The localized longitudinal index theorem for Lie groupoids and the van Est map

We define the “localized index” of longitudinal elliptic operators on Lie groupoids associated with Lie algebroid cohomology classes. We derive a topological expression for these numbers using the algebraic index theorem for Poisson manifolds on the dual of the Lie algebroid. Underlying the definition and computation of the localized index, is an action of the Hopf algebroid of jets around the unit space, and the characteristic map it induces on Lie algebroid cohomology. This map can be globalized to differentiable groupoid cohomology, giving a definition of the “global index”, that can be computed by localization. This correspondence between the “global” and “localized” index is given by the van Est map for Lie groupoids.     

Polymer-Nanoparticle Composites Composed of Poly(3-hydroxybutyrate-co-3-hydroxyvalerate) and Coated Silver Nanoparticles

The effects of addition of synthesized organic-suspension silver nanoparticles on the crystallization and thermal stability of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) were studied by transmission electron microscopy (TEM), differential scanning calorimetry (DSC), wide-angle X-ray diffraction (XRD), UV-Vis absorption spectroscopy, polarized optical microscopy (POM), and thermal gravimetric analysis (TGA). The TEM images showed the average primary size of the as-synthesized silver nanoparticles, coated with a monolayer of the surfactants consisting of oleic acid and an alkylamine, was about 5 nm with narrow distribution, and that they were uniformly dispersed in n-heptane. PHBV/silver nanocomposites were prepared by melt mixing in an internal mixer and then injection molded into rectangle-shaped specimens by a labscale injection molding device. The coated silver nanoparticles showed a homogenuous dispersion in the PHBV matrix when the content of coated silver nanoparticles was about 1%. Both the DSC and POM data showed the efficient heterogeneous nucleation by the coated silver nanoparticles for facilitating PHBV crystallization. The thermal stability of the PHBV/silver nanocomposites improved with the increase in the content of the coated silver nanoparticles.     

The study of phase,microstructure, and magnetocaloric properties in LaFe11.6*xSi1.4B0.1 alloys

The effect of Fe on the phase and magnetocaloric property of LaFe_11.6*xSi_1.4B_0.1 alloys with x = 1.0–1.4 have been studied. The results show that the excess of Fe will make the α-Fe phases increase, but the easy corrosion LaFeSi phase reduces in LaFe_11.6*xSi_1.4B_0.1 alloys. All LaFe_11.6*xSi_1.4B_0.1 alloys keep the first-order magnetic phase transition. The saturation magnetizations of LaFe_11.6*xSi_1.4B_0.1 alloys with x > 1 are much higher than LaFe_11.6Si_1.4B_0.1 alloy under 2T magnetic field. This results in the maximum isothermal magnetic entropy changes, and the relative cooling power of LaFe_11.6*xSi_1.4B_0.1 alloys is bigger than for LaFe_11.6Si_1.4B_0.1 alloys.     

A novel imaging tool for hepatic portal system using phase contrast technique with hydrogen peroxide‐generated O2 gas

The objective of this study was to investigate the potential of hydrogen peroxide‐generated oxygen gas‐based phase contrast imaging (PCI) for visualizing mouse hepatic portal veins. The O₂ gas was made from the reaction between H₂O₂ and catalase. The gas production was imaged by PCI in real time. The H₂O₂ was injected into the enteric cavity of the lower sigmoid colon to produce O₂ in the submucosal venous plexus. The generated O₂ gas could be finally drained into hepatic portal veins. Absorption contrast imaging (ACI) and PCI of O₂‐filled portal veins were performed and compared. PCI offers high resolution and real‐time visualization of the O₂ gas production. Compared with O₂‐based ACI, O₂‐based PCI significantly enhanced the revealing of the portal vein in vivo. It is concluded that O₂‐based PCI is a novel and promising imaging modality for future studies of portal venous disorders in mice models.     

流体压强与流速关系的教学设计

结合学生的生活实际和年龄特点,创造性地设计了一个讲授飞机升力的实验方法;并以"流体压强与流速关系的教学设计"为案例,展示了教学设计要注重给学生提供充分的实践体验和合作交流机会,既要关注知识的传授和技能的培养,又要关注学生学习兴趣的培养和创新能力的提高;要注重引导学生学会观察问题、提出问题和解决问题,并从中感受到大自然的美妙和合作交流的快乐.