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.     

基于视觉辐条图案识别方法的蓝宝石引晶机制研究

工业生产蓝宝石晶体过程中,引晶步骤有着至关重要的地位。引晶必须在温度梯度较小,温度分布趋于稳定的条件下进行。目前,工业生产蓝宝石主要依靠人工经验操控籽晶杆实现引晶操作,但是人工引晶操作的准确性不高会导致成品品质不佳、资源浪费。为此,本文提出一种基于蓝宝石视觉辐条图案识别方法来检测蓝宝石熔体状态自由液面状态,从而实现一种高效率引晶的机制。此方法利用经典骨架化算法细化辐条图案,Harris算子实现特征信息的提取,提取的特征信息放入运动轨迹模型中判断熔体稳定性,分析液面温度分布稳定性从而实现引晶。结果表明,此算法具有有效性,蓝宝石晶体引晶效率大大提高,生产出的成品良率也有提升,可有效指导蓝宝石的工业生产。     

A survey on book-embedding of planar graphs

The book-embedding problem arises in several area, such as very large scale integration (VLSI) design and routing multilayer printed circuit boards (PCBs). It can be used into various practical application fields. A book embedding of a graph G is an embedding of its vertices along the spine of a book, and an embedding of its edges to the pages such that edges embedded on the same page do not intersect. The minimum number of pages in which a graph G can be embedded is called the pagenumber or book-thickness of the graph G. It is an important measure of the quality for book-embedding. It is NP-hard to research the pagenumber of book-embedding for a graph G. This paper summarizes the studies on the book-embedding of planar graphs in recent years.     

Dynamic modeling and analysis of hybrid driven multi-link press mechanism considering non-uniform wear clearance of revolute joints

Meccanica - The multi-link press mechanism is developing in the direction of high speed and high precision. However, the non-uniform wear of joint clearance seriously affects the output motion...     

Asymptotics of Smoothed Wasserstein Distances

Potential Analysis - We investigate contraction of the Wasserstein distances on $\mathbb {R}^{d}$ under Gaussian smoothing. It is well known that the heat semigroup is exponentially contractive...     

Semi-Quantum Bi-Signature Scheme Based on W States

International Journal of Theoretical Physics - A semi-quantum bi-signature scheme based on W states is designed, in which two signers sign the same message. The unconditional security of the new...     

The Special “Morse Code” between Solvent Polarity and Morphology Flexibility in a POSS–Dendrimer Supramolecular System

An amazing phenomenon of the relative magnitude of modulus of two liquid-crystal (LC) gels is found inverted under/above their phase transition temperature T_LC-iso, which is further proved to be caused by their diverse morphology flexibility. By testing the polarity of two LCs, gelator POSS-G1-Boc (POSS=polyhedral oligomeric silsesquioxane) was discovered to self-assemble into more flexible structures in a relatively low polar LC, whereas more rigid ones are formed in higher polar LC. Hence, a fitting function to connect morphology flexibility with solvent polarity was established, which can even be generalized to a number of common solvents. Experimental observations and coarse-grained molecular dynamics simulations revealed that solvent polarity mirrors a “Morse code”, with each “code” corresponding to a specific morphology flexibility.     

Metal–Organic Framework (MOF)-Derived Carbon-Mediated Interfacial Reaction for the Synthesis of CeO2−MnO2 Catalysts

CeO₂-based catalysts are widely studied in catalysis fields. Developing one novel synthetic approach to increase the intimate contact between CeO₂ and secondary species is of particular importance for enhancing catalytic activities. Herein, an interfacial reaction between metal–organic framework (MOF)-derived carbon and KMnO₄ to synthesize CeO₂−MnO₂, in which carbon is derived from the pyrolysis of Ce-MOFs under an inert atmosphere, is described. The MOF-derived carbon is found to restrain the growth of CeO₂ crystallites under a high calcination temperature and, more importantly, intimate contact within CeO₂/C is conveyed to CeO₂/MnO₂ after the interfacial reaction; this is responsible for the high catalytic activity of CeO₂−MnO₂ towards CO oxidation.     

The Role of Polarization in Photocatalysis

Semiconductor photocatalysis as a desirable technology shows great potential in environmental remediation and renewable energy generation, but its efficiency is severely restricted by the rapid recombination of charge carriers in the bulk phase and on the surface of photocatalysts. Polarization has emerged as one of the most effective strategies for addressing the above‐mentioned issues, thus effectively promoting photocatalysis. This review summarizes the recent advances on improvements of photocatalytic activity by polarization‐promoted bulk and surface charge separation. Highlighted is the recent progress in charge separation advanced by different types of polarization, such as macroscopic polarization, piezoelectric polarization, ferroelectric polarization, and surface polarization, and the related mechanisms. Finally, the strategies and challenges for polarization enhancement to further enhance charge separation and photocatalysis are discussed.     

球形方解石的合成和表征

25℃下,用豆腐废水作为碳酸钙形貌调节剂,用Na2 CO3和CaCl,·6H2O作为原料合成碳酸钙,研究豆腐废水对产物组成和粒子形貌的影响.用粉末X-射线衍射仪(XRD)和红外光谱仪(FT-IR)对合成的产品晶型进行了表征,用扫描电子显微镜(SEM)观察研究粒子的形貌.研究结果显示,合成得到的产物是纯的方解石,粒子的形状是球形的或者是接近球形的.结果 说明,豆腐废水虽然不会影响碳酸钙的晶型,但是会影响碳酸钙粒子的形貌.