Duality, Vector Spaces and Absolutely Convex Modules

It is well-known (see Semadeni, Queen Pap. Pure Appl. Math., 33:1–98, 1973 and Pumplün and Röhrl, Commun. Algebra, 12(8):953–1019, 1984, 1985) that the embedding of vector spaces into the category of absolutely convex modules is reflective. As we will show, under a separatedness condition on these modules it is at the same time coreflective. This is a peculiar situation, see Kannan, Math. Ann., 195:168–174, (1972) and Hu $\textrm {\u{s}}It is well-known (see Semadeni, Queen Pap. Pure Appl. Math., 33:1–98, 1973 and Pumplün and R?hrl, Commun. Algebra, 12(8):953–1019, 1984, 1985) that the embedding of vector spaces into the category of absolutely convex modules is reflective. As we will show, under a separatedness condition on these modules it is at the same time coreflective. This is a peculiar situation, see Kannan, Math. Ann., 195:168–174, (1972) and Huek, Reflexive and coreflexive subcategories of unif and top, Seminar Uniform Spaces, Prague, 113–126, (1973), but we do find it also in the embedding (Lowen, Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad. Oxford Mathematical Monographs, Oxford University Press, London, UK, 1997) and, by extension, in the embedding (see Lowen and Verwulgen, Houst. J. Math, 30(4):1127–1142, 2004, and Sioen and Verwulgen, Appl. Gen. Topol., 4(2):263–279, 2003. We demonstrate that, in this setting, by duality arguments, absolutely convex modules are indeed the numerical counterpart of vector spaces. All these, at first sight unrelated facts, are comprised in the commutative scheme below with natural dualisation functors and their left adjoints.      

带非线性源项的Riesz回火分数阶扩散方程的预估校正方法

本文针对带非线性源项的Riesz回火分数阶扩散方程,利用预估校正方法离散时间偏导数,并用修正的二阶Lubich回火差分算子逼近Riesz空间回火的分数阶偏导数,构造出一类新的数值格式.给出了数值格式在一定条件下的稳定性与收敛性分析,且该格式的时间与空间收敛阶均为二阶.数值试验表明数值方法是有效的.     

Simulation of the interaction of light with 3-D metallic nanostructures using a proper orthogonal decomposition-Galerkin reduced-order discontinuous Galerkin time-domain method

In this artice, we report on a reduced-order model (ROM) based on the proper orthogonal decomposition (POD) technique for the system of 3-D time-domain Maxwell's equations coupled to a Drude dispersion model, which is employed to describe the interaction of light with nanometer scale metallic structures. By using the singular value decomposition (SVD) method, the POD basis vectors are extracted offline from the snapshots produced by a high order discontinuous Galerkin time-domain (DGTD) solver. With a Galerkin projection and a second order leap-frog (LF₂) time discretization, a discrete ROM is constructed. The stability condition of the ROM is then analyzed. In particular, when the boundary is a perfect electric conductor condition, the global energy of the ROM is bounded, which is consistent with the characteristics of global energy in the DGTD method. It is shown that the ROM based on Galerkin projection can maintain the stability characteristics of the original high dimensional model. Numerical experiments are presented to verify the accuracy, demonstrate the capabilities of the POD-based ROM and assess its efficiency for 3-D nanophotonic problems.     

Highly Strong Interaction between Fe/Fe3C Nanoparticles and N-Doped Carbon toward Enhanced Oxygen Reduction Reaction Performance

Transition metal compounds anchored on N-doped carbon (NC) show intrinsic activity and stability for oxygen reduction reaction (ORR). However, the interaction between the transition metal compounds and NC still needs to be strengthened for electron transfer at the compounds/carbon interface. Herein, Fe/Fe₃C hybrid nanoparticles encapsulated into N-doped carbon (Fe@NC) are used as high-performance ORR catalysts. Benefiting from the strong interaction at Fe/Fe₃C nanoparticles/NC interface, the electrons can transfer from Fe/Fe₃C hybrid nanoparticles to NC, redistributing the electron density of active sites and promoting the ORR process. The as-synthesized Fe@NC exhibits outstanding ORR catalytic activity with an onset potential of 1.01 V and a half-wave potential of 0.92 V in alkaline media. It also shows prominent cycling stability and tolerance to methanol crossover, superior to Pt/C catalyst. The theoretical analysis reveals that the Fe nanoparticles have regulated the electron distributions at the heterojunction interface. The Gibbs free energy diagrams for ORR illustrate that the rate-determining step is the conversion of OH* to OH⁻. In situ Raman spectra give evidence of O-containing intermediates to prove the ORR process.     

