Controlling global stochasticity of Hamiltonian systems by nonlinear perturbation

A method of controlling global stochasticity in Hamiltonian systems by applying nonlinear perturbation is proposed. With the well-known standard map we demonstrate that this control method can convert global stochasticity into regular motion in a wide chaotic region for arbitrary initial condition, in which the control signal remains very weak after a few kicks. The system in which chaos has been controlled approximates to the original Hamiltonian system, and this approach appears robust against small external noise. The mechanism underlying this high control efficiency is intuitively explained. Received 15 January 2002 Published online 6 June 2002     

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.     

La5Al3Ni2 – an Intermetallic Phase Observed upon Crystallization of La50Al25Ni25 Metallic Glass

The yet unknown intermetallic phase La₅Al₃Ni₂ was obtained by partially crystallizing amorphous La₅₀Al₂₅Ni₂₅ at 550 K (further heating above 600 K leads to irreversible disappearance of this phase), and its crystal structure was determined from X‐ray powder diffraction data. The crystal structure of the La₅Al₃Ni₂ phase constitutes a new structure type (Cmcm, a = 14.231Å, b = 6.914Å, c = 10.460Å, oC40) and is built from [Al₃Ni₂] chains surrounded by La atoms. In the ternary system La‐Al‐Ni La₅Al₃Ni₂ is located on the section La₅₀Al_50−nNi_n (0 ≤ n ≤ 50) with the binary compounds LaAl and LaNi as end members. Strikingly, also the crystal structures of the end members can be conceived as chain structures with Al and Ni chains surrounded by La, respectively.     

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.     

Trovacenchemie. 13 [1] Weg und Irrweg zu Di([5]trovacenyl)keton

Trovacene Chemistry. 13 [1] On Being Lead and Mislead in the Synthesis of Di([5]trovacenyl)ketone Di([5]trovacenyl)ketone ( 3¨ ) has been prepared from lithio‐[5]trovacene and dimethylcarbamoyl chloride and studied by X‐ray diffraction, cyclic voltammetry, magnetic susceptometry and EPR spectroscopy. Slight variation of the synthetic protocol affords an unusual trinuclear complex 5 ? that is also fully characterized. Spin‐spin exchange interaction is smaller in 3¨ than in 1,1‐di([5]trovacenylethene ( 2¨ ), which differs from 3¨ by a replacement of O for CH₂. The novel trinuclear complex 5 ? , however, displays exchange coupling very similar to that observed in 1‐methoxy‐2,5,6‐tri([5]trovacenyl)benzene ( 7 ? ). In both cases, an unsymmetrical triangular arrangement of S = 1/2 centers is encountered. These findings are discussed in terms of the nature of the respective spacers.