非线性规划问题的二阶对称对偶性

本文讨论了二阶凸和二阶凹条件下的二阶对称对偶问题,并利用有效性和真有效性概念证明了弱对偶、强对偶、逆对偶及自对偶定理。     

一类混合单调算子新的不动点定理及其应用

引入了广义Φ凹（-φ）凸算子这一概念,在非紧非连续条件下,得到了混合单调算子的几个新的不动点存在唯一性定理.最后给出了一个应用.     

A cubic quadrilateral spline element with concave shapes

Basic requirement for applying isoparametric element is that the element has to be convex and no violent distortion is allowed. In this paper, a cubic quadrilateral spline element with 12 nodes has been developed using the triangular area coordinates and the B-net method, which can exactly model the cubic field for quadrilateral element with both convex and concave shapes. Neither mapping nor coordinate transformation is required and the spline element can obtain high accuracy solutions and insensitive to mesh distortions.     

Design of Gold Nanoparticles in Dendritic Cell‐Based Vaccines

The design of effective cancer vaccines must be able to activate dendritic cells (DCs) of the innate immune system in order to induce immunity to pathogens and cancer. DCs patrol the body and once they encounter antigens, they orchestrate a complex mechanism of events and signals that can alert the adaptive immune system to action. However, DC‐based vaccines remain a challenge in part because the source and quality of antigens, the DC targeting molecule, type of adjuvant, and delivery vehicle must be optimized to induce a robust immune response. Gold nanoparticles (AuNPs) have now entered clinical trials as carriers due to their ease of functionalization with antigens, adjuvants, and targeting molecules. This progress report discusses how AuNPs can influence DC activation and maturation, as well as their potential impact on T helper (Th) differentiation. Ultimately, successful AuNP‐based DC vaccines are able to induce phagocytosis, activation/maturation, migration, T cell costimulation, and cytokine secretion, which is named AuNP‐induced DC tuning (AuNP‐DC tuning). Although at its infancy, understanding the processes of AuNP‐DC tuning will give a better understanding of how best to engineer AuNPs and will redefine the next generation of DC‐based vaccines.     

非正常凸多面体及凹多面体的落地概率

通过研究非正常凸、凹多边形板着地后的特点,得出了非正常凸多边形板及凹多边形板各边着地的概率.进而用立体角的概念,在分析非正常凸、凹多面体着地的特点后,得到了非正常凸多面体及凹多面体各面着地的概率.     

改进差分进化算法求解装载率凹费用装箱问题

研究了广泛存在于物流作业中一类新型的装箱问题,主要特征体现在箱子使用费用是关于装载率的凹函数。为求解问题,提出了一种基于分组编码策略的改进差分进化算法,以避免常规实数和整数编码方法存在放大搜索空间的不足。针对分组编码策略,定制化设计了以促进优秀基因传播为导向的新型变异和交叉操作,另外还嵌入了以物品置换为邻域的自适应局部搜索操作以增强局部搜索能力。对以往文献给出算例在不同凹费用函数下进行测试,实验结果显示所提出的算法明显优于BFD启发式算法,并且较遗传算法也有显著性改进。     

光栅周期包含的Bragg层数对Bragg型凹面衍射光栅的影响

单个衍射光栅周期所包含的Bragg周期层数是连续Bragg齿型凹面衍射光栅的主要参数之一,该参数可改变光栅齿结构,对凹面衍射光栅的分辨力.自由光谱范围及衍射效率有重要影响.本文通过理论分析与仿真模拟,对比了4种不同层数的Bragg型凹面衍射光栅的特性参数.研究结果表明:在衍射光栅尺寸不变的情况下,改变单个光栅周期包含的Bragg周期层数不会显著提高器件主衍射级次的分辨力;单个光栅周期包含的Bragg周期层数与光栅可衍射的级次数成正相关.单周期层数的Bragg凹面衍射光栅的主衍射级次效率最高,其可衍射的级次数最少,且其他衍射级次分散的能量最少;增加单个光栅周期所包含的Bragg周期层数会降低主衍射级次的自由光谱范围.该研究对于设计低插损、高分辨率、宽工作波段的波分复用器或光栅光谱仪具有重要的指导意义.     

Stochastic modeling of columnar dendritic grain growth in weld pool of Al‐Cu alloy

A multi‐scale model is used to simulate columnar dendritic growth in TIG (tungsten inert‐gas) weld molten pool of Al‐Cu alloy. The grain morphologies at the edge of the weld pool are studied. The simulated results indicate that the average primary dendrite spacing changes during the solidification process in the weld pool because of the complicated thermal field, solute diffusion field and competitive growth. And it is shown that the secondary dendrite arms grow insufficiently in the space between dendrite trunks if the primary dendrite spacing is small. And the phenomenon has been explained by analyzing the influence of the solute accumulation on the constitutional undercooling and undercooling gradient when there are two different opposite solute diffusion fields. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cobalt complexes based on dendritic PAMAM bridged salicylaldimine ligands: Synthesis,characterization and performance in ethylene oligomerization

Two novel dendritic poly(amido-amine) (PAMAM) bridged salicylaldimine ligands were synthesized by Schiff base reaction using 1.0 generation dendritic PAMAM as bridged groups. The cobalt complex with 1,4-butanediamine as core (C1) and the cobalt complex with 1,6-hexanediamine as core (C2) based on dendritic PAMAM bridged salicylaldimine ligands were prepared by metallic coordination reaction, respectively. The structures of the ligands and the dendritic cobalt complexes were characterized by fourier transform infrared (FTIR), ultraviolet spectra (UV), hydrogen nuclear magnetic resonance (¹H NMR) and electrospray ionization mass spectra (ESI-MS). The complexes C1 and C2 were evaluated as catalyst precursors for ethylene oligomerization after being activated with methylaluminoxane (MAO), diethylaluminum chloride (Et₂AlCl), ethylaluminium dichloride (EtAlCl₂) and ethylaluminum sesquichloride (EASC). The dendritic cobalt complexes exhibited the highest activity and selectivity for high carbon oligomers with EASC as activator. Under the conditions of 1.0 MPa, 25°C and Al/Co molar ratio 1500, the catalytic activity and selectivity for C₁₀–C₂₀ using C1 were 3.44×10⁶ g·(mol Co·h)^?1 and 76.53% after activation with EASC, and the catalytic activity and selectivity for C₁₀–C₂₀ using C2 were 3.42×10⁶ g·(mol Co·h)^?1 and 84.50%, respectively.     

Numerical simulation on dendritic growth of Al-Cu alloy under convection based on the cellular automaton lattice Boltzmann method

A numerical model is developed by coupling the cellular automaton (CA) method and the lattice Boltzmann method (LBM) to simulate the dendritic growth of Al-Cu alloy in both two and three dimensions. An improved decentered square algorithm is proposed to overcome the artificial anisotropy induced by the CA cells and to realize simulation of dendritic growth with arbitrary orientations. Based on the established CA-LBM model, effects of forced convection and gravity-driven natural convection on dendritic growth are studied. The simulation results show that the blocking effect of dendrites on melt flow is advanced with a larger number of seeds. The competitive growth of the converging columnar dendrites is determined by the interaction between heat flow and forced convection. Gravity-driven natural convection leads to highly asymmetric growth of equiaxed dendrites. With sinking downwards of the heavy solute, chimney-like or mushroom-like solute plumes are formed in the melt in front of the columnar dendrites when they grow along the gravitational direction. More details on dendritic growth of Al-Cu alloy under convection are revealed by 3D simulations.