Γ0(2)\Gamma^{0}(2) modular forms and anomaly cancellation formulas

In [5], [6] and [8], the authors gave some modular forms over $\Gamma^0(2)$. In this note, we proceed with the study of cancellation formulas relating to the modular forms.Comment: 16pages. arXiv admin note: substantial text overlap with arXiv:2308.1118

The J-twist D_J of the Dirac operator and the Kastler-Kalau-Walze type theorem for six-dimensional manifolds with boundary

In [22], the authors proved a Kastler-Kalau-Walze type theorem for the J-twist D_J of the Dirac operator on 3-dimensional and 4-dimensional almost product Riemannian spin manifold with boundary. In this paper, we develop the Kastler-Kalau-Walze type theorem for the J-twist D_J of the Dirac operator on a 6-dimensional almost product Riemannian spin manifold with boundary.Comment: 36 pages. arXiv admin note: substantial text overlap with arXiv:2203.1046

A note on modular forms and generalized anomaly cancellation formulas 2

In [7], Liu and Wang generalized the Han-Liu-Zhang cancellation formulas to the (a, b) type cancellation formulas. In this note, we prove some another (a, b) type cancellation formulas for even-dimensional Riemannian manifolds. And by transgression, we obtain some characteristic forms with modularity properties on odd-dimensional manifolds.Comment: 16 page

A Bootstrap Method for Spectral Statistics in High-Dimensional Elliptical Models

Although there is an extensive literature on the eigenvalues of high-dimensional sample covariance matrices, much of it is specialized to Mar\v{c}enko-Pastur (MP) models -- in which observations are represented as linear transformations of random vectors with independent entries. By contrast, less is known in the context of elliptical models, which violate the independence structure of MP models and exhibit quite different statistical phenomena. In particular, very little is known about the scope of bootstrap methods for doing inference with spectral statistics in high-dimensional elliptical models. To fill this gap, we show how a bootstrap approach developed previously for MP models can be extended to handle the different properties of elliptical models. Within this setting, our main theoretical result guarantees that the proposed method consistently approximates the distributions of linear spectral statistics, which play a fundamental role in multivariate analysis. Lastly, we provide empirical results showing that the proposed method also performs well for a variety of nonlinear spectral statistics

Estimation of Uncertainty in Air-­Water Exchange Flux 2 and Gross Volatilization Loss of PCBs: a Case Study 3 based on Passive Sampling in the Lower Great Lakes

Compared with dry and wet deposition fluxes, air–water exchange flux cannot be directly measured experimentally. Its model-based calculation contains considerable uncertainty because of the uncertainties in input parameters. To capture the inherent variability of air–water exchange flux of PCBs across the lower Great Lakes and to calculate their annual gross volatilization loss, 57 pairs of air and water samples from 19 sites across Lakes Erie and Ontario were collected using passive sampling technology during 2011–2012. Error propagation analysis and Monte Carlo simulation were applied to estimate uncertainty in the air–water exchange fluxes. Results from both methods were similar, but error propagation analysis estimated a smaller uncertainty than Monte Carlo simulation in cases of net deposition. Maximum likelihood estimations (MLE) of wind speed and air temperature were recommended to quantify the site-specific air–water exchange flux. An assumed 30–40% of relative uncertainty in overall air–water mass transfer velocity was confirmed. MLEs of volatilization fluxes of total PCBs across Lakes Erie and Ontario were 0.78 and 0.53 ng m–2 day–1, respectively, and gross volatilization losses of total PCBs over the whole lakes were 74 kg year–1 for Lake Erie and 63 kg year–1 for Lake Ontario. Mass balance analysis across Lake Ontario indicated that volatilization was the uppermost loss process of aqueous PCBs

Source Apportionment of Gaseous and Particulate PAHs from Traffic Emission Using Tunnel Measurements in Shanghai, China

Understanding sources and contributions of gaseous and particulate PAHs from traffic-related pollution can provide valuable information for alleviating air contamination from traffic in urban areas. On-road sampling campaigns were comprehensively conducted during 2011–2012 in an urban tunnel of Shanghai, China. 2–3 rings PAHs were abundant in the tunnel\u27s gas and particle phases. Diagnostic ratios of PAHs were statistically described; several were significantly different between the gas and particle phases. Principal component analysis (PCA), positive matrix factorization (PMF), bivariate correlation analysis and multiple linear regression analysis (MLRA) were applied to apportion sources of gaseous and particulate PAHs in the tunnel. Main sources of the gaseous PAHs included evaporative emission of fuel, high-temperature and low-temperature combustion of fuel, accounting for 50–51%, 30–36% and 13–20%, respectively. Unburned fuel particles (56.4–78.3%), high-temperature combustion of fuel (9.5–26.1%) and gas-to-particle condensation (12.2–17.5%) were major contributors to the particulate PAHs. The result reflected, to a large extent, PAH emissions from the urban traffic of Shanghai. Improving fuel efficiency of local vehicles will greatly reduce contribution of traffic emission to atmospheric PAHs in urban areas. Source apportionment of PM10 mass was also performed based on the organic component data. The results showed that high-temperature combustion of fuel and gas-to-particle condensation contributed to 15–18% and 7–8% of PM10 mass, respectively, but 55–57% of the particle mass was left unexplained. Although the results from the PCA and PMF models were comparable, the PMF method is recommended for source apportionment of PAHs in real traffic conditions. In addition, the combination of multivariate statistical method and bivariate correlation analysis is a useful tool to comprehensively assess sources of PAHs