拟矩形剖分上的样条空间的维数

矩形剖分~(记为$\Delta_{QR}$)~是指在矩形剖分~(记为$\Delta_{R}$)的基础上进行局部修改后得到的剖分,通常包括T-剖分~(记为$\Delta_{T}$)~和L-剖分~(记为$\Delta_{L}$).本文利用光滑余因子协调方法讨论了该剖分上的二元样条空间$S^\mu_k(\Delta_{QR})$的维数.在满足一定约束条件下, 得到了仅依赖于样条空间的次数,光滑度和剖分拓扑结构的显式维数公式.     

A polarity‐activation strategy for the high incorporation of 1‐alkenes into functional copolymers via RAFT copolymerization

A new synthetic methodology for the preparation of copolymers having high incorporation of 1‐alkene together with multifunctionalities has been developed by polarity‐activated reversible addition‐fragmentation chain transfer (RAFT) copolymerization. This approach provides well‐defined alternating poly(1‐decene‐alt‐maleic anhydride), expanding the monomer types for living copolymerizations. Although neither 1‐decene (DE) nor maleic anhydride (MAn) has significant reactivity in RAFT homopolymerization, their copolymers have been synthesized by RAFT copolymerizations. The controlled characteristics of DE‐MAn copolymerizations were verified by increased copolymer molecular weights during the copolymerization process. Ternary copolymers of DE and MAn, with high conversion of DE, could be obtained by using additive amounts (5 mol %) of vinyl acetate or styrene (ST), demonstrating further enhanced monomer reactivities and complex chain structures. When ST was selected as the third monomer, copolymers with block structures were obtained, because of fast consumption of ST in the copolymerization. Moreover, a wide variety of well‐defined multifunctional copolymers were prepared by RAFT copolymerizations of various functional 1‐alkenes with MAn. For each copolymerization, gel permeation chromatography analysis showed that the resulting copolymer had well‐controlled M_n values and fairly low polydispersities (PDI = 1.3–1.4), and ¹H and ¹³C NMR spectroscopies indicated strong alternating tendency during copolymerization with high incorporation of 1‐alkene units, up to 50 mol %. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3488–3498, 2008     

Liquid phase epitaxial growth and optical property of flower-like ZnO nanosheets on Zinc foil

Large scale flower-like ZnO nanosheets have been synthesized on Zinc foil by a simple hydrothermal method. Their morphology and microstructures were characterized and analyzed by X-ray spectroscopy (XRD), field emission scanning electron microscopy (FE-SEM) and high-resolution transmission electron microscopy (HRTEM). The as-synthesized flower-like nanosheets are hexagonal phase single crystal with 200-300 nm in width, 50 nm in thickness. The growth process follows the liquid phase epitaxial growth mechanism. In this approach, the ZnO buffer is used as substrate for the growth of flower-like ZnO nanosheets. The growth direction of the nanosheets is the preferential [0 0 0 1] growth direction of ZnO. The photoluminescence spectrum of the sample exhibits only a sharp and strong UV emission centered at 386 nm, which indicates that the flower-like ZnO nanosheets on Zn foil are of good optical property.     

Quantitative elemental analysis of Fe?Zn‐alloy coating by nondestructive method

A quantitative analytical method of iron content in Fe? Zn‐alloy coating by x‐ray diffraction (XRD) spectrum was proposed. This work aimed to replace the wet chemical analysis of Fe? Zn‐alloy coating with rapid and reproducible quantification by an XRD spectrum. Partial least‐squares (PLS) model was utilized to differentiate the spectral characteristic as well as to quantify each component in XRD spectrum. Fifteen standard samples were prepared by heat treatment and verified by the relationship between wet chemical analyses and the XRD spectrum for iron content. The suggested method showed satisfactory precision and accuracy in the analysis of Fe? Zn‐alloy coating. The accuracy for iron content in Fe? Zn‐alloy coating was 0.17 wt%. Copyright © 2008 John Wiley & Sons, Ltd.     

Realizing high hydrogen evolution activity under visible light using narrow band gap organic photocatalysts

The design and synthesis of conjugated semiconducting polymers for photocatalytic hydrogen evolution have engendered intense recent interest. However, most reported organic polymer photocatalysts show a relatively broad band gap with weak light absorption ability in the visible light region, which commonly leads to a low photocatalytic activity under visible light. Herein, we synthesize three novel dithieno[3,2-b:2′,3′-d]thiophene-S,S-dioxide (DTDO) containing conjugated polymer photocatalysts by a facile C–H arylation coupling polymerization reaction. The resulting polymers show a broad visible light absorption range up to 700 nm and a narrow band gap down to 1.81 eV due to the introduction of the DTDO unit. Benefiting from the donor–acceptor polymer structure and the high content of the DTDO unit, the three-dimensional polymer PyDTDO-3 without the addition of a Pt co-catalyst shows an attractive photocatalytic hydrogen evolution rate of 16.32 mmol h⁻¹ g⁻¹ under visible light irradiation, which is much higher than that of most reported organic polymer photocatalysts under visible light.

