On a problem of Hornik

In 1991,Hornik proved that the collection of single hidden layer feedforward neural networks(SLFNs)with continuous,bounded,and non-constant activation functionσis dense in C(K)where K is a compact set in R~s(see Neural Networks,4(2),251-257(1991)).Meanwhile,he pointed out"Whether or not the continuity assumption can entirely be dropped is still an open quite challenging problem".This paper replies in the affirmative to the problem and proves that for bounded and continuous almost everywhere(a.e.)activation functionσon R,the collection of SLFNs is dense in C(K)if and only ifσis un-constant a.e..     

Incommensurate Phase in Λ-cobalt (III) Sepulchrate Trinitrate Governed by Highly Competitive N−H⋅⋅⋅O and C−H⋅⋅⋅O Hydrogen Bond Networks**

Phase transitions in molecular crystals are often determined by intermolecular interactions. The cage complex of [Co(C₁₂H₃₀N₈)]³⁺ ⋅ 3 NO₃⁻ is reported to undergo a disorder-order phase transition at T_c1 ≈133 K upon cooling. Temperature-dependent neutron and synchrotron diffraction experiments revealed satellite reflections in addition to main reflections in the diffraction patterns below T_c1. The modulation wave vector varies as function of temperature and locks in at T_c3≈98 K. Here, we demonstrate that the crystal symmetry lowers from hexagonal to monoclinic in the incommensurately modulated phases in T_c1<T<T_c3. Distinctive levels of competitions: trade-off between longer N−H⋅⋅⋅O and shorter C−H⋅⋅⋅O hydrogen bonds; steric constraints to dense C−H⋅⋅⋅O bonds give rise to pronounced modulation of the basic structure. Severely frustrated crystal packing in the incommensurate phase is precursor to optimal balance of intermolecular interactions in the lock-in phase.     

Continuous Porous Aromatic Framework Membranes with Modifiable Sites for Optimized Gas Separation

Continuous microporous membranes are widely studied for gas separation, due to their low energy premium and strong molecular specificity. Porous aromatic frameworks (PAFs) with their exceptional stability and structural flexibility are suited to a wide range of separations. Main-stream PAF-based membranes are usually prepared with polymeric matrices, but their discrete entities and boundary defects weaken their selectivity and permeability. The synthesis of continuous PAF membranes is still a major challenge because PAFs are insoluble. Herein, we successfully synthesized a continuous PAF membrane for gas separation. Both pore size and chemistry of the PAF membrane were modified by ion-exchange, resulting in good selectivity and permeance for the gas mixtures H₂/N₂ and CO₂/N₂. The membrane with Br^? as a counter ion in the framework exhibited a H₂/N₂ selectivity of 72.7 with a H₂ permeance of 51844 gas permeation units (GPU). When the counter ions were replaced by BF₄^?, the membrane showed a CO₂ permeance of 23058 GPU, and an optimized CO₂/N₂ selectivity of 60.0. Our results show that continuous PAF membranes with modifiable pores are promising for various gas separation situations.     

Enhanced Static Modulated Fourier Transform Spectrometer for Fast Approximation in Field Application

We discuss the data sampling frequency, the spectral resolution, and the limit for non-aliasing in the static modulated Fourier transform spectrometer based on a modified Sagnac interferometer. The measurement was performed in a very short 4 ms, which is applicable for real time field operation. The improved spectrometer characteristics were used to investigate the spectral properties of an InGaAs light emitting diode. In addition, The measured spectral peak was shifted from 6420 cm⁻¹ to 6365 cm⁻¹, as the temperature increased from 25 °C to 40 °C, when the operating current is fixed to be 0.55 A. As the applied current increased from 0.30 A to 0.55 A at room temperature, the spectral width was broadened from 316 cm⁻¹ to 384 cm⁻¹. Compared to the conventional Fourier transform spectrometer, the measured spectral width by the static modulated Fourier transform spectrometer showed a deviation less than 10%, and the spectral peak shift according to the temperature rise showed a difference within 2%.     

How to Predict Excited State Geometry by Using Empirical Parameters Obtained from Franck-Condon Analysis of Optical Spectrum

Excited state geometries of molecules can be calculated with highly reliable wavefunction schemes. Most of such schemes, however, are applicable to small molecules and can hardly be viewed as error-free for excited state geometries. In this study, a theoretical approach is presented in which the excited state geometries of molecules can be predicted by using vibrationally resolved experimental absorption spectrum in combination with the theoretical modelling of vibrational pattern based on Franck-Condon approximation. Huang-Rhys factors have been empirically determined and used as input for revealing the structural changes occurring between the ground and the excited state geometries upon photoexcitation. Naphthalene molecule has been chosen as a test case to show the robustness of the proposed theoretical approach. Predicted 1B_2u excited state geometry of the naphthalene has similar but slightly different bond length alternation pattern when compared with the geometries calculated with CIS, B3LYP, and CC2 methods. Excited state geometries of perylene and pyrene molecules are also determined with the presented theoretical approach. This powerful method can be applied to other molecules and specifically to relatively large molecules rather easily as long as vibrationally resolved experimental spectra are available to use.     

