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Joint photoelectron spectroscopy and first-principles theory investigations indicate that the Pb-doped PbB₂(BO)_n⁻clusters (n= 0−2) undergo a transformation from σ + π doubly aromatic triangle PbB₂⁻to PbB₄(BO)₂^−/0complexes with a B≡B triple bond.

 

An employee's annual earnings fall by 13% in the first full calendar year after her firm's bankruptcy, and the present value of lost earnings from bankruptcy to six years following bankruptcy is 87% of pre‐bankruptcy annual earnings. More worker earnings are lost in thin labor markets and among small firms. Ex ante compensating wage differentials for this “bankruptcy risk” are up to 2% of firm value for a firm whose credit rating falls from AA to BBB, comparable in magnitude to debt tax benefits. Thus, wage premia for expected costs of bankruptcy are sufficiently large to be an important consideration in capital structure decisions.

 

Lode gold deposits, which are currently the world’s major gold supply, have been shown to be generated mostly by phase separation of metamorphic fluids and/or interaction between these fluids and wall rocks. Here we use garnet oxygen isotopes by secondary ion mass spectrometry to document the crucial role of magmatic hydrothermal fluids and their mixing with meteoric water in the formation of the world-class Dongping gold deposit in the North China Craton. Garnet grains from quartz veins of various paragenetic stages and the mineralized alteration envelope at Dongping have dynamic δ 18 O variations of 3.8 to −11.0‰, with large intragrain fluctuations up to 5.3‰. These values correspond to calculated δ 18 O values of 6.1 to −9.1‰ for the hydrothermal fluids from which the garnet formed. The isotope data, notably the cyclic alternation in δ 18 O within individual garnet grains, are best interpreted to reflect multiple pulses of magmatically derived fluids and subsequent mixing of each pulse with variable amounts of meteoric water. The results presented here allow us to quantify the significant interplay between magmatic hydrothermal fluids and meteoric water that spanned the entire mineralization history and triggered gold deposition of a lode gold deposit. This study highlights the potential use of in situ oxygen isotope analysis of garnet in tracing the origin and evolution of hydrothermal fluids in the Earth’s crust that may have formed other giant ore deposits. 

Despite its electron deficiency, boron can form multiple bonds with a variety of elements. However, multiple bonds between boron and main-group metal elements are relatively rare. Here we report the observation of boron-lead multiple bonds in PbB₂O^–and PbB₃O₂^–, which are produced and characterized in a cluster beam. PbB₂O^–is found to have an open-shell linear structure, in which the bond order of B☱Pb is 2.5, while the closed-shell [Pb≡B–B≡O]^2–contains a B≡Pb triple bond. PbB₃O₂^–is shown to have a Y-shaped structure with a terminal B = Pb double bond coordinated by two boronyl ligands. Comparison between [Pb≡B–B≡O]^2–/[Pb=B(B≡O)₂]^–and the isoelectronic [Pb≡B–C≡O]^–/[Pb=B(C≡O)₂]⁺carbonyl counterparts further reveals transition-metal-like behaviors for the central B atoms. Additional theoretical studies show that Ge and Sn can form similar boron species as Pb, suggesting the possibilities to synthesize new compounds containing multiple boron bonds with heavy group-14 elements.

 

Positron emission tomography (PET) is traditionally modeled as discrete systems. Such models may be viewed as piecewise constant approximations of the underlying continuous model for the physical processes and geometry of the PET imaging. Due to the low accuracy of piecewise constant approximations, discrete models introduce an irreducible modeling error which fundamentally limits the quality of reconstructed images. To address this bottleneck, we propose an integral equation model for the PET imaging based on the physical and geometrical considerations, which describes accurately the true coincidences. We show that the proposed integral equation model is equivalent to the existing idealized model in terms of line integrals which is accurate but not suitable for numerical approximation. The proposed model allows us to discretize it using higher accuracy approximation methods. In particular, we discretize the integral equation by using the collocation principle with piecewise linear polynomials. The discretization leads to new ill-conditioned discrete systems for the PET reconstruction, which are further regularized by a novel wavelet-based regularizer. The resulting non-smooth optimization problem is then solved by a preconditioned proximity fixed-point algorithm. Convergence of the algorithm is established for a range of parameters involved in the algorithm. The proposed integral equation model combined with the discretization, regularization, and optimization algorithm provides a new PET image reconstruction method. Numerical results reveal that the proposed model substantially outperforms the conventional discrete model in terms of the consistency to simulated projection data and reconstructed image quality. This indicates that the proposed integral equation model with appropriate discretization and regularizer can significantly reduce modeling errors and suppress noise, which leads to improved image quality and projection data estimation.