Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Stability control of the electrooptic effect with new maleimide copolymers containing photoreactive tricyanopyrrolidene‐based chromophores

New photocrosslinkable maleimide copolymers have been synthesized by the attachment of a tricyanopyrrolidene‐based chromophore. The 2‐(3‐cyano‐4‐(2‐{4‐[hexyl‐(6‐hydroxy‐hexyl)‐amino]‐phenyl}‐vinyl)‐5‐oxo‐1‐{4‐[4‐(3‐oxo‐3‐phenyl‐propenyl)‐ phenoxy]‐butyl}‐1,5‐dihydro‐pyrrol‐2‐ylidene)‐malononitrile chromophore exhibits nonlinear optical activity and contains a chalcone moiety that is sensitive to UV light (λ = 330–360 nm) for crosslink formation. The maleimide monomers have also been functionalized with chalcone moieties. The resultant copolymers exhibit great processability, and one of them shows a maximum electrooptic coefficient of 90 pm/V at 1300 nm. We could control the thermal stability of the electrooptic coefficient with the newly synthesized photoreactive copolymers successfully. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 531–542, 2007     

Degradative chain transfer in vinyl acetate polymerizations using toluene as solvent

In this work, we propose that retardation in vinyl acetate polymerization rate in the presence of toluene is due to degradative chain transfer. The transfer constant to toluene (C_trs) determined using the Mayo method is equal to 3.8 × 10^?3, which is remarkably similar to the value calculated from the rate data, assuming degradative chain transfer (2.7 × 10^?3). Simulations, including chain‐length‐dependent termination, were carried out to compare our degradative chain transfer model with experimental results. The conversion–time profiles showed excellent agreement between experiment and simulation. Good agreement was found for the M_n data as a function of conversion. The experimental and simulation data strongly support the postulate that degradative chain transfer is the dominant kinetic mechanism. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3620–3625, 2007     

Glass transitions and mixed phases in block SBS

Differential scanning calorimetry (DSC) does not allow for easy determination of the glass‐transition temperature (T_g) of the polystyrene (PS) block in styrene–butadiene–styrene (SBS) block copolymers. Modulated DSC (MDSC), which deconvolutes the standard DSC signal into reversing and nonreversing signals, was used to determine the (T_g) of both the polybutadiene (PB) and PS blocks in SBS. The T_g of the PB block was sharp, at ?92 °C, but that for the PS blocks was extremely broad, from ?60 to 125 °C with a maximum at 68 °C because of blending with PB. PS blocks were found only to exist in a mixed PS–PB phase. This concurred with the results from dynamic mechanical analysis. Annealing did not allow for a segregation of the PS blocks into a pure phase, but allowed for the segregation of the mixed phase into two mixed phases, one that was PB‐rich and the other that was PS‐rich. It is concluded that three phases coexist in SBS: PB, PB‐rich, and PS‐rich phases. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 276–279, 2005     

三种群食物链交错扩散模型的整体

本文应用能量估计方法和Gagliardo-Nirenberg型不等式证明了一类强耦合反应扩散系统整体解的存在性和一致有界性，该系统是带自扩散和交错扩散项的三种群Lotka-Volterra食物链模型．通过构造Lyapunov函数给出了该模型正平衡点全局渐近稳定的充分条件．     

Chemical Constituents of Ligusticum sinensis Oliv.

The new phenylpropanoid diglycoside ligusinenoside A ( 1 ), and the two new 8,4′‐oxyneolignan(‘8‐O‐4′‐neolignan’) diglycosides ligusinenosides B ( 2 ) and C ( 3 ), together with nine known compounds, were isolated from the rhizomes of Ligusticum sinensis Oliv. The structures of 1 – 3 were elucidated on the basis of spectroscopic analyses.     

Isothermal crystallization kinetics of poly(3‐hydroxybutyrate)/layered double hydroxide nanocomposites

Poly(3‐hydroxybutyrate) (PHB)/layered double hydroxides (LDHs) nanocomposites were prepared by mixing PHB and poly(ethylene glycol) phosphonates (PEOPAs)‐modified LDH (PMLDH) in chloroform solution. Both X‐ray diffraction data and TEM micrographs of PHB/PMLDH nanocomposites indicate that the PMLDHs are randomly dispersed and exfoliated into the PHB matrix. In this study, the effect of PMLDH on the isothermal crystallization behavior of PHB was investigated using a differential scanning calorimeter (DSC) and polarized optical microscopy. Isothermal crystallization results of PHB/PMLDH nanocomposites show that the addition of 2 wt % PMLDH into PHB induced more heterogeneous nucleation in the crystallization significantly increasing the crystallization rate and reducing their activation energy. By adding more PMLDH into the PHB probably causes more steric hindrance of the diffusion of PHB, reducing the transportation ability of polymer chains during crystallization, thus increasing the activation energy. The correlation among crystallization kinetics, melting behavior and crystalline structure of PHB/PMLDH nanocomposites can also be discussed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3337–3347, 2006     

An implicit method for linear ill‐posed problems with perturbed operators

An implicit iterative method is applied to solving linear ill‐posed problems with perturbed operators. It is proved that the optimal convergence rate can be obtained after choosing suitable number of iterations. A generalized Morozov's discrepancy principle is proposed for the problems, and then the optimal convergence rate can also be obtained by an a posteriori strategy. The convergence results show that the algorithm is a robust regularization method. Copyright © 2006 John Wiley & Sons, Ltd.