Narrow band gap conjugated polymer photocatalysts containing dithieno[3,2-b:2′,3′-d]thiophene-S,S-dioxide show an attractive photocatalytic hydrogen evolution rate of 16.32 mmol h⁻¹ g⁻¹ under visible light irradiation.     

Electrochemical properties of niosomes‐modified Au electrode and its interaction with 1‐anilino‐8‐naphthalene‐sulfonate

The gold electrode was modified by noisomes, prepared by sonicating the mixed solution of PEG 6000/Tween 80/Span 80/H₂O. Electrochemical cyclic voltammetry (CV) and impedance spectroscopy (EIS) were performed for characterizing the modification. The construction of multilayer films of octadecanethiol (ODT)‐niosomes had almost no pinholes, which elicited that niosomes‐coated electrode through ODT assembly was more effective immobilization compared to direct modification method. A large semicircle formation in the entire range of frequency indicated the complete electron‐transfer control for the redox reaction, implying a perfect blocking behavior. The Nyquist plot was consisting of two depressed semicircles after storage for 36 h in air, which implied a progressive and uniform construction manner, as expected for porous coatings. The modified electrode was used to investigate the interaction between 1‐anilino‐8‐naphthalene‐sulfonate (ANS) and noisomes. It was found that the low‐frequency semicircular arcs increase in diameter, indicating that the increase in the resistance R_p attributed mainly to the niosomes/solution interface. It was due to the binding of ANS to the niosomes‐modified electrode surface, exhibited against diffusing species through the pores. Copyright © 2009 John Wiley & Sons, Ltd.     

关于次加泛函的一点注记

In this note we obtained a both sufficient and necessary condition there exist non-zero β′ degree abslutely homogeneous, continuous and subadditive unctionals in metric linear spaces (E, ‖·‖_β) for C < β≤β′ ≤1 . APPlying our result, a simpler proof of theorem in[1,§1] was given.     

An efficient approach to synthesize polysaccharides‐graft‐poly(p‐dioxanone) copolymers as potential drug carriers

Starch and poly(p‐dioxanone) (PPDO) are the natural and synthetic biodegradable and biocompatible polymers, respectively. Their copolymers can find extensive applications in biomedical materials. However, it is very difficult to synthesize starch‐graft‐PPDO copolymers in common organic solvents with very good solubility. In this article, well‐defined polysaccharides‐graft‐poly(p‐dioxanone) (SA_n‐PPDO) copolymers were successfully synthesized via the ring‐opening polymerization of p‐dioxanone (PDO) with an acetylated starch (SA) initiator and a Sn(Oct)₂ catalyst in bulk. The copolymers were characterized via Fourier transform infrared spectroscopy, ¹H NMR, gel permeation chromatography, thermogravimetric analysis (TG), differential scanning calorimetry, and wide angle x‐ray diffraction. The in vitro degradation results showed that the introduction of SA segments into the backbone chains of the copolymers led to an enhancement of the degradation rate, and the degradation rate of SA_n‐PPDO increased with the increase of SA wt %. Microspheres with an average volume diameter of 20 μm, which will have potential applications in controlled release of drugs, were successfully prepared by using these new copolymers. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5344–5353, 2009     

Asymmetric bromolactonization using amino-thiocarbamate catalyst

A novel amino-thiocarbamate-catalyzed bromolactonization of unsaturated carboxylic acids has been developed. The scope of the reaction is evidenced by 22 examples of γ-lactones with up to 99% yield and 93% ee. The protocol was applied in the enantioselective synthesis of the key intermediates of VLA-4 antagonists.     

Reinforcement of natural rubber/high density polyethylene blends with electron beam irradiated liquid natural rubber-coated rice husk

Coating of rice husk (RH) surface with liquid natural rubber (LNR) and exposure to electron beam irradiation in air were studied. FTIR analysis on the LNR-coated RH (RHR) exposed to electron beam (EB) showed a decrease in the double bonds and an increase in hydroxyl and hydrogen bonded carbonyl groups arising from the chemical interaction between the active groups on RH surface with LNR. The scanning electron micrograph showed that the LNR formed a coating on the RH particles which transformed to a fine and clear fibrous layer at 20 kGy irradiation. The LNR film appeared as patches at 50 kGy irradiation due to degradation of rubber. Composites of natural rubber (NR)/high density polyethylene (HDPE)/RHR showed an optimum at 20–30 kGy dosage with the maximum stress, tensile modulus and impact strength of 6.5, 79 and 13.2 kJ/m², respectively. The interfacial interaction between the modified RH and TPNR matrix had improved on exposure of RHR to e-beam at 20–30 kGy dosage.