Avoiding Patterns in the Abelian Sense

We classify all 3 letter patterns that are avoidable in the abelian sense. A short list of four letter patterns for which abelian avoidance is undecided is given. Using a generalization of Zimin words we deduce some properties of ω-words avoiding these patterns.Research of both authors supported by NSERC Operating Grants.https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/avoiding-patterns-in-the-abelian-sense/42148B0781A38A6618A537AAD7D39B8

Teacher Perceptions of Parent Involvement in Literacy Education

Parent involvement appears to hold great potential for the improvement of literacy education. Without the coordination and support ofthe classroom teacher, however, the effects of such involvement may not be maximized. A question central to the development of parent involvement programs is, Do teachers recognize and support parent involvement as a significant component of children\u27s education? The purpose of this informal study was to describe perceptions of parent involvement in literacy education. Over sixty teachers from a cross section of schools in a Midwestern metropolitan area were interviewed in depth about their attitudes toward parent involvement in reading. A structured interview combining closed and open-ended questions was used to gather data. Results indicated that teacher perceptions of what constitutes parent involvement differed by grade level. Over 90 percent of the teachers recognized the importance of involving parents. Less than 5 percent, however, supported involving parents as partners. Teacher perceptions of the role of parents appeared to restrict involvement and limit dialogue

Differential Dynamic Microscopy of Bacterial Motility

We demonstrate 'differential dynamic microscopy' (DDM) for the fast, high throughput characterization of the dynamics of active particles. Specifically, we characterize the swimming speed distribution and the fraction of motile cells in suspensions of Escherichia coli bacteria. By averaging over ~10^4 cells, our results are highly accurate compared to conventional tracking. The diffusivity of non-motile cells is enhanced by an amount proportional to the concentration of motile cells.Comment: 4 pages, 4 figures. In this updated version we have added simulations to support our interpretation, and changed the model for the swimming speed probability distribution from log-normal to a Schulz distribution. Neither modification significantly changes our conclusion

Enhanced gas-liquid mass transfer of an oscillatory constricted-tubular reactor

The mass transfer performance has been tested for gas-liquid flow in a new tubular reactor system, the oscillating mesotube (OMT), which features the oscillatory movement of fluid across a series of smooth constrictions located periodically along the vertical 4.4 mm internal diameter tube. The effect of the fluid oscillations (frequency,f, and center-to-peak amplitude, x(0), in the range of 0-20 s(-1) and 0-3 mm, respectively) on the overall volumetric mass transfer coefficient (k(L)a) has been tested by measuring the oxygen saturation levels with a fiber-optical microprobe (oxygen micro-optrode), and a mathematical model has been produced to describe the oxygen mass transport in the OMT. The oxygen mass transfer rates were about I order of magnitude higher (k(L)a values up to 0.16 s(-1)) than those values reported for gas-liquid contacting in a 50 mm internal diameter oscillatory flow reactor (OFR), for the same peak fluid oscillatory velocity, i.e., 2 pi fx(0). This represents remarkable oxygen transfer efficiencies, especially when considering the very low mean superficial gas velocity involved in this work (0.37 mm s(-1)). The narrower constrictions helped to increase the gas fraction (holdup) by reducing the rise velocity of the bubbles. However, the extent of radial mixing and the detachment of vortex rings from the surface of the periodic constrictions are actually the main causes of bubbles retention and effective gas-liquid contacting and are, thus, responsible for the enhancement of k(L)a in the OMT.N.R. thanks the Portuguese Foundation for Science and Technology (FCT) for financial support of his work (SFRH/BD/6954/2001)

Transport and Noise Properties of sub-100-nm Planar Nb Josephson Junctions with Metallic Hf-Ti Barriers for nano-SQUID Applications

We analyze electric transport and noise properties at 4.2 K of self-shunted superconductor-normal metal-superconductor (SNS) sandwich-type Josephson junctions, comprising Nb as the superconductor and Hf-Ti as the normal conducting material, with lateral dimensions down to approximately 80 nm. The junctions are fabricated with an optimized multilayer Nb technology based on nanopatterning by electron-beam lithography and chemical-mechanical polishing. The dependence of transport properties on the junction geometry (lateral size and barrier thickness d(Hf-Ti)) is studied, yielding a characteristic voltage V-c up to approximately 100 mu V for the smallest d(Hf-Ti) = 17 nm. The observed small hysteresis in the current-voltage curves of devices with high V-c and large size can be attributed to self-heating of the junctions and fitted with an extended version of the resistively shunted junction model. Measurements of voltage noise of single junctions are consistent with the model including self-heating effects. The potential of our technology for further miniaturization of nanoscale superconducting quantum interference devices and for the improvement of their performance is discussed

Determination of mass transfer resistances of fast reactions in three-phase mechanically agitated slurry reactors

A methodology for the determination of mass transfer resistances of fast reactions in three-phase mechanically agitated slurry reactors under the reaction conditions is presented. The mass transfer resistances affect significantly the overall mass transfer rate, the design equation and consequently the scale up of the reactor. There is not established methodology to separate the mass transfer resistances under reaction conditions by changing catalyst loading and manipulating the process variables, pressure and agitation speed. This allows to avoid the use of different catalyst particles and give the chance to calculate the mass transfer resistances without caring about the type of catalyst. We calculate each mass transfer resistance under conditions which do not allow to neglect any of the resistances. It is shown that the level off of mass transfer rate which is developed in the plot of mass transfer rate against agitation speed plots is not enough to determine the limiting regime. The hydrogenation of styrene over Pd/C (5% catalyst content) is used as case study to demonstrate the methodology

YBa2Cu3O7 and Nb NanoSQUIDs for the Investigation of Magnetization Reversal of Individual Magnetic Nanoparticles

We report on the fabrication, performance and application of sensitive YBa2Cu3O7 (YBCO) and Nb nanoSQUIDs to magnetization reversal measurements of individual magnetic nanoparticles. The YBCO SQUIDs are based on grain boundary Josephson junctions and are patterned in a single layer of epitaxially grown YBCO films by Ga focused ion beam milling. The Nb SQUIDs contain sandwich-type Josephson junctions with normal conducting HfTi barriers; they are fabricated with a multilayer technology that includes patterning by e-beam lithography and a combination of milling techniques and chemical-mechanical polishing. Due to the small inductance of the SQUID loops, ultralow white flux noise at 4.2 K can be achieved, which yields spin sensitivities of down to a few Bohr magnetons per unit bandwidth for a magnetic nanoparticle placed at 10 nm distance to the SQUID loop

Filling an Emulsion Drop with Motile Bacteria

We have measured the spatial distribution of motile Escherichia coli inside spherical water droplets emulsified in oil. At low cell concentrations, the cell density peaks at the water-oil interface; at increasing concentration, the bulk of each droplet fills up uniformly while the surface peak remains. Simulations and theory show that the bulk density results from a `traffic' of cells leaving the surface layer, increasingly due to cell-cell scattering as the surface coverage rises above $\sim 10\%$. Our findings show similarities with the physics of a rarefied gas in a spherical cavity with attractive walls.Comment: 5 pages, 4 figures, Supporting Information (5 pages, 5 figures