Application of N,N‐bis(diphenylphosphino)aniline palladium(II) complexes as pre‐catalysts in Heck coupling reactions

Palladium(II) complexes with N,N‐bis(diphenylphosphino)aniline ligands catalyse the Heck reaction between styrene and aryl bromides, affording stilbenes in good yield. The structures of two of the complexes used as pre‐catalysts have been determined by single‐crystal X‐ray diffraction. Copyright © 2007 John Wiley & Sons, Ltd.     

The Exact Solutions of Some (2 + 1)-Dimensional Integrable Systems

The equivalence of three (2 1)-dimensional soliton equations is proved, and the quite generalsolutionswitha some arbitrary functions of x, t and y respectively are obtained. By selecting the arbitrary functions, many specialtypes of the localized excitations like the solitoff solitons, multi-dromion solutions, lump, and multi-ring soliton solutionsare obtained.     

Integral-Type Darboux Transformations for the mKdV Hierarchy with Self-Consistent Sources

We present integral-type Darboux transformation for the mKdV hierarchy and for the mKdV hierarchy withself-consistent sources. In contrast with the normal Darboux transformation, the integral-type Darboux transformationscan offer non-auto-Backlund transformation between two (2n 1)-th mKdV equations with self-consistent sources withdifferent degrees. This kind of Darboux transformation enables us to construct the N-soliton solution for the mKdVhierarchy with self-consistent sources. We also propose the formulas for the m times repeated integral-type Darbouxtransformations for both mKdV hierarchy and mKdV hierarchy with self-consistent sources.     

Theoretical and numerical analysis on multispectral bioluminescence tomography

Recently, molecular imaging has been rapidly developed to studyphysiological and pathological processes in vivo at the cellularand molecular levels. Among molecular imaging modalities, opticalimaging has attracted a major attention for its unique advantages.In this paper, we establish a mathematical framework for multispectralbioluminescence tomography (BLT) that allows simultaneous studiesof multiple optical reporters. We show solution existence, uniquenessand continuous dependence on data as well as the limiting behaviourswhen the regularization parameter approaches zero or when thepenalty parameter approaches infinity. Then, we propose twonumerical schemes for multispectral BLT and derive error estimatesfor the corresponding solutions.     

Amine‐blocked polyisocyanates. I. Synthesis of novel N‐methylaniline‐blocked polyisocyanates and deblocking studies using hot‐stage fourier transform infrared spectroscopy

A series of substituted N‐methylaniline‐blocked polyisocyanates based on 4,4′‐methylenebis(phenyl isocyanate) and poly(tetrahydrofuran) were prepared and characterized thoroughly with FTIR, ¹H NMR, and ¹³C NMR spectroscopy methods. Compared with unsubstituted N‐methylaniline, a blocking agent with an electron‐releasing substituent at the para position took a shorter time, whereas those with an electron‐releasing substituent at the ortho position or an electron‐withdrawing substituent at the ortho and para positions took longer times for the blocking reaction. The thermal dissociation reactions of blocked polyisocyanates were carried out with an FTIR spectrophotometer attached to hot‐stage accessories under dynamic and isothermal conditions. The dynamic method was used to determine the deblocking temperature, and the isothermal method was used to calculate the deblocking kinetics and activation parameters. The cure times of blocked polyisocyanates with hydroxyl‐terminated polybutadiene were also determined. The deblocking temperatures, the results of cure‐time studies, and the kinetic parameters revealed that the thermal dissociation of the N‐methylaniline‐blocked polyisocyanates was retarded by electron‐donating substituents and facilitated by electron‐withdrawing substituents. The action of N‐methylanilines as blocking agents for isocyanate was explained by the formation of a four‐center, intramolecularly hydrogen‐bonded ring structure during the thermal dissociation of the blocked polyisocyanates. The formation of such a hydrogen‐bonded ring structure was confirmed and supported by variable‐temperature ¹H NMR studies and entropy parameters, respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1557–1570, 2007     

Influence of preparation methods on structure and properties of PA6/PA66 blends: A comparison of melt‐mixing and in situ blending

