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.     

The effect of non-linear delay costs on workforce mix

This paper formulates a simple model to examine the appropriate mix of dedicated and flexible maintenance technicians (servers) required when total delay cost is a non-linear function of mean delay time. The primary decision variable is the number of flexible servers needed to minimize system-related costs. Non-linear delay costs appear to significantly increase the level of cross-training required compared with previous research using a linear cost function, which showed that a small proportion of flexible servers was sufficient. This has important implications for service system designers in regard to the amount of cross-training that might be appropriate.     

CO‐irredundant Ramsey numbers for graphs

The study of the CO‐irredundant Ramsey numbers t(n₁, ···, n_k) is initiated. It is shown that several values and bounds for these numbers may be obtained from the well‐studied generalized graph Ramsey numbers and the values of t(4, 5), t(4, 6) and t(3, 3, m) are calculated. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 258–268, 2000     

Quantum Dot Research: Current State and Future Prospects

This article reviews the current state of research involving semiconductor quantum dots, provides a brief review of the theory behind their unique properties, and an introduction explaining the importance of quantum dot research. The characteristic shifting of the band gap energy with quantum dot size, as predicted from the density of states for low-dimensional structures, allows experimental measurements to determine the extent to which quantum confinement effects play a role in the resulting properties. A few of the current techniques used to measure the presence and physical characteristics of quantum dots and their energy levels is reviewed, including transmission electron microscopy, optical transmission, and Raman and photoluminescence spectroscopy. Finally, some of the more exciting applications for quantum dots currently being researched for use in the field of optoelectronics are reviewed, including quantum dot infrared photodetectors, quantum dot lasers, and quantum dot solar cells. Comments are made on the current progress and the future prospects of quantum dot research and device applications.     

Rapid crack growth in a thermoelastic solid under mixed-mode thermomechanical loading

A two-dimensional steady-sate analysis of semi-infinite brittlecrack growth at a constant subcritical rate in an unboundedfully-coupled thermoelastic solid under mixed-mode thermomechanicalloading is made. The loading consists of normal and shear tractionsand heat fluxes applied as point sources (line loads in theout-of-plane direction). A related problem is solved exactly in an integral transformspace, and robust asymptotic forms used to reduce the originalproblem to a set of integral equations. The equations are partiallycoupled and exhibit operators of both Cauchy and Abel types,yet can be solved analytically. The temperature change field at a distance from the moving crackedge is then constructed, and its dominant term is found tobe controlled by the imposed heat fluxes. The role of this termis, indeed, enhanced if the heat fluxes serve to render thecrack as a net heat source/sink for the solid, as opposed tobeing a transmitter of heat across its plane. More generally,the influence of the thermoelastic coupling on this field, aswell as other functions, is found to increase with crack speed.     

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.