关于W_2~1[a,b]能否扩大的一些问题

讨论了W12[a,b]能否扩大为含有有间断点函数的再生核空间的问题.结论是:若再生核空间W W12[a,b]含有有间断点的函数,则间断点必固定、间断点个数必有限且非端点a,b.进一步,我们构造了函数含有n个间断点的再生核空间并给出其再生核表达式.     

Effects of the H-bond donor structure on the properties of supramolecular side chain liquid crystalline polymers based on poly(3-carboxypropylmethylsiloxane-co-dimethylsiloxane)s and stilbazoles

Supramolecular side chain liquid crystalline polymers (SCLCPs) based on poly(3-carboxypropylmethylsiloxane-co-dimethylsiloxane) (PSIX, X=100, 76, 60, 41 or 23, denoting the mole percentage of 3-carboxypropylmethylsiloxane unit in the polymer) and stilbazole derivatives have been obtained through intermolecular hydrogen bonding (H-bonding) interactions between the carboxylic acid and the pyridyl moieties. The formation of H-bonding and self-assembly results in the formation of new mesogenic units, in which H-bonds function as molecular connectors. FTIR shows the existence of H-bonding in the complexes. The polymeric complexes behave as single component liquid crystalline polymers and exhibit stable and enantiotropic mesophases. The liquid crystalline properties of the supramolecular SCLCPs were studied using differential scanning calorimetry, polarizing optical microscopy and X-ray diffraction, and were found to exhibit smectic A phases with focal-conic textures. The thermal stability of the SCLCP increases on increasing the carboxylic acid content in the polysiloxane and the concentration of the stilbazole derivative in the complex. However, the thermal stability decreases on increasing the chain length of the stilbazole derivative. The crystal phase was not formed even on cooling to the glass transition temperature of the polymeric complex.     

A theory of coupled diffusion and large deformation in polymeric gels

A large quantity of small molecules may migrate into a network of long polymers, causing the network to swell, forming an aggregate known as a polymeric gel. This paper formulates a theory of the coupled mass transport and large deformation. The free energy of the gel results from two molecular processes: stretching the network and mixing the network with the small molecules. Both the small molecules and the long polymers are taken to be incompressible, a constraint that we enforce by using a Lagrange multiplier, which coincides with the osmosis pressure or the swelling stress. The gel can undergo large deformation of two modes. The first mode results from the fast process of local rearrangement of molecules, allowing the gel to change shape but not volume. The second mode results from the slow process of long-range migration of the small molecules, allowing the gel to change both shape and volume. We assume that the local rearrangement is instantaneous, and model the long-range migration by assuming that the small molecules diffuse inside the gel. The theory is illustrated with a layer of a gel constrained in its plane and subject to a weight in the normal direction. We also predict the scaling behavior of a gel under a conical indenter.     

Structural and dynamic properties of polyoxyethylene sorbitan monooleate micelle in water dispersion studied by pulsed field gradient NMR

The diffusion phenomenon of a nonionic surfactant, polyoxyethylene sorbitan monooleate (POE-SMO), micelle in aqueous solution was investigated by pulsed field gradient nuclear magnetic resonance (PFG NMR) with a high gradient strength of 17.4 T/m at the diffusion timet _d varied from 3 to 300 ms. This high gradient strength allowed us to measure the slow self-diffusion coefficient of POE-SMO micelle, and the short diffusion time below 10 ms showed the restricted diffusion of the micelle. At the shortt _d the self-diffusion of the micelle was restricted and the restricted sizes were 1.8, 1.5, and 0.8 μm for the POE-SMO concentration of 100, 200 and 300 mM, respectively, and 0.6 μm for the POE-SMO only. The possible reason of this restriction was assumed to be the formation of a spatial network or a micellar clustering. Furthermore, a proton exchange between water molecule and surfactant OH group on the micelle surface was proposed. With respect to this proposal, the residence time of the proton at the micelle surface and the thickness of the surface were investigated from proton self-diffusion coefficients by PFG NMR.     

An algorithm for three-way data analysis that alternatively minimizes coupled vector (COV) resolution error and PARAFAC error.

A novel algorithm, alternatively minimizing coupled vector (COV) resolution error and PARAFAC error algorithm, is proposed in this paper. This algorithm can overcome the problem of slow convergence and is insensitive to the estimation of component number, such problems are unavoidable while using the traditional parallel factors analysis (PARAFAC) algorithm. In other words, this algorithm is capable of improving the computing speed and providing accurate resolutions provided that the number of factors used in the computation is no less than that of the actual underlying ones. The characteristic performances were demonstrated with a novel fluorescence data array.     

Complete Higher Dimensional Global Embedding Structures of Various Black Holes

We study global flat embeddings inside and outside of event horizons of black holes such as Schwarzschild and Reissner-Nordström black holes, and of de Sitter space. On these overall patches of the curved manifolds we investigate four accelerations and Hawking temperatures by introducing relevant Killing vectors.     

Envelop solitons in dusty plasmas for warm dust

A nonlinear Schrödinger equation is obtained for the warm dusty plasmas. The modulational instability of envelop soliton is investigated in this paper. Both the temperature of the dust grains and the charge variations of dust grains affect the instability regions of the dusty plasmas. It also affect the amplitude and the width of the envelop soliton.     

Nonlinear rheological behavior of silica filled solution‐polymerized styrene butadiene rubber

The reinforcement and nonlinear viscoelastic behavior have been investigated for silica (SiO₂) filled solution‐polymerized styrene butadiene rubber (SSBR). Experimental results reveal that the nonlinear viscoelastic behavior of the filled rubber is similar to that of unfilled SSBR, which is inconsistent with the general concept that this characteristic comes from the breakdown and reformation of the filler network. It is interesting that the curves of either dynamic storage modulus (G′) or loss tangent (tan δ) versus strain amplitude (γ) for the filled rubber can be superposed, respectively, on those for the unfilled one, suggesting that the primary mechanism for the Payne effect is mainly involved in the nature of the entanglement network in rubbery matrix. It is believed there exists a cooperation between the breakdown and reformation of the filler network and the molecular disentanglement, resulting in enhancing the Payne effect and improving the mechanical hysteresis at high strain amplitudes. Moreover, the vertical and the horizontal shift factors for constructing the master curves could be well understood on the basis of the reinforcement factor f(φ) and the strain amplification factor A(φ), respectively. The surface modification of SiO₂ causes a decrease in f(φ), which is ascribed to weakeness of the filler–filler interaction and improvement of the filler dispersion. However, the surface nature of SiO₂ hardly affects A(φ). © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2594‐2602, 2007     

PECVDSiON薄膜的工艺控制,性质及其潜在应用

研究了等离子增强化学气相淀积氮氧化硅薄膜的工艺控制、性质以及薄膜波导在超大规模集成电路光互连中的潜在应用。