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.     

Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds

This paper is devoted to the proof of almost global existence results for Klein‐Gordon equations on Zoll manifolds (e.g., spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof relies on Birkhoff normal form methods and on the specific distribution of eigenvalues of the Laplacian perturbed by a potential on Zoll manifolds. © 2007 Wiley Periodicals, Inc.     

Einstein relation in chemically doped organic semiconductors

Based on the assumption of Gaussian energy distributions of the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO), analytical expressions of generalized Einstein relation in chemically doped organic semiconductor are developed, by approximation of Coulomb traps with a rectangle potential well. Numerical calculations show that traditional Einstein relations do not hold for chemically doped organic semiconductors. Similar to physical doping, the dependence of diffusion coefficient to mobility D/μ ratio on the carrier concentration has a maximum. An essential difference between chemical doping and physical doping is that, the D/μ ratio in chemically doped organic semiconductors depends not only on carrier concentration and doping concentration, but also on the applied electric field. PACS 71.20.Rv; 72.90.+y; 73.50.-h     

A note on model diagnostics in longitudinal data analysis

Longitudinal study has become one of the most commonly adopted designs in medical research. The generalized estimating equations (GEE) method and/or mixed effects models are employed very often in causal inferences. The related model diagnostic procedures are not yet fully formalized, and perhaps never will be. The potential causes of major problems are the high variety of the dependence within subjects and/or the number of repeated measurements. A single testing procedure, e.g., run test, is not possible to resolve all model diagnostics problems in longitudinal data analysis. Multiple quantitative indexes for model diagnostics are needed to take into account this variety. We propose eight testing procedures for randomness accompanied with some conventional and/or non-conventional plots to remedy model diagnostics in longitudinal data analysis. The proposed issue in this paper is well illustrated with four clinical studies in Taiwan.     

Vibrational EELS and DFT study of propionic acid and pyruvic acid on Ni(1 0 0): Effects of keto group substitution on room-temperature adsorption and thermal chemistry

The room-temperature adsorption and thermally induced processes of propionic acid and pyruvic acid on Ni(1 0 0) have been investigated by electron energy loss spectroscopy (EELS). Computational vibrational analysis of the optimized bidentate structures for acid-Ni model complexes (involving the organic acid and a Ni atom) has been performed by using the two-layer ONIOM method with the Density Functional Theory and used to interpret the vibrational EELS data. Dehydrogenation of the hydroxyl group is found to result in bonding of the carboxylate group in the propionate and pyruvate adspecies to either a single Ni surface atom in a bidentate configuration or two neighbouring Ni atoms in a bridge configuration. Given the similarities in the total energies and related vibrational frequencies obtained by the calculations in the case of pyruvate adspecies, it is difficult to differentiate the alternate adsorption structure, in which the keto O and hydroxyl O atoms are bonded to a Ni atom in a five-member chelate ring configuration. Furthermore, temperature-dependent EELS studies show that both the propionate and pyruvate adspecies could decompose upon annealing to above 400 K and further dissociate to CO adspecies above 550 K and to C and/or O above 600 K.     

The electron ionization rate in multilayered semiconductor structures

We present theoretical results of the electron impact ionization rate in GaAs/AlGaAs multiquantum well structures as a function of applied electric field for various geometries, i.e., well and barrier widths. In addition, we present preliminary measurements of the current-voltage characteristics of MBE grown devices which demonstrate very low leakage current as well as sharp breakdwon behavior. It is found that the net ionization rate, determined by averaging over the constitutent GaAs and AlGaAs layers, approaches the weighted average of the constituent bulk rates at high electric field strengths; the potential discontinuity is relatively unimportant. The electron ionization rate within the well regions alone is still higher than that in bulk GaAs, but is insufficiently enhanced to compensate for the much lower rate in the AlGaAs layers. As the field is lowered to 250.0 kV/cm, the average ionization rate in the multiquantum well structure becomes larger than in the bulk.     

Studies on calcium‐containing poly(urethane ether)s

The calcium salt of mono(hydroxyethoxyethyl)phthalate [Ca(HEEP)₂] was synthesized by the reaction of diethylene glycol, phthalic anhydride, and calcium acetate. Calcium‐containing poly(urethane ether)s (PUEs) were synthesized by the reaction of hexamethylene diisocyanate (HMDI) or tolylene 2,4‐diisocyanate (TDI) with a mixture of Ca(HEEP)₂ and poly(ethylene glycol) (PEG₃₀₀ or PEG₄₀₀) with di‐n‐butyltin dilaurate as a catalyst. A series of calcium‐containing PUEs of different compositions were synthesized with Ca(HEEP)₂/PEG₃₀₀ (or PEG₄₀₀)/diisocyanate (HMDI or TDI) molar ratios of 2:2:4, 3:1:4, and 1:3:4 so that the coating properties of the PUEs could be studied. Blank PUEs without calcium‐containing ionic diols were also prepared by the reaction of PEG₃₀₀ or PEG₄₀₀ with HMDI or TDI. The PUEs were well characterized by Fourier transform infrared, ¹H and ¹³C NMR, solid‐state cross‐polarity/magic‐angle‐spinning ¹³C NMR, viscosity, solubility, and X‐ray diffraction studies. The thermal properties of the polymers were also studied with thermogravimetric analysis and differential scanning calorimetry. The PUEs were applied as top coats on acrylic‐coated leather, and their physicomechanical properties were also studied. The coating properties of PUEs, such as the tensile strength, elongation at break, tear strength, water vapor permeability, flexing endurance, cold crack resistance, abrasion resistance, color fastness, and adhesive strength, were better than the standard values. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2865–2878, 2003     

Large deviations for random walks in a mixing random environment and other (non‐Markov) random walks

We extend a recent work by S. R. S. Varadhan [8] on large deviations for random walks in a product random environment to include more general random walks on the lattice. In particular, some reinforced random walks and several classes of random walks in Gibbs fields are included. © 2004 Wiley Periodicals, Inc.