Avoiding abelian squares in partial words

Erd?s raised the question whether there exist infinite abelian square-free words over a given alphabet, that is, words in which no two adjacent subwords are permutations of each other. It can easily be checked that no such word exists over a three-letter alphabet. However, infinite abelian square-free words have been constructed over alphabets of sizes as small as four. In this paper, we investigate the problem of avoiding abelian squares in partial words, or sequences that may contain some holes. In particular, we give lower and upper bounds for the number of letters needed to construct infinite abelian square-free partial words with finitely or infinitely many holes. Several of our constructions are based on iterating morphisms. In the case of one hole, we prove that the minimal alphabet size is four, while in the case of more than one hole, we prove that it is five. We also investigate the number of partial words of length n with a fixed number of holes over a five-letter alphabet that avoid abelian squares and show that this number grows exponentially with n.     

Another look at complete positivity in generalized quantum dynamics: Reply to Raggio and Primas

In this rejoinder to a critique by Raggio and Primas of our paper, On Completely Positive Maps in Generalized Quantum Dynamics, we acknowledge that, contrary to our original assertion, the Bloch equations are indeed completely positive. We then explain briefly why this modification of our analysis does not alter its main conclusions.     

Molecular dynamics studies of brittle fracture in vitreous silica: Review and recent progress

The dynamics of brittle fracture in vitreous silica has been a subject of many molecular dynamics (MD) simulations and experiments. A striking similarity between both simulations and experiments is the observation of nanoscale voids that eventually coalesce leading to failure. In this work, we review the above MD simulations and carry out further MD investigations using two variations of classical 2-body potentials. We study the effect of charge-transfer, an important aspect neglected by previous simulations. Further, we examine the growth of ‘critical’ voids and characterize regions surrounding the voids.     

Amber‐Woody Scent: Alcohols with Divergent Structure Present Common Olfactory Characteristics and Sharp Enantiomer Differentiation

Only one out of the four possible trans isomers of the important perfumery alcohol Norlimbanol^® ( 1 ) possesses a very strong amber‐woody smell, the isomer 1A with (1′R,3S,6′S) absolute configuration. Its enantiomer 1B is almost odorless and devoid of amber‐woody character, whereas the diastereoisomers 1C and 1D are considerably weaker and perceptible only by the most‐sensitive persons. The same is true for a whole series of perceptual analogs of 1 , including β‐alkoxy alcohols. These ethers belong to two structural classes: [(2,2,6‐trimethylcyclohexyl)oxy]‐ (see 3, 4 , and 16 ) or {[2‐(tert‐butyl)cyclohexyl]oxy}alkan‐2‐ol derivatives (see 19 and 20 ; Table). A superimposition model allowing for good overlap of the respective hydroxylated side chains offers a tentative explanation for the shared perceptual characteristics of the two classes (Fig. 5). The lipophilic cyclohexane moieties present only a minimal overlap in this model, suggesting that quite larger molecules might possess the same smell. (S)‐Configured β‐alkoxy alcohols can conveniently be obtained on a larger scale by enantioselective reduction of the corresponding ketones (Scheme 9).     

Origin of the oscillator strength of the triplet state of a trion in a magnetic field

The dynamics of the spin-triplet trion state, under high magnetic field in a GaAs/AlGaAs quantum well, are studied using time resolved spectroscopy. The oscillator strength of the triplet transition is shown to rise with increasing electron density, in good agreement with a theoretical model where the trion interacts with excess electrons in the quantum well. This analysis suggests that the spin-triplet trion state, which is expected to be an optically "dark" state, is experimentally observable due to the interactions with the excess electrons, demonstrating that X- cannot be regarded as an isolated three particle complex.     

Kondo effect in a quantum antidot

We report Kondo-like behavior in a quantum antidot (a submicron depleted region in a two-dimensional electron gas) in the quantum-Hall regime. When both spins of the lowest Landau level are present all around the antidot, the resonances between extended edge states via antidot bound states show an abnormal feature in alternate Coulomb-blockaded regions. The feature becomes suppressed when the temperature or source-drain bias is raised as for Kondo resonances in quantum dots. Although the exact mechanism is unknown, Kondo-like correlated tunneling may arise from a Skyrmion-type edge reconstruction. This observation demonstrates the generality of the Kondo phenomenon.     

Maximal non- hamilton-laceable graphs

For bipartite graphs the property of being Hamilton laceable is analogous to the property of being Hamilton connected for simple graphs. in this paper it is proven that all of the graphs obtained by deleting fewer than m ? 1 edges from either of the complete bipartite graphs K_{m, m} or K_{m, m+1} are Hamilton laceable. It is also proven that the deletion of m ? 1 edges results in a non-Hamiltonlaceable graph if and only if the graph is either the complement of the star K_1,m?1 in K_{m, m} or K_{m, m+1} or else the complement in K_3,3 of a pair of nonadjacent edges.     

Shock wave interaction with laser-generated single bubbles

The interaction of a lithotripter shock wave (LSW) with laser-generated single vapor bubbles in water is investigated using high-speed photography and pressure measurement via a fiber-optic probe hydrophone. The interaction leads to nonspherical collapse of the bubble with secondary shock wave emission and microjet formation along the LSW propagation direction. The maximum pressure amplification is produced during the collapse phase of the bubble oscillation when the compressive pulse duration of the LSW matches with the forced collapse time of the bubble.     

Synthesis and characterization of near‐monodisperse electron acceptor homopolymers of 2‐[(3,5‐dinitrobenzoyl)oxy]ethyl methacrylate

Homopolymers of 2‐(trimethylsiloxy)ethyl methacrylate of degrees of polymerization from 5 to 50 were synthesized by group transfer polymerization in tetrahydrofuran (THF) using 1‐methoxy‐1‐(trimethylsiloxy)‐2‐methyl propene as the initiator and tetrabutylammonium bibenzoate as the catalyst. These polymers were first converted to poly[2‐(hydroxy)ethyl methacrylate]s by removal of the trimethylsilyl‐protecting groups by acidic hydrolysis, and subsequently transformed to poly{2‐[(3,5‐dinitrobenzoyl)oxy]ethyl methacrylate}s by reaction with 3,5‐dinitrobenzoyl chloride in the presence of triethylamine. Gel permeation chromatography in THF and proton nuclear magnetic resonance (¹H NMR) spectroscopy in CDCl₃ and d₆ dimethyl sulfoxide were used to characterize the polymers in terms of their molecular weight and composition. The molecular weights were found to be close to the values expected from the polymerization stoichiometry and the molecular weight distributions were narrow, with polydispersity indices around 1.1. The hydrolysis and reesterification steps were found to be almost quantitative for all polymers. Differential scanning calorimetry and thermal gravimetric analysis were also employed to measure the glass transition temperatures (T_g 's) and decomposition temperatures, which were determined to be approximately 80 and 320 °C, respectively. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1457–1465, 2000