A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Accelerating Effect in Kerr-Newman-Kasuya Field

We have obtained expressions of the accelerating effect in Kerr-Newman Kasuya field. These expressionsinclude four parameters: mass m, angular momentum a, electric charge q, and magnetic charge φ. Furthermore we studyits special case (vi = 0). We get the following conclusion. In the gravitation field of souse mass with electric charge qand magnetic charge b, the acceleration of test particle has not only radial component but also transverse component.When θ = 0, the acceleration is minimum, and when θ = π/2, the acceleration is maximum. Furthermore, we discussthe effects of electric charge q and magnetic charge φ respectively.     

A new alternating‐direction finite element method for hyperbolic equation

A modified backward difference time discretization is presented for Galerkin approximations for nonlinear hyperbolic equation in two space variables. This procedure uses a local approximation of the coefficients based on patches of finite elements with these procedures, a multidimensional problem can be solved as a series of one‐dimensional problems. Optimal order H₀¹ and L² error estimates are derived. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

On path lengths modulo three

We show that between any two nodes of a cubic, planar, three-connected graph there are three paths whose lengths are 0, 1, and 2 modulo 3, respectively. The proof is by a rather extensive case analysis. Counterexamples show that all three hypotheses (i.e., planarity, degree-three, and three-connectivity) are necessary.     

Apparatus for High-Resolution Solid Hydrogen Matrix Isolation Spectroscopy and Its Application

Apparatus integrating a Fourier transform-infrared (FT-IR) spectrometer and a mid-infrared difference frequency generation (DFG) laser spectrometer was built for the study of the matrix isolation spectrum in solid molecular hydrogen. A 3-cm-long molecular hydrogen crystal was grown in a liquid-helium Dewar, and its infrared absorption spectrum in the 1-5 μm region was recorded to test the system. The W₀(0) (ν=0←0, J=6←0) line around 2410 cm⁻¹ of solid hydrogen was investigated with the DFG laser spectroscopy. High-resolution matrix isolation spectrum of CO² co-deposited with hydrogen on a BaF₂ cold plate at liquid-helium temperature was studied.     

Synthesis of optically active poly(N‐propargylsulfamides) with helical conformation

A novel chiral N‐propargylsulfamide monomer ( 1a ) and its enantiomer ( 1b ) were synthesized and polymerized with (nbd)Rh⁺B^?(C₆H₅)₄ as a catalyst providing poly(1) (poly( 1a ) and poly( 1b )) in high yields (≥99%). Poly(1) could take stable helices in less polar solvents (chloroform and THF), demonstrated by strong circular dichroism signals and UV–vis absorption peaks at about 415 nm and the large specific rotations; but in more polar solvents including DMF and DMSO, poly(1) failed to form helix. Quantitative evaluation with anisotropy factor showed that the helical screw sense had a relatively high thermal stability. These results together with the IR spectra measured in solvents showed that hydrogen bonding between the neighboring sulfamide groups is one of the main driving forces for poly(1) to adopt stable helices. In addition, copolymerization of monomer 1a and monomer 2 was conducted, the solubility of poly(1) was improved drastically. However, the copolymerization had adverse effects on the formation of stable helices in the copolymers. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 500–508, 2007     

Synthesis of grafted poly(p‐phenyleneethynylene) with energy donor–acceptor architecture via atom transfer radical polymerization: Towards nonaggregating and hole‐facilitating light‐emitting material

In this contribution, we demonstrate a new effective methodology for constructing highly efficient and durable poly(p‐phenyleneethynylene) (PPE) containing emissive material with nonaggregating and hole‐facilitating properties through the introduction of hole‐transporting blocks into the PPE system as the grafting coils as well as building the energy donor–acceptor architecture between the grafting coils and the PPE backbone. Poly(2‐(carbazol‐9‐yl)ethyl methacrylate) (PCzEMA), herein, is chosen as the hole‐transporting blocks, and incorporated into the PPE system as the grafting coils via atom transfer radical polymerization. The chemical structure of the resultant copolymer, PPE‐g‐PCzEMA, was characterized by NMR and gel permeation chromatography, showing that the desirable copolymer was obtained with the narrow polydispersity. The increased thermal stability of PPE‐g‐PCzEMA was confirmed by thermogravimetric analysis and differential scanning calorimetry along with its macroinitiator. The optoelectronic properties of this copolymer were studied in detail by ultraviolet‐visible absorption, photoluminescence emission and excitation spectra, and cyclic voltammogram (CV). The results indicate that PPE‐g‐PCzEMA exhibits the solid‐state luminescent property dominated by individual lumophores, and also the energy transfer process from the PCzEMA blocks to the PPE backbone with a relatively higher energy transfer efficiency in the solid‐state compared to that of the solution state. Additionally, the hole‐injection property is greatly facilitated due to the presence of PCzEMA, as confirmed by CV profiles. All these data indicate that PPE‐g‐PCzEMA is a good candidate for use in optoelectronic devices. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3776–3787, 2007     

Atom transfer radical polymerization directly from poly(vinylidene fluoride): Surface and antifouling properties

The direct preparation of grafting polymer brushes from commercial poly (vinylidene fluoride) (PVDF) films with surface‐initiated atom transfer radical polymerization (ATRP) is demonstrated. The direct initiation of the secondary fluorinated site of PVDF facilitated grafting of the hydrophilic monomers from the PVDF surface. Homopolymer brushes of 2‐(N,N‐dimethylamino)ethyl methacrylate (DMAEMA) and poly (ethylene glycol) monomethacrylate (PEGMA) were prepared by ATRP from the PVDF surface. The chemical composition and surface topography of the graft‐functionalized PVDF surfaces were characterized by X‐ray photoelectron spectroscopy, attenuated total reflectance/Fourier transform infrared spectroscopy, and atomic force microscopy. A kinetic study revealed a linear increase in the graft concentration of poly[2‐(N,N‐dimethylamino)ethyl methacrylate] (PDMAEMA) and poly[poly(ethylene glycol) monomethacrylate] (PPEGMA) with the reaction time, indicating that the chain growth from the surface was consistent with a controlled or living process. The living chain ends were used as macroinitiators for the synthesis of diblock copolymer brushes. The water contact angles on PVDF films were reduced by the surface grafting of DMAEMA and PEGMA. Protein adsorption experiments revealed a substantial antifouling property of PPEGMA‐grafted PVDF films and PDMAEMA‐grafted PVDF films in comparison with the pristine PVDF surface. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3434–3443, 2006     

Pulsed photothermal phase-shift spectroscopy for weak absorption measurement

A novel photothermal phase-shift spectroscopy configuration based on the retro-reflected beam interference has been developed and its operational principle is described. The weak absorption measurement ability of this technique is experimentally proven with a water/ethanol solution of standard Pyronine G dye and the limit of detection is found to be 1.8 x 10(-6) absorbance. Potential applications of the technique are discussed.