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.     

THE DEVELOPMENT OF NATIONAL ZHOU PEIYUAN COMPETITION ON MECHANICS

全国周培源大学生力学竞赛为《力学与实践》编委会发起并承办的一项大学生科技赛事,经过三十多年的发展,已经成功举办了12届,也成为展示高校力学教学水平的一个窗口。在《力学与实践》创刊40周之际,本文对全国周培源大学生力学竞赛的发展历程和组织模式进行了较为系统的回顾和梳理;对各届的组织规模和创新形式进行归纳与汇总;并通过案例说明力学竞赛对力学教学和人才培养所发挥的作用。     

Efficient immobilization of silver nanoparticles on metal substrates through various thiol molecules to utilize a gap mode in surface enhanced Raman scattering

To utilize a gap mode in surface enhanced Raman scattering, we elucidated the interaction between adsorbed species and Ag nanoparticles (AgNPs). Various thiol molecules such as normal alkanethiols, thiols with a phenyl, cyclohexane or naphthalene ring on Ag films immobilized AgNPs through van der Waals force, and electrostatic interaction. Immobilized AgNPs provided enormous Raman enhancement by a factor of 10⁷–10¹⁰ for thiol molecules at a nanogap, in consistent with that anticipated by finite difference time domain calculations. Only alkanethiols with a tert-methyl group and those with a carboxylic group did not immobilize any AgNPs probably owing to steric hindrance. A gap mode is relevant for a variety of metals even with large damping like Pt and Fe, indicating a crucial role of electric multipoles in AgNPs generated by a localized surface plasmon and induced mirror images in metal substrates for markedly enhanced electric field at a nanogap.     

Magnetic Micromotors for Multiple Motile Sperm Cells Capture,Transport, and Enzymatic Release

An integrated system combining a magnetically-driven micromotor and a synthetized protein-based hyaluronic acid (HA) microflake is presented for the in situ selection and transport of multiple motile sperm cells (ca. 50). The system appeals for targeted sperm delivery in the reproductive system to assist fertilization or to deliver drugs. The binding mechanism between the HA microflake and sperm relies on the interactions between HA and the corresponding sperm HA receptors. Once sperm are captured within the HA microflake, the assembly is trapped and transported by a magnetically-driven helical microcarrier. The trapping of the sperm-microflake occurs by a local vortex induced by the microcarrier during rotation-translation under a rotating magnetic field. After transport, the microflake is enzymatically hydrolyzed by local proteases, allowing sperm to escape and finally reach the target location. This cargo-delivery system represents a new concept to transport not only multiple motile sperm but also other actively moving biological cargoes.     

基于CDIO导向的微项目驱动交叉混合教学模式——以“日化用品制造技术”教学为例

分析了传统教学模式的优缺点,运用CDIO理念导向的工程教育模式构建了融合教学目标和教学内容的微项目,教师的“教”和学生的“学”与“做”交叉混合进行,形成了一种新的积极高效的教学模式,并在“日化用品制造技术”的教学中尝试开展了这种新的教学模式。实践表明在这种新的教学模式下,学生的学习积极性得以充分调动,学习效果有一定程度的提高,该教学模式有积极的现实意义。     

Infrared Spectral Assignment of Pyrimidine and Pyrazine in the CH Stretching Region by an Effective Spectroscopic Hamiltonian

Mid-Infrared spectra of pyrimidine (PM) and pyrazine (PZ) were recorded in the gas phase using a multi-pass long path gas cell. The IR band structure of these compounds above and below 3000 cm⁻¹ is very broad and contains many humps and shoulders. These humps and shoulders are due to various higher quantum excitation of low-frequency vibrational modes, which participate in Fermi resonance with the nearby CH stretch fundamentals and appears in this region. We constructed an Effective Spectroscopic Hamiltonian (ESH) in a mixed local mode (LM) normal mode (NM) basis to assign the various overtone and combination bands in the CH stretching region of these compounds. The CH stretching vibrations of both PZ and PM were treated as symmetrized anharmonic Morse oscillators in local coordinates and the in-plane deformations down to 1000 cm⁻¹ were treated as normal coordinates. The ESHs were diagonalized and the resulting eigenvalues were subsequently fitted in a given parameter space with the experimentally observed bands. The eigenvalues of the converged Hamiltonian are the anharmonic frequencies and the transition intensities were obtained by summing the squared eigenvector components. The overtone and combination transitions near 3000 cm⁻¹ of both PM and PZ were identified and assigned from the eigenvector coefficients of the ESH matrix. The wavefunctions of a pure CH stretch, overtone of the HCC in-plane bend and due to Type 1 Fermi coupling (resonance between a fundamental with an overtones of a low frequency mode, in this case resonance between the CH strech and the overtone of HCC in-plane bending modes) has been demonstrated pictorially.     

Characterization of complex,heterogeneous lipid A samples using HPLC‐MS/MS technique III. Positive‐ion mode tandem mass spectrometry to reveal phosphorylation and acylation patterns of lipid A

In this study, we report the detailed analysis of the fragmentation patterns of positively charged lipid A species based on their tandem mass spectra obtained under low‐energy collision‐induced dissociation conditions of an electrospray quadrupole time‐of‐flight mass spectrometer. The tandem mass spectrometry experiments were performed after the separation of the compounds with a reversed‐phase high performance liquid chromatography method. We found that both, phosphorylated and nonphosphorylated lipid A molecules can be readily ionized in the positive‐ion mode by adduct formation with triethylamine added to the eluent. The tandem mass spectra of the lipid A triethylammonium adduct ions showed several product ions corresponding to inter‐ring glycosidic cleavages of the sugar residues, as well as consecutive and competitive eliminations of fatty acids, phosphoric acid, and water following the neutral loss of triethylamine. Characteristic product ions provided direct information on the phosphorylation site(s), also when phosphorylation isomers (ie, containing either a C1 or a C4′ phosphate group) were simultaneously present in the sample. Continuous series of high‐abundance B‐type and low‐abundance Y‐type inter‐ring fragment ions were indicative of the fatty acyl distribution between the nonreducing and reducing ends of the lipid A backbone. The previously reported lipid A structures of Proteus morganii O34 and Escherichia coli O111 bacteria were used as standards. Although, the fragmentation pathways of the differently phosphorylated lipid A species significantly differed in the negative‐ion mode, they were very similar in the positive‐ion mode. The complementary use of positive‐ion and negative‐ion mode tandem mass spectrometry was found to be essential for the full structural characterization of the C1‐monophosphorylated lipid A species.     

Average Arrival Time: an Alternative Approach for Studying Fluorescent Behavior of Single Quantum Dots?

Due to photoluminescence intermittency of single colloidal quantum dots (QDs), the traditional exponential fluorescence lifetime analysis is not perfect to characterize QDs' fluorescent emission behavior. In this work we used the time-tagged time-resolved (TTTR) mode to record the fluorescent photons from single QDs. We showed that this method is compatible with the traditional lifetime analysis. In addition, by constructing the trajectory over time and the distribution of average arrival time (AAT) of the fluorescent photons, more details about the emission behavior of QDs were revealed.     

Continuous Selections for Continuous Set-Valued Mappings and Finite-Dimensional Sets

The paper is devoted to selection theorems for continuous set-valued mappings which are not necessarily convex-valued on finite-dimensional subsets of the domain. As a result, we get natural generalizations of the famous Kuratowski–Dugundji extension theorem. The technique, developed in the paper, applies to l.s.c. mappings with paracompact, or similar, domain as well. Also, it leads us to a new construction of set-valued continuous selections that involves dimension-type arguments.