Cellulose dimethylphenylcarbamate-bonded carbon-clad zirconia for chiral separation in high performance liquid chromatography.

Porous zirconia particles are very robust material and have received considerable attention as a stationary phase support for HPLC. We prepared cellulose dimethylphenylcarbamate-bonded carbon-clad zirconia (CDMPCCZ) as a chiral stationary phase (CSP) for separation of enantiomers of a set of 14 racemic compounds in normal phase (NP) and reversed-phase (RP) liquid chromatography. Retention and enantioselectivity on CDMPCCZ were compared to those on CDMPC-coated zirconia (CDMPCZ) to see how the change in immobilization method of the chiral selector affects the retention and chiral selectivity. In NPLC, retention was longer and the number of resolved racemates was smaller on CDMPCCZ than on CDMPCZ. However, chiral selectivity factors for some resolved racemates were better on CDMPCCZ than on CDMPCZ. The longer retention on CDMPCCZ is likely due to strong, non-chiral discriminating interactions with the carbon layer on CDMPCZ. In RPLC only two racemates were resolved on CDMPCCZ, but retention times were shorter than, and resolutions were comparable to, those in NPLC, indicating a potential for improving chromatographic performance of the CDMPCCZ column in RPLC with optimized column preparation and separation conditions.     

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 efficient construction of period-2 bulbs in the cubic Mandelbrot set with parametric boundaries

A parametric boundary equation is established for the principal period-2 bulb in the cubic Mandelbrot set. Using its geometry, an efficient escape-time algorithm which reduces the construction time for the period-2 bulbs in the cubic Mandelbrot set is introduced and the implementation graphic results display the fascinating fractal beauty     

Entanglement system,Casimir energy and black hole

We investigate the connection between the entanglement system in Minkowski spacetime and the black hole using the scaling analysis. Here we show that the entanglement system satisfies the Bekenstein entropy bound. Even though the entropies of two systems are the same form, the entanglement energy is different from the black hole energy. Introducing the Casimir energy of the vacuum energy fluctuations rather than the entanglement energy, it shows a feature of the black hole energy. Hence the Casimir energy is more close to the black hole than the entanglement energy. Finally, we find that the entanglement system behaves like the black hole if the gravitational effects are included properly.     

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.     

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.