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     

Measuring length of business cycles across countries using a new non‐stationary unit‐root cyclical approach

This article examines the length of the cycles in the gross domestic product (GDP) real per capita series of 15 countries by means of new statistical techniques based on unit root cycles. We propose tests for unit root cycles at each of the frequencies of the process. Using this approach, we are able to approximate the number of periods per cycle. The results show that the cycles have a periodicity of approximately six years when the disturbances are white noise. However, if we permit autocorrelation, they may also occur at smaller intervals of time. Copyright © 2006 John Wiley & Sons, Ltd.     

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     

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.     

Locating and counting bifurcation points of satellite components from the main component in the degree-n bifurcation set

The bifurcation point where a satellite component buds from another component is characterized by the existence of the common tangent line between the two osculating components appearing in the degree-n bifurcation set. We investigate the existence, location and number of bifurcation points for satellite components budding from the main component in the degree-n bifurcation set as well as a parametric boundary equation of the main component of the degree-n bifurcation set. Cusp points are also located on the boundary of the main component. Typical degree-n bifurcation sets and their components are illustrated with some computational results.