Efficient Synthesis of Submicrometer-Sized Active Pharmaceuticals by Laser Fragmentation in a Liquid-Jet Passage Reactor with Minimum Degradation

One challenge in the development of new drug formulations is overcoming their low solubility in relevant aqueous media. Reducing the particle size of drug powders to a few hundred nanometers is a well-known method that leads to an increase in solubility due to an elevated total surface area. However, state-of-the-art comminution techniques like cryo-milling suffer from degradation and contamination of the drugs, particularly when sub-micrometer diameters are aspired that require long processing times. In this work, picosecond-pulsed laser fragmentation in liquids (LFL) of dispersed drug particles in a liquid-jet passage reactor is used as a wear-free comminution technique using the hydrophobic oral model drugs naproxen, prednisolone, ketoconazole, and megestrol acetate. Particle size and morphology of the drug particles are characterized using scanning electron microscopy (SEM) and changes in particle size distributions upon irradiation are quantified using an analytical centrifuge. The findings highlight the superior fragmentation efficiency of the liquid-jet passage reactor setup, with a 100 times higher fraction of submicrometer particles (SMP) of the drugs compared to the batch control, which enhances solubility and goes along with minimal chemical degradation (<1%), determined by attenuated total reflection-Fourier transform infrared spectroscopy (ATR-FTIR), high-performance liquid chromatography (HPLC), and X-ray diffraction (XRD). Moreover, the underlying predominantly photo-mechanically induced laser fragmentation mechanisms of organic microparticles (MP) are discussed.     

Effect of plasma-activated water and buffer solution combined with ultrasound on fungicide degradation and quality of cherry tomato during storage

The purpose of this study was to examine plasma-activated buffer solution (PABS) and plasma-activated water (PAW) combined with ultrasonication (U) treatment on the reduction of chlorothalonil fungicide and the quality of tomato fruits during storage. To obtain PAW and PABS, an atmospheric air plasma jet was used to treat buffer solution and deionized water at different treatment times (5 and 10 min). For combined treatments, fruits were submerged in PAW and PABS, then sonicated for 15 min, and individual treatment without sonication. As per the results, the maximum chlorothalonil reduction of 89.29% was detected in PAW-U₁₀, followed by 85.43% in PABS. At the end of the storage period, the maximum reduction of 97.25% was recorded in PAW-U₁₀, followed by 93.14% in PABS-U₁₀. PAW, PABS, and both combined with ultrasound did not significantly affect the overall tomato fruit quality in the storage period. Our results revealed that PAW combined with sonication had a significant impact on post-harvest agrochemical degradation and retention of tomato quality than PABS. Conclusively, the integrated hurdle technologies effectively reduce agrochemical residues, which helps to lower health hazards and foodborne illnesses.     

