Spectra and Transport in Almost Periodic Dimers

We study spectral properties of discrete Schrödinger operators with potentials obtained via dimerization of a class of aperiodic sequences. It is shown that both the nature of the autocorrelation measure of a regular sequence and the presence of generic (full probability) singular continuous spectrum in the hull of primitive and palindromic (four block substitution) potentials are robust under dimerization. Generic results also hold for circle potentials. We illustrate these results with numerical studies of the quantum mean square displacement as a function of time. The numerical techniques provide a very fast algorithm for the time evolution of wave packets.     

Finite-Band Potentials with Trigonal Curves

We construct Dubrovin equations and trace formulas for finite-band operators with trigonal curves and present some examples.     

Generalized lattice model of liquid state and its relation to Ginzburg–Landau theory

Basic principles of the generalized lattice model of multicomponent condensed systems are formulated. Short-range parts of interatomic interactions are taken into account by means of the geometric constraints method. Long-range parts of the interactions are taken into account in mean field approximation. The expression for Helmholtz free energy is obtained. A system of integral equations for the equilibrium distributions of components is derived. The asymptotic properties of its solutions are investigated. Moment expansion of interatomic interactions and localization of integral terms in free energy is obtained. A Ginzburg–Landau-like functional of free energy is derived.     

Effects of self evaluation on late ERP components

High-density event-related potentials (ERPs) were measured when participants were required to evaluate oneself, significant others (father and mother) and the most familiar public figures (Lei Feng and Jiang Qing) based on trait adjectives. There were three referential conditions and a non-referential control condition including self-evaluation (SE), significant other-evaluation (SOE), general other-evaluation (GOE), and semantic positivity-evaluation (SPE). The behavioral data showed that RTs to GOE condition were longer than the other three conditions. Scalp ERP analysis revealed that (1) SPE condition elicited a more negative N2 than SE condition, which was associated with inhibition of responses; (2) SE condition elicited a more positive P300 than SPE condition, which was an index of attention to self-relevant stimuli; (3) there was no difference on the amplitude and latency of P300 between SE and SOE conditions, which reflected that the concept of “self” included intimate others (e.g., father and mother) in Chinese culture.     

Structure and Structural Nonrigidity of Tetrachlorodibenzo-p-Dioxin Radical Cations

Ab initio calculations showed that the tetrachlorodibenzo-para-dioxin radical cations (TCDD RCs) with a planar structure have two steady states with asymmetric dioxin cycles. The activation barriers between these states are up to 2 kcal/mole, so that the RCs may be regarded as being structurally nonrigid within the dioxin cycle. The 2,3,7,8-TCDD RC is more stable than the 1,4,6,9-TCDD RC, the energy difference being 5.2 kcal/mole. The adiabatic ionization potential of 2,3,7,8-TCDD (7.54 eV) is 0.1 eV smaller than the corresponding potential of 1,4,6,9-TCDD. These factors account for the increased hemoproteide affinity and hence increased biological activity of 2,3,7,8-TCDD.     

Performance of various activators in ethylene polymerization based on an iron(II) catalyst system

Ethylisobutylaluminoxane (EBAO) and its analogues were synthesized by a reaction between an triethylaluminum (Et₃Al)/triisobutylaluminum (i‐Bu₃Al) mixture and 4‐fluorobenzeneboronic acid, phenylboronic acid, or n‐butaneboronic acid and subsequent hydrolysis with water. They were used as cocatalysts in ethylene polymerization catalyzed by an iron complex {[(ArN?C(Me))₂C₅H₃N]FeCl₂, where Ar is 2,6‐diisopropylphenyl}. Polyethylene with a high molecular weight and a narrow molecular weight distribution was prepared with modified EBAOs, and the performance of the iron complex at high polymerization temperatures was greatly improved. The activators for the iron complex also affected the polymerization activity and the molecular weight of the resultant polyethylene. It was suggested that the stereo and electronic effects of the substitute groups of aluminoxane contributed to the improved performance of the new activators. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1093–1099, 2004     

Spectral Theory for Slowly Oscillating Potentials II. Schrödinger Operators

This paper continues the investigation about the singularity theory in dual rich quasi–Banach spaces given in T. Runst [Ru 2]. The abstract results are applied to the study of the solution structure of semilinear elliptic boundary value problems in spaces of Besov – Triebel – Lizorkin type.     

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.     

An ERP study for the degrees of the difficulty in visual search

The present study mainly probed the relationships between ERP components and the degrees of difficulty in visual search. Three experimental and one controlled conditions were randomly selected. Results showed that the P1, N1, and P2 amplitudes and latencies had no significant differences among the three experimental and one controlled conditions, and the ERP waveforms of low perceptual load of visual search were different from that of high perceptual load. These results might indicate that the latencies and amplitudes of initial P1, N1 and P2 in high and low perceptual load conditions were almost the same. The ERP waveforms of parallel search were very different from that of serial search, and the ERP waveforms of serial search were very similar. The P3 amplitudes increased as the degrees of the difficulty in visual search decreased.     

Looking at Fokker-Planck dynamics with a noisy instrument

We consider the class of experiments which can be characterized by a Fokker-PIanck dynamics corresponding to the overdamped motion of a state point in a suitable stochastic potential. We assume that the general form of the potential is known (or can be guessed with reasonable accuracy), but that its parameters are to be determined experimentally by measurements made with a noisy instrument. This possible method for determining the potential parameters, which exploits the system's own internal stochastic motion in order to explore rapidly its available parameter space, is substantially more efficient than traditional methods involving time averages of single point measurements, and yet does not appear to have been previously considered. The method could be important when, for example, the experiment must be completed in a limited time owing either to the expense of the experimental materials or to the temporary stationarity of the preparation, situations which are commonly encountered in experimental biochemistry and biology.