Coordinating the Edge Defects of Bismuth with Sulfur for Enhanced CO2 Electroreduction to Formate

Bismuth-based materials have been recognized as promising catalysts for the electrocatalytic CO₂ reduction reaction (ECO₂RR). However, they show poor selectivity due to competing hydrogen evolution reaction (HER). In this study, we have developed an edge defect modulation strategy for Bi by coordinating the edge defects of bismuth (Bi) with sulfur, to promote ECO₂RR selectivity and inhibit the competing HER. The prepared catalysts demonstrate excellent product selectivity, with a high HCOO⁻ Faraday efficiency of ≈95 % and an HCOO⁻ partial current of ≈250 mA cm⁻² under alkaline electrolytes. Density function theory calculations reveal that sulfur tends to bind to the Bi edge defects, reducing the coordination-unsaturated Bi sites (*H adsorption sites), and regulating the charge states of neighboring Bi sites to improve *OCHO adsorption. This work deepens our understanding of ECO₂RR mechanism on bismuth-based catalysts, guiding for the design of advanced ECO₂RR catalysts.     

Dynamically Restructuring NixCryO Electrocatalyst for Stable Oxygen Evolution Reaction in Real Seawater

In the pursuit of long-term stability for oxygen evolution reaction (OER) in seawater, retaining the intrinsic catalytic activity is essential but has remained challenging. Herein, we developed a Ni_xCr_yO electrocatalyst that manifested exceptional OER stability in alkaline condition while improving the activity over time by dynamic self-restructuring. In 1 M KOH, Ni_xCr_yO required overpotentials of only 270 and 320 mV to achieve current densities of 100 and 500 mA cm⁻², respectively, with excellent long-term stability exceeding 475 h at 100 mA cm⁻² and 280 h at 500 mA cm⁻². The combination of electrochemical measurements and in situ studies revealed that leaching and redistribution of Cr during the prolonged electrolysis resulted in increased electrochemically active surface area. This eventually enhanced the catalyst porosity and improved OER activity. Ni_xCr_yO was further applied in real seawater from the Red Sea (without purification, 1 M KOH added), envisaging that the dynamically evolving porosity can offset the adverse active site-blocking effect posed by the seawater impurities. Remarkably, Ni_xCr_yO exhibited stable operation for 2000, 275 and 100 h in seawater at 10, 100 and 500 mA cm⁻², respectively. The proposed catalyst and the mechanistic insights represented a step towards realization of non-noble metal-based direct seawater splitting.     

Reconstruction of Sparse Polynomials via Quasi-Orthogonal Matching Pursuit Method

In this paper, we propose a Quasi-Orthogonal Matching Pursuit (QOMP) algorithm for constructing a sparse approximation of functions in terms of expansion by orthonormal polynomials. For the two kinds of sampled data, data with noises and without noises, we apply the mutual coherence of measurement matrix to establish the convergence of the QOMP algorithm which can reconstruct $s$-sparse Legendre polynomials, Chebyshev polynomials and trigonometric polynomials in $s$ step iterations. The results are also extended to general bounded orthogonal system including tensor product of these three univariate orthogonal polynomials. Finally, numerical experiments will be presented to verify the effectiveness of the QOMP method.     

An Inverse Problem in Periodic Diffractive Optics: Reconstruction of Lipschitz Grating Profiles

We consider the problem of recovering a two-dimensional periodic structure from scattered waves measured above the structure. Following an approach by Kirsch and Kress, this inverse problem is reformulated as a nonlinear optimization problem. We develop a theoretical basis for the reconstruction method in the case of an arbitrary Lipschitz grating profile. The convergence analysis is based on new perturbation and stability results for the forward problem.     

Reconstruction of n-dimensional convex bodies from surface tensors

In this paper, we derive uniqueness and stability results for surface tensors. Further, we develop two algorithms that reconstruct shape of n-dimensional convex bodies. One algorithm requires knowledge of a finite number of surface tensors, whereas the other algorithm is based on noisy measurements of a finite number of harmonic intrinsic volumes. The derived stability results ensure consistency of the two algorithms. Examples that illustrate the feasibility of the algorithms are presented.     

Refractive index imaging from radiative transfer equation-based reconstruction algorithm: Fundamentals

We present the first reconstruction algorithm for refractive index imaging, which is based on the radiative transfer equation (RTE). An objective function is iteratively minimized to find a solution to the problem of inversion of the refractive index field. The function describes the discrepancies of the emerging light measurements on the surface of the sample to be probed with predicted data from the corresponding numerical model. The unknown refractive index field is updated within each reconstruction iteration according to a search direction on the index distribution given by the adjoint model to the RTE. In this paper, emphasis is placed on the theoretical aspects. Preliminary tests are demonstrated on generic phantoms.     

基于改进的多轴差分吸收光谱层析技术的烟羽浓度峰重建

建立了被动多轴差分吸收光谱层析系统,实现烟羽气体的时空浓度分布测量,分别采用传统的同步迭代重建算法(SIRT)和改进的SIRT对测量数据进行了重建分析,克服了一些实际测试中不能获 取大量投影数据或投影分布不均匀、存在噪声的问题,精确地重建出大气痕量气体的二维空间分布．在不同的模型及评价指标下,通过数值模拟对两种重建算法的效果进行比较,改变改进的SIRT算法中的松弛因子,在5500次的迭代过程中,指标d从0.435降到了0.044,指标r从0.376降到了0.044,改进的SIRT算法具有更好的重建效果．外场重建试验中成功重建了大气痕量气体的二维空间．     

Manifold Reconstruction in Arbitrary Dimensions Using Witness Complexes

It is a well-established fact that the witness complex is closely related to the restricted Delaunay triangulation in low dimensions. Specifically, it has been proved that the witness complex coincides with the restricted Delaunay triangulation on curves, and is still a subset of it on surfaces, under mild sampling conditions. In this paper, we prove that these results do not extend to higher-dimensional manifolds, even under strong sampling conditions such as uniform point density. On the positive side, we show how the sets of witnesses and landmarks can be enriched, so that the nice relations that exist between restricted Delaunay triangulation and witness complex hold on higher-dimensional manifolds as well. We derive from our structural results an algorithm that reconstructs manifolds of any arbitrary dimension or co-dimension at different scales. The algorithm combines a farthest-point refinement scheme with a vertex pumping strategy. It is very simple conceptually, and it does not require the input point sample to be sparse. Its running time is bounded by c(d)n ², where n is the size of the input point cloud, and c(d) is a constant depending solely (yet exponentially) on the dimension d of the ambient space. Although this running time makes our reconstruction algorithm rather theoretical, recent work has shown that a variant of our approach can be made tractable in arbitrary dimensions, by building upon the results of this paper. This work was done while S.Y. Oudot was a post-doctoral fellow at Stanford University. His email there is no longer valid.     

Optimal cubature formulas on compact homogeneous manifolds

We find lower bounds for the rate of convergence of optimal cubature formulas on sets of differentiable functions on compact homogeneous manifolds of rank I or two-point homogeneous spaces. It is shown that these lower bounds are sharp in the power scale in the case of S², the unit sphere in R³.