熵极小动力系统的复杂性

设X是一个紧致度量空间,f:X→X是一个连续映射,(X,f)是熵极小的.该文首先证明了f是强遍历的;另外,如果还假设X中存在f的一个真的(拟)弱几乎周期点,则得到f具有正拓扑熵且对任意的n1,f~n是遍历敏感依赖的.因此,f在Li-Yorke和Takens-Ruelle意义下是混沌的.该文所得结论改进和推广了最近的一些结论.     

小时滞梯度系统的动力学行为

该文研究下列具有小时滞的一般非线性梯度型发展方程_tu+Au=f(u(t),u(t-τ)).证明了当时间趋于无穷大时,时滞方程的每一个有界解将收敛于某一个平衡点,只要时滞足够小,这意味着时滞系统的行为非常类似非时滞系统.这里的方法主要是基于梯度系统不变集的Morse结构和发展方程的几何理论.这个结果的证明分两步完成:首先,在梯度系统和有限个孤立平衡点的假设下,证明了一定存在一个足够小的时滞使得时滞方程的任一个有界解将会最终进入并停留在某一个平衡点的邻域里面;其次,在双曲平衡点的假设下,运用指数二分性和一系列的估计,证明了一定存在ε0和足够小的τ0使得任一个落于某个平衡点ε-邻域内的解最终收敛于该平衡点,当时间趋于无穷大时.     

Thermal Behavior of Polypropylene-g-glycidyl Methacrylate Prepared by Melt Grafting

The thermal behaviors of glycidyl methacrylate (GMA)-grafted polypropylene (PP) (PP-g-GMA) with two different grafting degrees, namely, GPP1 and GPP2, were investigated by differential scanning calorimetry (DSC), polarized optical microscopy (POM), wide-angle X-ray diffraction (WAXD), dynamic mechanical analysis (DMA), and thermogravimetrical analysis (TGA). DSC results suggested that the GMA grafted PP exhibited higher crystallization temperature T_c, higher melting temperature T_m, and higher crystallinity compared with the neat PP. The isothermal crystallization kinetics was analyzed with the Avrami equation and the total crystallization activation energy was calculated. It was concluded that the crystallization processes of PP and the grafted PP were controlled by nucleation and the values of the crystallization activation energy of PP and the grafted PP were almost identical. POM results suggested that the GMA grafted PP exhibited smaller spherulites size compared with the neat PP. WAXD patterns indicated that the neat PP encouraged the formation of γ phase, compared with the grafted PP, during the crystallization process. DMA results showed that melt grafting did not induce a clear effect on the γ-transition and β-transition of the amorphous phase but resulted in a decrease in mobility of the PP chains in the crystals. TGA curves suggested that the melt grafting slightly improved the thermal stability of PP.     

R~N上具有渐近线性项的奇异椭圆问题的研究（英文）

本文通过变分方法,证明包含Hardy位势的奇异椭圆问题-Δu(x)-μ/|x|2u(x)=K(x)f(u),x ∈RN,x在u∈D1,2(RN)中至少有一个非平凡解,其中N≥3,0≤μ≤∶=((N-2)/2)2,f(t)是在R上的连续函数并且在无穷远处渐近线性.     

Studies on the Thermodynamic and Kinetic Properties of the Reactions of Ti+ with Sulfur Transfer Reagent SCO Along the C═S Bond Activation Branch at 200–1200K

Theoretical studies on the thermodynamic and kinetic properties of the reactions of Ti⁺ with sulfur transfer reagent SCO via the C═S bond activation pathway have been carried on using DFT/B3LYP method, general statistical thermodynamics, and Eyring transition state theory with Wigner correction. The relevant reactions include reaction 1 ⁴ Ti⁺+¹SCO → ⁴ IM ₁ → ⁴ TS ₁ → ⁴ IM ₂ → ⁴ TiS⁺+ ¹ CO, and reaction 2 ⁴Ti⁺+¹SCO →⁴IM₁→ CP →²IM₂→²TiS⁺+¹CO in which the spin multiplicity changes from the quartet state to the doublet state in the crossing region. It is concluded that the increase of the temperature is favored to the reaction 1 process, since the equilibrium constants (K) rises from 0.566 × 10[P]-9 at 200 K to 0.109 × 10⁰ at 1200 K, and the reaction rate constant (k) from 0.222 × 10⁰ s[P]-1 at 200 K to 0.540 × 10 ¹¹ s[P]-1 at 1200 K. Moreover, reaction 1 is endothermic, and non-spontaneous in the way the entropy increases, while reaction 2 is exothermic and spontaneous in the way their entropy decreases. The reaction path 2 is the energetically favorable channel, and its thermodynamic data change not largely with the rise of temperature.     

Hydrosilylation Catalyzed with Rh(PPh3)3Cl/Ionic-Liquid–Functionalized SiO2

Ionic liquid–modified silica has been prepared by a “one-pot” reaction of activated silica, 3-chloropropyltriethoxysilane, and alkylimidazole or pyridine. It was found that the catalytic activity and β-adduct selectivity of the supported catalyst Rh(PPh₃)₃Cl/ionic-liquid–modified-SiO₂ for the hydrosilylation reaction of alkenes with triethoxysilane was significantly improved. Furthermore, the catalyst system could be recovered easily.     

