅ and 2ν₉ line intensities for H¹⁵NO₃ were satisfactorily computed using the ν₅ and 2ν₉ transition moment operators achieved previously for the ¹⁴N (main) isotopic species. In this way, the transfer of intensities from the ν₅ fundamental (and presumably strong) band to the 2ν₉ overtone (and presumably weak) band could be explained for H¹⁵NO₃ as it was done previously for the ¹⁴N (main) isotopic species. Finally, the position of the H¹⁵NO₃ν₅ + ν₉ − ν₉ hot band was identified at 875.245 cm⁻¹.     

Global fittings of NNO and NNO vibrational-rotational line positions using the effective Hamiltonian approach

An effective Hamiltonian built up to sixth order in the Amat-Nielsen ordering scheme describing all rovibrational energy levels in the ground electronic state and containing in explicit form all resonance interaction terms due to the approximate relations between harmonic frequencies ω₁≈2ω₂ and ω₃≈4ω₂ was applied to model the observed rovibrational line positions (collected from the literature) of ¹⁴N¹⁵N¹⁶O and ¹⁵N¹⁴N¹⁶O isotopologues of nitrous oxide. For ¹⁴N¹⁵N¹⁶O, 124 effective Hamiltonian parameters were fitted to near 28 000 observed line positions covering the 0.8-8860 cm⁻¹ spectral range. The RMS of the weighted fit is 0.00126 cm⁻¹ and dimensionless standard deviation is 1.48. For ¹⁵N¹⁴N¹⁶O, 121 effective Hamiltonian parameters were fitted to more than 31 000 observed line positions covering the same spectral interval. The RMS of the weighted fit is 0.00185 cm⁻¹ and dimensionless standard deviation is 1.85. In both cases the models describe all available line positions with precision compatible to the measurement uncertainties. A number of local resonance perturbations was found and discussed. Among these perturbations there are interpolyad resonance Coriolis interactions. A comparison of HITRAN-2008 data with the calculations based on the fitted models is presented.     

Regularization in quantum field theory from the causal point of view

The causal approach to perturbative quantum field theory is presented in detail, which goes back to a seminal work by Henri Epstein and Vladimir Jurko Glaser in 1973 [12]. Causal perturbation theory is a mathematically rigorous approach to renormalization theory, which makes it possible to put the theoretical setup of perturbative quantum field theory on a sound mathematical basis. Epstein and Glaser solved this problem for a special class of distributions, the time-ordered products, that fulfill a causality condition, which itself is a basic requirement in axiomatic quantum field theory. In their original work, Epstein and Glaser studied only theories involving scalar particles. In this review, the extension of the method to theories with higher spin, including gravity, is presented. Furthermore, specific examples are presented in order to highlight the technical differences between the causal method and other regularization methods, like, e.g. dimensional regularization.     

Effects of fish farm loading on sea grass Posidonia oceanica at Vrgada Island (Central Adriatic): a nitrogen stable isotope study

Analyses of nitrogen stable isotopes in the marine sea grass Posidonia oceanica were used to investigate the influence of fish farming on the coastal ecosystem of Vrgada Island in the Murter Sea, Central Adriatic. The results show a statistically significant ¹⁵N enrichment (up to 4.7‰ at p?<?0.005) in P. oceanica leaf and shoot tissues from fish cage sites with respect to the unaffected offshore reference site of Lumbarda Reef Flat (Kornati Islands). Heavy nitrogen enrichment was also detected in other benthic organisms analysed during this study and is attributed to the absorption and assimilation of ¹⁵N-enriched fish farm derived nitrogen waste.     

Characterising ontogenetic niche shifts in Nile crocodile using stable isotope (δ13C, δ15N) analyses of scute keratin

Nile crocodiles undergo a three to five order of magnitude increase in body size during their lifespan. This shift coincides with a change in resource and habitat use which influences the strength, type and symmetry of interactions with other species. Identifying size-specific crocodile groups displaying similar traits is important for conservation planning. Here, we illustrate how stable carbon (δ¹³ C) and nitrogen (δ¹⁵ N) isotope analysis of scute keratin, together with breakpoint modelling analysis can be used to characterise ontogenetic niche shifts. Using a sample set of 238 crocodiles from the Okavango Delta, Botswana (35–463 cm total length), we found prominent size-related changes in the scute keratin δ¹³ C and δ¹⁵ N profiles close to 40 and 119 cm snout-vent length. The first shift corroborated the findings of a traditional stomach-content study conducted on the same population at the same time, and the second conformed to known crocodile ecology. This approach can be used as a first approximation to identify size-specific groups within crocodile populations, and these can then be investigated further using isotopic or other methods.     

Oxygen and nitrogen isotopic composition of nitrate in commercial fertilizers,nitric acid,and reagent salts

Nitrate is a key component of synthetic fertilizers that can be beneficial to crop production in agro-ecosystems, but can also cause damage to natural ecosystems if it is exported in large amounts. Stable isotopes, both oxygen and nitrogen, have been used to trace the sources and fate of nitrate in various ecosystems. However, the oxygen isotope composition of synthetic and organic nitrates is poorly constrained. Here, we present a study on the N and O isotope composition of nitrate-based fertilizers. The δ¹⁵N values of synthetic and natural nitrates were 0?±?2?‰ similar to the air N₂ from which they are derived. The δ¹⁸O values of synthetic nitrates were 23?±?3?‰, similar to air O₂, and natural nitrate fertilizer δ¹⁸O values (55?±?5?‰) were similar to those observed in atmospheric nitrate. The Δ¹⁷O values of synthetic fertilizer nitrate were approximately zero following a mass-dependent isotope relationship, while natural nitrate fertilizers had Δ¹⁷O values of 18?±?2?‰ similar to nitrate produced photochemically in the atmosphere. These narrow ranges of values can be used to assess the amount of nitrate arising from fertilizers in mixed systems where more than one nitrate source exists (soil, rivers, and lakes) using simple isotope mixing models.