On the stability of Riemannian manifold with parallel spinors

Inspired by the recent work [HHM03], we prove two stability results for compact Riemannian manifolds with nonzero parallel spinors. Our first result says that Ricci flat metrics which also admit nonzero parallel spinors are stable (in the direction of changes in conformal structures) as the critical points of the total scalar curvature functional. Our second result, which is a local version of the first one, shows that any metric of positive scalar curvature cannot lie too close to a metric with nonzero parallel spinor. We also prove a rigidity result for special holonomy metrics. In the case of SU(m) holonomy, the rigidity result implies that scalar flat deformations of Calabi-Yau metric must be Calabi-Yau. Finally we explore the connection with a positive mass theorem of [D03], which presents another approach to proving these stability and rigidity results. Dedicated to Jeff Cheeger for his sixtieth birthday     

The effects of crystal structure on optical absorption/photoluminescence of bis(8-hydroxyquinoline)zinc

In this paper, the transformation processes of two types of bis(8-hydroxyquinoline)zinc: Znq₂ dihydrate and anhydrous (Znq₂)₄ were investigated by X-ray diffraction (XRD), infrared spectra (IR), scanning electron microscope (SEM), differential scanning calorimetry (DSC) and thermogravimetry (TG). The effects of crystal structure on optical properties of bis(8-hydroxyquinoiline)zinc were analyzed. Znq₂ dihydrate can be transformed into anhydrous (Znq₂)₄ during heating under vacuum. Reversal transformation occurs by the interaction between chloroform and (Znq₂)₄. But (Znq₂)₄ was partially transformed into Znq₂ dihydrate by the interaction between ethanol and (Znq₂)₄. The different molecular structure results in different crystal stacking and electronic structure, thereby affect its optical properties.     

Existence, Multiplicity and Infinite Solvability of Positive Solutions for One-Dimensional p-Laplacian

The existence, multiplicity and infinite solvability of positive solutions are established for some two-point boundary value problems of one-dimensional p-Laplacian. In this paper, by multiplicity we mean the existence of m solutions, where m is an arbitrary natural number.     

Effect of ion impinging on the microstructure and field emission of carbon nanotubes

Effects of ion impinging on the microstructure and field electron emission properties of screen-printed carbon nanotube films were investigated. We observed that the plasma treatment modified the microstructure of CNTs along with the remarkable increase of emission site density. With the prolongation of ion impinging time, the emission current falls down first, and then rises up to higher than that of the untreated films. It is proposed that the change of emission characteristics is due to the different emission mechanisms. After the treatment, electrons are emitted predominantly from the nano-nodes on the tube wall instead from the nanotube tips.     

Crystallization and morphology of poly(vinylidene fluoride)/poly(3‐hydroxybutyrate) blends. I. Spherulitic morphology and growth by polarized microscopy

The development of the poly(3‐hydroxybutyrate) (PHB) morphology in the presence of already existent poly(vinylidene fluoride) (PVDF) spherulites was studied by two‐stage solidification with two separate crystallization temperatures. PVDF formed irregular dendrites at lower temperatures and regular, banded spherulites at elevated temperatures. The transition temperature of the spherulitic morphology from dendrites to regular, banded spherulites increased with increasing PVDF content. A remarkable amount of PHB was included in the PVDF dendrites, whereas PHB was rejected into the remaining melt from the banded spherulites. When PVDF crystallized as banded spherulites, PHB could consequently crystallize only around them, if at all. In contrast, PHB crystallized with a common growth front, starting from a defined site in the interfibrillar regions of volume‐filling PVDF dendrites. It formed by itself dendritic spherulites that included a large number of PVDF spherulites. For blends with a PHB content of more than 80 wt %, for which the PVDF dendrites were not volume‐filling, PHB first formed regular spherulites. Their growth started from outside the PVDF dendrites but could later interpenetrate them, and this made their own morphology dendritic. These PHB spherulites melted stepwise because the lamellae inside the PVDF dendrites melted at a lower temperature than those from outside. This reflected the regularity of the two fractions of the lamellae because that of those inside the dendrites of PVDF was controlled by the intraspherulitic order of PVDF, whereas that from outside was only controlled by the temperature and the melt composition. The described morphologies developed without mutual nucleating efficiency of the components. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 873–882, 2003     

Crystallographic report: catena‐Aqua(2,2′‐bipyrimidine)lithium(I) perchlorate

A lithium(I) coordination polymer has been formed from LiClO₄ and the 2,2′‐bipyrimidine (bpym) ligand in which each square pyramidal lithium(I) atom is coordinated in the basal plane by four nitrogen donor atoms derived from two bpym ligands and one water molecule at the apical position. These are connected into a layer structure via hydrogen‐bonding interactions involving the perchlorate anions. Copyright © 2004 John Wiley & Sons, Ltd.     

Mono-dispersed cross-linked polystyrene micro-spheres prepared by seed swelling polymerization method

A two-step swelling procedure was adopted to synthesize mono-dispersed and highly cross-linked poly (St-divinylbenzene) particles with PSt micro-spheres (1.80 μm in diameter). The PSt micro-spheres were prepared by a dispersion polymerization method and used as seeds. The effects of monomer concentration, ratio of ethanol to water, swelling reagents, crosslinking reagents, swelling temperature and agitation speed on particle size were investigated in detail. The morphologies and size distributions of these micro-spheres were examined by SEM and particle size analysis (PSA). The T _g of the micro-spheres was measured by DSC. The results indicate that the particles (6.20 μm in diameter) exhibit excellent mono dispersed property and high crosslinking degree when the concentration of the swelling reagent was 25%, the concentration of the crosslinking reagents was 23%, the swelling temperature was 30°C and the stirring speed was 150 r/min. __________ Translated from Chinese Journal of Applied Chemistry, 2007, 24(11): 1289–1294     

Buckling of a stiff thin film on a compliant substrate in large deformation

A finite-deformation theory is developed to study the mechanics of thin buckled films on compliant substrates. Perturbation analysis is performed for this highly nonlinear system to obtain the analytical solution. The results agree well with experiments and finite element analysis in wavelength and amplitude. In particular, it is found that the wavelength depends on the strain. Based on the accurate wavelength and amplitude, the membrane and peak strains in thin films, and stretchability and compressibility of the system are also obtained analytically.     

稀疏过程在破产问题中的应用

本讨论一类人寿保险的风险过程，其中保单到达服从齐次Poisson过程。而描述退保及索赔发生的计数过程分别为这一过程的q-稀疏与p-稀疏．对此模型给出其破产概率的具体上界，并与其它一类风险模型进行比较．