改进的PNC方法及其在非线性偏微分方程多解问题中的应用

2017年，李昭祥等提出了一种偏牛顿-校正法（Partial Newton-Correction Method，简记为PNC方法），并利用它成功地计算出了三类非线性偏微分方程的多重不稳定解.本文在PNC方法的基础上，提出并发展了一种改进的PNC方法.首先，利用Nehari流形$\mathcal{N}$与零平凡解的可分离性，建立并证明了$\mathcal{N}$的某特殊子流形$\mathcal{M}$上的全局分离定理及其推广（即局部分离定理）.全局分离定理只跟非线性偏微分算子或相应的非线性泛函本身有关，而与具体的计算方法无关.对一些典型的非线性偏微分方程多解问题（比如，Henon方程问题），该全局分离定理的分离条件，经验证是成立的.另一个方面，通过修改或补充原辅助变换的定义，去掉了原辅助变换的奇异性；接着建立并证明了某些非线性偏微分方程问题的新未知解与该非线性偏微分算子零核空间的密切关系；在证明中，去掉了在原奇异变换下所需的标准收敛（standard convergence）假设.最后，计算实例与数值结果验证了改进的PNC方法的可行性和有效性；同时表明子流形$\mathcal{M}$与已知解的可分离性是PNC方法和本文新方法能成功找到多解的关键.     

基于压缩全息和空分复用的多彩色图像加密

针对现有光学加密方法进行彩色图像加密时加密容量低、解密图像失真度高等问题,提出一种基于压缩全息和空分复用的多彩色图像加密方法.在光学加密阶段,结合改进的Mach-Zehnder干涉仪与空分复用技术,通过不同的随机相位掩膜对多幅彩色图像进行同时加密,仅需单次曝光即可得到由多幅彩色图像加密的全息图.在解密过程中,由于记录全息图的过程可建模为压缩感知过程,使用两步迭代收缩/阈值算法即可求解.实验结果表明,提出的加密系统加密容量大,解密重建图像质量高,结合压缩感知理论,有效地消除了同轴全息中平方场项对解密重建性能的影响,解密图像平均峰值信噪比仅下降约2～5dB;密钥安全性高,随机相位掩膜与传播距离均起到密钥的作用,在随机相位掩膜错误或传播距离仅偏移0.25%时,便无法解密出原始彩色图像;且对噪声与遮挡性攻击具有良好的鲁棒性,解密重建性能随噪声增大下降趋势缓慢,加密全息图80%信息受到遮挡性攻击时,仍可取得良好的解密重建结果.     

Adsorption Site Regulation to Guide Atomic Design of Ni–Ga Catalysts for Acetylene Semi‐Hydrogenation

Atomic regulation of metal catalysts has emerged as an intriguing yet challenging strategy to boost product selectivity. Here, we report a density functional theory‐guided atomic design strategy for the fabrication of a NiGa intermetallic catalyst with completely isolated Ni sites to optimize acetylene semi‐hydrogenation processes. Such Ni sites show not only preferential acetylene π‐adsorption, but also enhanced ethylene desorption. The characteristics of the Ni sites are confirmed by multiple characterization techniques, including aberration‐corrected high‐resolution scanning transmission electron microscopy and X‐ray absorption spectrometry measurements. The superior performance is also confirmed experimentally against a Ni₅Ga₃ intermetallic catalyst with partially isolated Ni sites and against a Ni catalyst with multi‐atomic ensemble Ni sites. Accordingly, the NiGa intermetallic catalyst with the completely isolated Ni sites shows significantly enhanced selectivity to ethylene and suppressed coke formation.     

Pseudo-2D Layered Organic-Inorganic Manganese Bromide with a Near-Unity Photoluminescence Quantum Yield for White Light-Emitting Diode and X-Ray Scintillator

Eco-friendly lead-free organic–inorganic manganese halides (OIMHs) have attracted considerable attention in various optoelectronic applications because of their superior optical properties and flexible solution processibility. Herein, we report a novel pseudo-2D layered OIMH (MTP)₂MnBr₄ (MTP: methyltriphenylphosphonium), which exhibits intense green emission under UV/blue or X-ray excitation, with a near-unity photoluminescence quantum yield, high resistance to thermal quenching (I_{150 °C}=84.1 %) and good photochemical stability. These features enable (MTP)₂MnBr₄ as an efficient green phosphor for blue-converted white light-emitting diodes, demonstrating a commercial-level luminous efficiency of 101 lm W⁻¹ and a wide color gamut of 116 % NTSC. Moreover, these (MTP)₂MnBr₄ crystals showcase outstanding X-ray scintillation properties, delivering a light yield of 67000 photon MeV⁻¹, a detection limit of 82.4 nGy s⁻¹, and a competitive spatial resolution of 6.2 lp mm⁻¹ for X-ray imaging. This work presents a new avenue for the exploration of eco-friendly luminescent OIMHs towards multifunctional light-emitting applications.     

