The modified characteristic finite difference fractional steps method for the coupled system of fluid dynamics in porous media and its analysis

For the coupled system of multilayer fluid dynamics in porous media, the modified characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward and two‐dimensional and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L² norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 665–681, 2003.     

Prädikatives und funktionales Denken in der Wahrscheinlichkeitsrechnung

In order to emphasize functional thinking in mathematical education, arguments are brought forward for an early and frequent use of tree diagrams in teaching stochastics. Since set and tree diagrams can be regarded as two sides of the same matter, Bayes’ theorem, which is strongly associated with predicative set diagrams, need not be dealt with explicitly any longer. Set diagrams are replaced by tree diagrams that are labelled in detail and by tree inversion as a functional instrument of dealing with conditioned probabilities. This technique is demonstrated by three typical problems in the context of conditioned probability. Finally, two letters by Pascal to Fermat are analysed in order to illustrate that predicative and functional approaches were already pursued in the early stages of probability calculus in the 17^th century.     

Syntheses,crystal structures and blue emission of three zinc(II) coordination polymers with a 4,4′‐dicarboxybiphenyl sulfone ligand

Three novel zinc complexes [Zn(dbsf)(H₂O)₂] ( 1 ), [Zn(dbsf)(2,2′‐bpy)(H₂O)]·(i‐C₃H₇OH) ( 2 ) and [Zn(dbsf)(DMF)] ( 3 ) (H₂dbsf = 4,4′‐dicarboxybiphenyl sulfone, 2,2′‐bpy = 2,2′‐bipyridine, i‐C₃H₇OH = iso‐propanol, DMF = N,N‐dimethylformamide) were first obtained and characterized by single crystal X‐ray crystallography. Although the results show that all the complexes 1–3 have one‐dimensional chains formed via coordination bonds, unique three‐dimensional supramolecular structures are formed due to different coordination modes and configuration of the dbsf^2? ligand, hydrogen bonds and π–π interactions. Iso‐propanol molecules are in open channels of 2 while larger empty channels are formed in 3 . As compared with emission band of the free H₂dbsf ligand, emission peaks of the complexes 1–3 are red‐shifted, and they show blue emission, which originates from enlarging conjugation upon coordination. Copyright © 2006 John Wiley & Sons, Ltd.     

Synthesis and application as polymer electrolyte of hyperbranched polyether made by cationic ring‐opening polymerization of 3‐{2‐[2‐(2‐hydroxyethoxy)ethoxy]ethoxymethyl}‐3′‐methyl‐oxetane

A novel cyclic ether monomer 3‐{2‐[2‐(2‐hydroxyethoxy)ethoxy]ethoxy‐methyl}‐3′‐methyloxetane (HEMO) was prepared from the reaction of 3‐hydroxymethyl‐3′‐methyloxetane tosylate with triethylene glycol. The corresponding hyperbranched polyether (PHEMO) was synthesized using BF₃·Et₂O as initiator through cationic ring‐opening polymerization. The evidence from ¹H and ¹³C NMR analyses revealed that the hyperbranched structure is constructed by the competition between two chain propagation mechanisms, i.e. active chain end and activated monomer mechanism. The terminal structure of PHEMO with a cyclic fragment was definitely detected by MALDI‐TOF measurement. A DSC test implied that the resulting polyether has excellent segment motion performance potentially beneficial for the ion transport of polymer electrolytes. Moreover, a TGA assay showed that this hyperbranched polymer possesses high thermostability as compared to its liquid counterpart. The ion conductivity was measured to reach 5.6 × 10^?5 S/cm at room temperature and 6.3 × 10^?4 S/cm at 80 °C after doped with LiTFSI at a ratio of Li:O = 0.05, presenting the promise to meet the practical requirement of lithium ion batteries for polymer electrolytes. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3650–3665, 2006     

Synthesis,characterization, and electrical properties of polypyrrole/multiwalled carbon nanotube composites

Size‐controllable polypyrrole (PPy)/multiwalled carbon nanotube (MWCNT) composites have been synthesized by in situ chemical oxidation polymerization directed by various concentrations of cationic surfactant cetyltrimethylammonium bromide (CTAB). Raman spectra, FTIR, SEM, and TEM were used to characterize their structure and morphology. These results showed that the composites are core (MWCNT)–shell (PPy) tubular structures with the thickness of the PPy layer in the range of 20–40 nm, depending on the concentration of CTAB. Raman and FTIR spectra of the composites are almost identical to those of PPy alone. The electrical conductivities of these composites are 1–2 orders of magnitude higher than those of PPy without MWCNTs. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6449–6457, 2006     

Synthesis and characterization of polyimides derived from (3‐amino‐2,4,6‐trimethylphenyl)‐(3′‐aminophenyl)methanone and aromatic dianhydrides

