优化端点条件的平面二次均匀B样条插值曲线

在利用反求法构造B样条插值曲线时，往往需要选取端点条件。 因此，可对端点条件进行优化选取，使得构造的B样条插值曲线满足特定要求。提出了一种利用曲线内能极小选取平面二次均匀B样条插值曲线端点条件的算法。首先给出了二次均匀B样条插值曲线分控制顶点与首个控制顶点（即端点条件）的递推关系式；然后给出了利用曲线内能极小优化选取首个控制顶点的算法，证明了利用该算法构造的C¹连续二次均匀B样条插值曲线为保形插值，并通过数值算例证明了算法的有效性；最后，为便于实际应用，基于MATLAB平台设计了算法所对应的图形用户界面，用户通过简单的操作即可获得光顺的C¹连续二次均匀B样条保形插值曲线。     

Selective CO2-to-C2H4 Photoconversion Enabled by Oxygen-Mediated Triatomic Sites in Partially Oxidized Bimetallic Sulfide

Selective CO₂ photoreduction into C₂ fuels under mild conditions suffers from low product yield and poor selectivity owing to the kinetic challenge of C−C coupling. Here, triatomic sites are introduced into bimetallic sulfide to promote C−C coupling for selectively forming C₂ products. As an example, FeCoS₂ atomic layers with different oxidation degrees are first synthesized, demonstrated by X-ray photoelectron spectroscopy and X-ray absorption near edge spectroscopy spectra. Both experiment and theoretical calculation verify more charges aggregate around the introduced oxygen atom, which enables the original Co−Fe dual sites to turn into Co−O−Fe triatomic sites, thus promoting C−C coupling of double *COOH intermediates. Accordingly, the mildly oxidized FeCoS₂ atomic layers exhibit C₂H₄ formation rate of 20.1 μmol g⁻¹ h⁻¹, with the product selectivity and electron selectivity of 82.9 % and 96.7 %, outperforming most previously reported photocatalysts under similar conditions.     

反应温度对蒙脱石载银量及其缓释性能的影响

以钠基蒙脱石(Na-MMT)为载体,氧化银与氨水反应形成的银氨络合物[Ag(NH₃)₂OH]为前驱体,通过离子交换和三乙醇胺(TEA)还原两步法制备了载银蒙脱石(Ag-MMT)。 用佛尔哈德法测定了载银蒙脱石(Ag-MMT)的载银量,探讨了反应温度对MMT 载银量及其缓释性能的影响,并用FI-IR、XRD等技术手段对Na-MMT和Ag-MMT的结构进行了表征。 结果表明,在蒙脱石与Ag⁺的质量比为20:1、离子交换时间为1 h、反应温度50 ℃,然后再加入三乙醇胺和聚乙烯吡咯烷酮,50 ℃下反应2 h,MMT的载银量最大,银的利用率达到86.89%,释放时间最持久,并且MMT的层状结构没有被破坏。     

Singly Periodic Solutions of the Allen-Cahn Equation and the Toda Lattice

The Allen-Cahn equation ? Δu = u ? u ³ in ?² has family of trivial singly periodic solutions that come from the one dimensional periodic solutions of the problem ?u″ =u ? u ³. In this paper we construct a non-trivial family of singly periodic solutions to the Allen-Cahn equation. Our construction relies on the connection between this equation and the infinite Toda lattice. We show that for each one-soliton solution to the infinite Toda lattice we can find a singly periodic solution to the Allen-Cahn equation, such that its level set is close to the scaled one-soliton. The solutions we construct are analogues of the family of Riemann minimal surfaces in ?³.     

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本文用概率函数分析方法研究了乒乓球拍形状和尺寸对乒乓球迎击概率的影响．基于将球拍的外轮廓线视为一条等概率曲线，导出了满足最高迎击球概率的球拍外轮廓线的数学表达式，给出了相应的计算结果．计算结果表明，现有球拍平面形状和尺寸有待进一步改进和完善，减小打漏球的失误，使其具有最大的迎击球概率．     

Singular Limits of a Two-Dimensional Boundary Value Problem Arising in Corrosion Modelling

We consider the boundary value problem where Ω is a smooth and bounded domain in ℝ² and λ > 0. We prove that for any integer k ≧ 1 there exist at least two solutions u _λ with the property that the boundary flux satisfies up to subsequences λ → 0, where the ξ _j are points of ∂Ω ordered clockwise in j.