Infection Microenvironment-Sensitive Photothermal Nanotherapeutic Platform to Inhibit Methicillin-Resistant Staphylococcus aureus Infection

Methicillin-resistant Staphylococcus aureus (MRSA) can induce multiple inflammations. The biofilm formed by MRSA is resistant to a variety of antibiotics and is extremely difficult to cure, which seriously threatens human health. Herein, a nanoparticle encapsulating berberine with polypyrrole core and pH-sensitive shell to provide chemo-photothermal dual therapy for MRSA infection is reported. By integrating photothermal agent polypyrrole, berberine, acid-degradable crosslinker, and acid-induced charge reversal polymer, the nanoparticle exhibited highly efficient MRSA infection treatment. In normal uninfected areas and bloodstream, nanoparticles showed negatively charged, demonstrating high biocompatibility and excellent hemocompatibility. However, once arriving at the MRSA infection site, the nanoparticle can penetrate and accumulate in the biofilm within 2 h. Simultaneously, berberine can be released into biofilm rapidly. Under the combined effect of photothermal response and berberine inhibition, 88.7% of the biofilm is removed at 1000 µg mL⁻¹. Moreover, the nanoparticles have an excellent inhibitory effect on biofilm formation, the biofilm inhibition capacity can reach up to 90.3%. Taken together, this pH-tunable nanoparticle can be employed as a new generation treatment strategy to fight against the fast-growing MRSA infection.     

A Convenient Preparation of Fluorinating Reagent F‐TEDA Bearing Bisphenylsulfonylimide Counterion and Its Fluorination to Oxindoles

The direct preparation of a kind of fluorinating reagent 1 [F‐TEDA‐N(SO₂Ph)₂] was realized in high yield via the complexation of N‐fluorobenzenesulfonimide (NFSI) with 1‐(chloromethyl)‐1,4‐diazabicyclo[2.2.2]octan‐1‐ium N′,N′‐bis‐(benzenesulfonylimide) salt. In its fluorination to oxindoles, the fluorinating products 6 were afforded in moderate to high yields.     

Guanidinoamidized linear polyethyleneimine for gene delivery

Guanidine was introduced to low molecular weight linear polyethyleneimine(LPEI) via amide groups, to explore the effect of both guanidine degree and pendant chain length on its transfection behavior. The resulting guanidinoamidized LPEIs(GLPEIs) could dramatically reduce LPEI's toxicity, enhance its DNA-packaging capability, cellular uptake and therefore transfection efficiency. These polyplexes were taken up very efficiently via caveolae-mediated endocytosis and their transfection efficiencies in ovarian cancer cells were significantly improved compared to native LPEI10 k polyplexes. Among these GLPEIs, LPEI-C3-G100 showed higher DNA affinity even than LPEI25 k and the highest transfection efficiency, probably due to the optimization of polymer chain flexibility. Of notice, LPEI-C3-G100 polyplexes could more effectively accumulate into cytoplasm than LPEI25 k, although the transfection efficiency of LPEI-C3-G100 polyplexes was not superior to that of LPEI25 k polyplexes, which would be probably attributed to the more efficient release of LPEI25 k polyplexes than LPEI-C3-G100 polyplexes in the cytoplasm.     

BC/CoNi2S4@PPy柔性复合电极材料的制备及电化学性能

本文采用溶剂热、原位聚合和真空抽滤相结合的方法制备了用于超级电容器的细菌纤维素/镍钴硫化物/聚吡咯(BC/CoNi₂S₄@PPy)柔性电极材料,通过X射线衍射、场发射扫描电镜、红外光谱、氮气吸脱附、拉伸强度和接触角表征了材料的形貌结构、组成、机械性能和亲水性,并采用循环伏安法和恒电流充放电测试了复合材料的电化学性能。结果表明,表面含氧官能团丰富的BC纤维网络结构对氧化还原活性物质CoNi₂S₄的生长和导电聚合物PPy的分布具有引导作用,CoNi₂S₄均匀分布在BC网络中,且PPy均匀包覆在BC纤维和CoNi₂S₄纳米球表面构成具有丰富孔隙结构的三维导电网络,使得该复合材料具有较好的机械性(抗拉强度达28.0±0.1 MPa)、亲水性(对6 mol·L^-1 KOH的瞬间接触角为43.6°)及良好的导电性。该电极材料在1 A·g^-1下比电容高达2670 F·g^-1,充放电循环10000次后比电容的保持率为82.73%,且经1000次反复弯曲后电化学性能保持不变。此外,将其与活性炭组成的非对称超级电容器,在1 A·g^-1下比电容为1428 F·g^-1,最高能量密度和功率密度分别达49.8 Wh·kg^-1和741.8 W·kg^-1。