Allosteric Modulation of the CB1 Cannabinoid Receptor by Cannabidiol—A Molecular Modeling Study of the N-Terminal Domain and the Allosteric-Orthosteric Coupling

The CB₁ cannabinoid receptor (CB₁R) contains one of the longest N termini among class A G protein-coupled receptors. Mutagenesis studies suggest that the allosteric binding site of cannabidiol (CBD) involves residues from the N terminal domain. In order to study the allosteric binding of CBD to CB₁R we modeled the whole N-terminus of this receptor using the replica exchange molecular dynamics with solute tempering (REST2) approach. Then, the obtained structures of CB₁R with the N terminus were used for ligand docking. A natural cannabinoid receptor agonist, Δ⁹-THC, was docked to the orthosteric site and a negative allosteric modulator, CBD, to the allosteric site positioned between extracellular ends of helices TM1 and TM2. The molecular dynamics simulations were then performed for CB₁R with ligands: (i) CBD together with THC, and (ii) THC-only. Analyses of the differences in the residue-residue interaction patterns between those two cases allowed us to elucidate the allosteric network responsible for the modulation of the CB₁R by CBD. In addition, we identified the changes in the orthosteric binding mode of Δ⁹-THC, as well as the changes in its binding energy, caused by the CBD allosteric binding. We have also found that the presence of a complete N-terminal domain is essential for a stable binding of CBD in the allosteric site of CB₁R as well as for the allosteric-orthosteric coupling mechanism.     

Recent advances in BiOBr-based photocatalysts for environmental remediation

The efficient utilization of solar energy through photocatalysis is ideal for solving environmental issues and the development sustainable future. BiOBr-based semiconductors possess unique narrowed bandgaps and layered structures, thereby widely studied as photocatalysts for environmental remediation. However, a little has been focused on the comprehensive reviewing of BiOBr despite its extensive and promising applications. In this review, the state-of-the-art developments of BiOBr-based photocatalysts for environmental remediation are summarized. Particular focus is paid to the synthetic strategies for the control of the resulting morphologies, as well as efficient modification strategies for improving the photocatalytic activities. These include boosting the bulk phase by charge separation, enhancing the spatial charge separation, and engineering the surface states. The environmental uses of BiOBr-based photocatalysts are also reviewed in terms of purification of pollutants and CO₂ reduction. Finally, future challenges and opportunities of BiOBr-based materials in photocatalysis are discussed. Overall, this review provides a good basis for future exploration of high-efficiency solar-driven photocatalysts for environmental sustainability.     

调制激光场中Rydberg原子的电磁感应透明

本文主要研究了调制探测激光场中铯Rydberg 原子阶梯型三能级系统的电磁感应透明(EIT) 效应. 铯原子基态6S_1/2, 第一激发态6P_3/2 和Rydberg 态形成阶梯型三能级系统, 探测光作用于6S_1/2 (F = 4)→6P_3/2(F' = 5) 的跃迁, 耦合光在Rydberg 跃迁线6P_3/2→49S_1/2 附近扫描, 形成Rydberg 原子EIT. 当对探测光频率施加一个几kHz 的调制时, 调制解调后的EIT 信号分裂为两个峰, 双峰间距与调制频率无关,而与调制幅度导致的失谐量大小(频率调制幅度) 成正比, 双峰间隔的一半等于探测光频率调制幅度的λ_p/λ_c = 1.67 倍. 实验结果与理论计算相一致. 本文的研究结果可应用于激光线型和频率抖动的实时监测.     

光谱偏振调制器的高精度装调方法

为了提高光谱偏振调制器的探测精度,提出了光谱偏振调制器的高精度装调方法。首先,分析了光谱偏振调制器的调制原理,提出了采用三片多级相位延迟器加线偏振器的装调方案;然后,建立了调制器装调的数理模型,设计了校准多级相位延迟器的厚度;最后,对成像过程进行了计算机仿真实验验证,并模拟了成像系统的装调过程。结果表明:利用该方法能够灵敏检测偏振器件间的微小相对旋转角度误差,可实现调制器的高精度装调,在输入本文设定的校准光谱条件下,绝对精度可达0.2°。该方法保留了传统光谱调制器充分利用通道带宽的优势,保证了复原光谱的分辨率,为强度调制型光谱偏振成像系统的精密装调提供了一定的理论参考。     

二维金属有机框架材料的合成及电催化应用

二维金属有机框架材料(MOFs)由于具备高比表面积、 多孔性以及丰富的活性位点等优异特性而受到广泛关注, 并且在电催化领域展现出巨大的应用潜力. 研究者们已在二维MOFs的可控制备与电催化性能调控方面取得许多突破性进展, 显示出相关研究对开发高性能电催化剂的关键作用. 本文总结了二维MOFs的自上而下和自下而上合成策略以及二维MOFs衍生物的典型合成方法, 概述了二维MOFs在各尺度下的电催化性能调控策略, 并介绍了各种合成方法和调控策略在电催化中的应用. 最后讨论了该领域面临的挑战, 并对未来的发展方向进行了展望.