The blends composed of polyamide 6 (PA6) and polyamide 66 (PA66) were obtained using two different preparation methods, one of which was the melt‐mixing through a twin‐screw extruder and the subsequent injection molding; and the other, the in situ blending through anionic polymerization of ε‐caprolactam in the presence of PA66. For the former, there existed a remarkable improvement in toughness but a drastic drop in strength and modulus; however, for the latter, a reverse but less significant trend of mechanical properties change appeared. Various characterizations were conducted, including the analyses of crystalline morphology, crystallographic form, and crystallization and melting behaviors using polarized optical microscopy (POM), wide‐angle X‐ray diffraction (WAXD), and differential scanning calorimetry (DSC), respectively; observation of morphology of fractured surface with scanning electron microscope (SEM); measurement of glass transition through dynamic mechanical analysis (DMA); and the intermolecular interaction as well as the interchange reaction between the two components by Fourier transform infrared spectrometry (FT‐IR) and ¹³C solution NMR. The presence and absence of interchange reaction was verified for the in situ and melt‐mixed blends, respectively. It is believed that the transreaction resulted in a drop in glass transition temperature (T_g) for the in situ blends, contrary to an increase of T_g with increasing PA66 content for the melt‐mixed ones. And the two kinds of fabrication methods led to significant differences in the crystallographic form, spherulite size and crystalline content and perfection as well. Accordingly, it is attempted to explain the reasons for the opposite trends of changes in the mechanical properties for these two blends. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1176–1186, 2007     

Insight into chain dimensions in PEO/water solutions

Small‐Angle Neutron Scattering has been performed from poly(ethylene oxide) in deuterated water at temperature ranging from 10 to 80 °C. A simple fitting model was used to obtain a correlation length and a Porod exponent. The correlation length L characterizes the average distance between entanglements in the semidilute region and is proportional to the individual coil sizes in the dilute region. L was found to increase with temperature in the semidilute region but it decreases with temperature in the dilute region. This decrease is the precursor to the single‐chain collapse which applies to very dilute polymer solutions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2196–2200, 2007     

Viscometric properties of dilute polystyrene/dioctyl phthalate solutions

We report viscometric data collected in a Couette rheometry on dilute, single‐solvent polystyrene (PS)/dioctyl phthalate (DOP) solutions over a variety of polymer molecular weights (5.5 × 10⁵ ≤ M_w ≤ 3.0 × 10⁶ Da) and system temperatures (288 K ≤ T ≤ 318 K). In view of the essential viscometric features, the current data may be classified into three categories: The first concerns all the investigated solutions at low shear rates, where the solution properties are found to agree excellently with the Zimm model predictions. The second includes all sample solutions, except for high‐molecular‐weight PS samples (M_w ≥ 2.0 × 10⁶ Da), where excellent time–temperature superposition is observed for the steady‐state polymer viscosity at constant polymer molecular weights. No similar superposition applies at a constant temperature but varied polymer molecular weights, however. The third appears to be characteristic of dilute high‐molecular‐weight polymer solutions, for which the effects of temperature on the viscosity curve are further complicated at high shear rates. The implications concerning the relative importance of hydrodynamic interactions, segmental interactions, and chain extensibility with increasing polymer molecular weight, system temperature, and shear rate are discussed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 787–794, 2006     

An algebraic multigrid solver for Navier-Stokes problems

An efficient numerical method is presented for solving the equations of motion for viscous fluids. The equations are discretized on the basis of unstructured finite element meshes and then solved by direct iteration. Advective fluxes are temporarily fixed at each iteration to provide a linearized set of coupled equations which are then also solved by iteration using a fully implicit algebraic multigrid (AMG) scheme. A rapid convergence to machine accuracy is achieved that is almost mesh-independent. The scaling of computing time with mesh size is therefore close to the optimum.     

集值映射的切导数与向量优化问题的最优性条件

利用集值映射切导数与半可微概念，给出了无约束与具约束的集值向量优化问题局部真有效解与局部强有效解的最优性条件。