Nitroxide‐mediated Living Radical Polymerization of Styrene with Fluorescent Initiator

A fluorescence method was used for determination of marked chain ends in polystyrene samples prepared by 4‐substituted TEMPO type nitroxide‐mediated living free radical polymerization of styrene. 2,2,6,6‐Tetramethyl‐1‐(1‐phenylethoxy)‐piperidin‐4‐yl‐4‐pyren‐1‐ylbutanoate (PYNOR) was prepared and used as an unimolecular initiator bearing pyrene as a fluorescence mark on mediating nitroxide fragment. The bulk polymerization of styrene at 120°C, in the presence of new unimolecular initiator, was a typical nitroxide mediated living radical polymerization. For comparison, two different molar ratios of initiator and monomer (1∶400 and 1∶1000 initiator ‐ monomer [I:M]) were used for polymerization. When I:M=1∶400, the obtained polydispersity was 1.12 and maximum molecular weight 27,000 g/mol was obtained at 62% conversion. For ratio 1∶1000, slightly higher polydispersity was obtained ?1.26 and the molecular weight was 53,000 g/mol at 70% conversion. The content of the polystyrene chains bearing mediating nitroxide fragment was determined by fluorescence spectroscopy. The intensity of pyrene fluorescence decreased as the molar mass, and the conversion increased as well. The extent of the incorporation of chromophore at propagating chain end or “livingness” of polymerization decreased despite the fact that the polydispersity did not change. The extent of side reaction leading to broadening of polydispersity is suppressed due to the high viscosity of the system at higher conversion. A low extent of “livingness” will have a very negative effect on possible preparation of block copolymers.     

Synthesis and Characterization of Amphiphilic Copolymer Acrylic Acid-co-p-Chloromethylstyrene

The free radical copolymerization of acrylic acid (M₁) with p-chloromethylstyrene (M₂) in dioxane and in the presence of α,α′-azobisisobutyronitrile (AIBN) at 65°C is reported. Copolymer compositions of six copolymer samples obtained from feed ratios of M₁:M₂ = 95.2:4.8 to 21.4:78.6 were determined by ¹H-NMR. The reactivity ratios of AA/p-CMS copolymerization system calculated by the F-R method were r ₁ = 0.50 ± 0.06 and r ₂ = 1.52 ± 0.15, almost the same as r ₁ = 0.43 ± 0.21 and r ₂ = 1.31 ± 0.14 by the extended K-T method. On the basis of the reactivity ratios of two monomers, the sequence length distribution in the AA/p-CMS copolymers was obtained. For f₂ = 4.77%, the monomer unit of p-CMS is individually separated in the chain of AA; for f₂ = 35.53%, the alternating tendency prevails and a large number of mono-sequences are formed. The number-average ( _n) and weight-average ( _w) molecular weights were determined by gel permeation chromatography. The effect on molecular weights of feed composition is also discussed. In the presence of constant initiator concentration, the gradual increase in the ratio of M₂:M₁ (from14.7:85.3 to 78.6:21.4) was accompanied by a decrease in molecular weights ( _n from 11907 to 3961).     

A Novel Fission Process in Mini-emulsion RAFT Polymerization: Shell Crosslinked Nanoparticles as a Model

Shell crosslinked nanoparticles, prepared from copolymerization of styrene and disulfide crosslinker, using poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA) as stabilizer and macroinitiator, exhibited a special fission behavior during the mini-emulsion RAFT polymerization process.     

Inclusion Interactions of Cucurbit[7]uril with Adenine and its Derivatives

Interactions of cucurbit[7]uril (Q[7] host) with guest adenine (g1), adenosine (g2) and 2′,3′-o-isopropylideneadenosine (g3) were studied in details by ¹H NMR, UV absorption spectroscopy, fluorescence spectroscopy and high performance liquid chromatography (HPLC) methods. We found that the suitable pH range for interaction was between 1 and 7, and the optimal pH range was between 2 and 4. The ¹H NMR analysis indicated that Q[7] selectively interacted with the adenine moiety of the guests g1 and g2, while Q[7] selectively interacted with the D-ribose sugar ring moiety of the guest g3. Moreover, ¹H NMR spectra showed that the exchange between the bound guest and the free guest was fast on the NMR time scale for the Q[7]-g1 and Q[7]-g2 systems. However, an obvious equilibrium between the bound host/guest and the unbound host/guest were observed in the Q[7]-g3 complex. Several methods were used to determine quantitatively the stability of the three host–guest inclusion complexes formed between Q[7] and the guests. The formation constants by UV and fluorescence were 1.90 × 10⁵ L mol^? 1 and 1.34 × 10⁵ L mol^? 1 for Q[7]-g1, 9.41 × 10⁴ L mol^? 1 and 4.24 × 10⁴ L mol^? 1 for Q[7]-g2, 4.50 × 10⁴ L mol^? 1 and 3.62 × 10⁴ L mol^? 1 for Q[7]-g3, respectively. HPLC method was also introduced to explore the interactions between Q[7] and the adenine and its derivatives. The formation constants of the host–guest inclusion complexes, as determined by HPLC, were 6.76 × 10⁴ L mol^? 1 for Q[7]-g1, 1.80 × 10⁴ L mol^? 1 for Q[7]-g2, 3.01 × 10⁴ L mol^? 1 for Q[7]-g3 respectively. Our study suggested that Q[7] could be a suitable host for the delivery of bioactive molecules, such as the adenine and its derivatives.