Insights into the nature of X(3872) through B meson decays

We study the \begin{document}$ B_{c,u,d}\to X(3872)P $\end{document} decays in the perturbative QCD (PQCD) approach, involving the puzzling resonance \begin{document}$ X(3872) $\end{document}, where P represents a light pseudoscalar meson (K or π). Assuming \begin{document}$ X(3872) $\end{document} to be a \begin{document}$ 1^{++} $\end{document} charmonium state, we obtain the following results. (a) The branching ratios of the \begin{document}$ B^+_c\to X(3872)\pi^+ $\end{document} and \begin{document}$ B^+_c\to X(3872) K^+ $\end{document} decays are consistent with the results predicted by the covariant light-front approach within errors; however, they are larger than those given by the generalized factorization approach. (b) The branching ratio of the \begin{document}$ B^+\to X(3872)K^+ $\end{document} decay is predicted as \begin{document}$ (3.8^{+1.1}_{-1.0})\times10^{-4} $\end{document}, which is smaller than the previous PQCD calculation result but still slightly larger than the upper limits set by Belle and BaBar. Hence, we suggest that the\begin{document}$ B^{0,+}\to X(3872)K^{0,+} $\end{document} decays should be precisely measured by the LHCb and Belle II experiments to help probe the inner structure of \begin{document}$ X(3872) $\end{document}. (c) Compared with the \begin{document}$ B_{u,d}\to X(3872)K $\end{document}decays, the \begin{document}$ B_{u,d}\to X(3872)\pi $\end{document} decays have significantly smaller branching ratios, which drop to values as low as \begin{document}$ 10^{-6} $\end{document}. (d) The direct CP violations of these considered decays are small (\begin{document}$ 10^{-3}\sim 10^{-2} $\end{document}) because the penguin contributions are loop suppressed compared to the tree contributions. The mixing-induced CP violation of the \begin{document}$ B\to X(3872)K^0_S $\end{document} decay is highly consistent with the current world average value \begin{document}$ \sin2\beta=(69.9\pm1.7)$\end{document}%. Experimentally testing the results for the branching ratios and CP violations, including the implicit \begin{document}$S U(3)$\end{document} and isospin symmetries of these decays, helps probe the nature of \begin{document}$ X(3872) $\end{document}.     

An ultra-wideband coding polarizer for beam control and RCS reduction

Pancharatnam−Berry (PB) phase metasurface, as a special class of gradient metasurfaces, has been paid much attention owing to the robust performance for phase control of circularly polarized waves. Herein, we present an element-based polarizer for the first step, which enables the incident electromagnetic waves into the cross-polarized waves with the relative bandwidth of 71%, and the polarization conversion ratio exceeds 90% at 6.9−14.5 GHz. Then an eight-elements coding polarizer based on the PB phase is presented for the applications on beam control and radar cross section reduction. The simulated values indicate that the reduction of radar cross section is more than 10 dB at 6−16 GHz. Our work reveals the availability of manipulating the waves, beamforming in communication systems and electromagnetic stealth, and so on.     

回转体表面条纹沟槽减阻水洞实验研究

本文在条纹沟槽表面减阻理论分析的基础上,对条纹沟槽表面回转体进行了大量的水洞实验研究。实验模型表面条纹沟槽采用直接加工方法,头部线型为双参数平方根圆头曲线,尾部线型为双参数尖尾曲线。实验结果分析表明,与相同形状、尺寸的光滑表面回转体相比,条纹沟槽表面回转体在一定速度范围内存在很好的减阻效果,最大减阻量超过6%,且在小攻角范围内减阻量基本稳定,对回转体升力特性也没有影响。对比不同尺寸条纹沟槽的减阻效果发现,降阻量不但随条纹沟槽宽度S变化,而且随来流速度U∞变化,即与无因次沟槽宽度S (文中近似取S =S.LRe2Ckx,其中k为总阻力Cx的修正因子)存在着一定的关系。对于V型条纹沟槽具有减阻效果的S 的范围在10到60之间。本文研究证明,条纹沟槽表面减阻技术在水下航行器设计领域有着很好的应用前景,同时文中所取得的研究成果对该技术的应用具有一定的促进作用。     

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 在条纹沟槽表面减阻的研究发展及其优点的基础上 对条纹沟槽表面减阻进行水洞实验,研究在航行器外表面加工条纹沟槽所具有的阻 力特性. 通过对光体、0.1mmV型条纹沟槽表面和0.2mmV型条纹沟槽表面3 种不同模型在零攻角、不同水流速度下进行阻力测量, 测得条纹沟槽表面减阻特 性曲线. 从特性曲线中可以看出减阻效果约为8.3%. 实验的结果表明, 条纹沟槽 表面能明显降低水下航行器的阻力.