A series of new polyimides were prepared via the polycondensation of (3‐amino‐2,4,6‐trimethylphenyl)‐(3′‐aminophenyl)methanone and aromatic dianhydrides, that is, 3,3′,4,4′‐biphenyltetracarboxylic dianhydride (BPDA), 4,4′‐oxydiphthalic anhydride, 3,3′,4,4′‐benzophenone tetracarboxylic dianhydride, and 2,2′‐bis(3,4‐dicarboxyphenyl) hexafluoropropane dianhydride. The structures of the polyimides were characterized by Fourier transform infrared and NMR measurements. The properties were evaluated by solubility tests, ultraviolet–visible analysis, differential scanning calorimetry, and thermogravimetric analysis. The two different meta‐position‐located amino groups with respect to the carbonyl bridge in the diamine monomer provided it with an unsymmetrical structure. This led to a restriction on the close packing of the resulting polymer chains and reduced interchain interactions, which contributed to the solubility increase. All the polyimides except that derived from BPDA had good solubility in strong aprotic solvents, such as N‐methyl‐2‐pyrrolidinone, N,N′‐dimethylacetamide, N,N‐dimethylformamide, and dimethyl sulfone, and in common organic solvents, such as cyclohexanone and chloroform. In addition, these polyimides exhibited high glass‐transition values and excellent thermal properties, with an initial thermal decomposition temperature above 470 °C and glass‐transition temperatures in the range of 280–320 °C. The polyimide films also exhibited good transparency in the visible‐light region, with transmittance higher than 80% at 450 nm and a cutoff wavelength lower than 370 nm. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1291–1298, 2006     

Characterization and electrical properties of polypyrrole/multiwalled carbon nanotube composites synthesized by in situ chemical oxidative polymerization

This study describes the preparation of polypyrrole (PPy)/multiwalled carbon nanotube (MWNT) composites by in situ chemical oxidative polymerization. Various ratios of MWNTs, which served as hard templates, were first dispersed in aqueous solutions with the surfactant cetyltrimethylammonium bromide to form micelle/MWNT templates and overcome the difficulty of MWNTs dispersing into insoluble solutions of pyrrole monomer, and PPy was then synthesized via in situ chemical oxidative polymerization on the surface of the templates. Raman spectroscopy, Fourier transform infrared (FTIR), field‐emission scanning electron microscopy (FESEM), and high‐resolution transmission electron microscopy (HRTEM) were used to characterize the structure and morphology of the fabricated composites. Structural analysis using FESEM and HRTEM showed that the PPy/MWNT composites were core (MWNT)–shell (PPy) tubular structures. Raman and FTIR spectra of the composites were almost identical to those of PPy, supporting the idea that MWNTs served as the core in the formation of a coaxial nanostructure for the composites. The conductivities of these PPy/MWNT composites were about 150% higher than those of PPy without MWNTs. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1413–1418, 2006     

Rapid determination of vitellogenin in fish plasma by anion exchange high performance liquid chromatography using postcolumn fluorescence derivatization with o-phthalaldehyde.

An analytical method involving anion exchange high performance liquid chromatographic determination of vitellogenin (Vtg) in fish plasma after postcolumn fluorescence derivatization with o-phthalaldehyde (OPA) was developed. The retention time of Vtg was about 11 min. The reagent variables for derivatization were optimized. The fluorophore was excited at 335 nm and detected at 435 nm. A calibration curve was established ranging from 0.13 to 11.28 microg. The determination limit of Vtg was found to be as low as 0.13 microg. The spiked recovery was 93.6% and interassay variability was less than 4%. The method developed was used to determine Vtg in fish plasma obtained from red sea bream (Pagrosomus major), black porgy (Sparus macrocephalus) and skew band grunt (Hapalogenys nitens), without complicated sample pretreatment. The results confirmed that the method showed advantages of being simple, rapid, reproducible and sensitive.     

Percolation and electrical resistivity in the YBa2Cu3O7−Ag composite system

We have measured the resistivity of the YBa₂Cu₃O₇–Ag composite system with Ag volume fraction,p _Ag ranging from 0–100%. The percolation behavior and the normal-state resistivity are studied. We find a three-dimensional threshold for the Ag matrix occurring atp _Ag 20% and a threshold for the superconducting matrix occurring at 1–p _Ag30%. The electrical resistivity is interpreted in terms of a resistivity model for granular YBa₂Cu₃O₇ proposed by Halbritter et al. [Z. Phys. B —Condensed Matter71, 411 (1988)]. Based on this model, we show that the resistivities between the YBa₂Cu₃O₇ grains and flaws in the grains are greatly diminished in the samples, indicating significantly improved grain growth behavior of the YBa₂Cu₃O₇ phase resulting from the addition of Ag. With the diminishing of the grain boundary resistivities, an intrinsic value for the temperature coefficient of resistivity, (1/gr)(d/dT), can be inferred, which is 3.3×10^–3/K at 300 K. This value is very close to that observed in the Cu–O₂ planes in single crystals and epitaxial films of YBa₂Cu₃O₇.