Observations on the determination of electron mean free paths from RF size effect measurements

Numerical calculations of the line shape of the rf size effect for 0.1 mm thick potassium plates in the transmission geometry at 1.25 MHz, show that the amplitude of the fundamental resonance is proportional to exp (?1.22d/l), while that of the second resonance is proportional to exp (?0.92d/l), whered andl are the plate thickness and electron mean-free path, respectively. In the case of the fundamental, our result differs significantly from the exp (?1.57d/l) dependence usually assumed for the purpose of determiningl, and indicates that the conventional analysis leads to an overestimate ofl by approximately 30%. The amplitude dependence found here can be explained physically in terms of the finite skin depth, and in the case of the second resonance, in terms of the strength of the electric field splash at the center of the plate.     

Loss effects on adhesively-bonded multilayer ultrasonic transducers by self-heating

Multilayer ultrasonic transducers are widely being used for high power applications. In these applications, typical Langevin/Tonpilz structures without any adhesive bondings however have the disadvantage of limited bandwidth. Therefore adhesively-bonded structures are still a potential solution for this issue. In this paper, two-layer piezoelectric ceramic ultrasonic transducers with two different adhesive bondlines were investigated comparing to a single-layer transducer in terms of loss effects during operation with excitation signals sufficient to cause self-heating. The theoretical functions fitted to the measured time–temperature dependency data are compared with experimental results of different piezoelectric transducers. Theoretical analysis of loss characteristics at various surface displacements and the relationship with increasing temperature are reported. The effects of self-heating on the practical performance of multilayer ultrasonic transducers with adhesive bondlines are discussed.     

Exploring the Link between Reformed Teaching Practices and Pupil Learning in Elementary School Mathematics

This study examined the classroom practices of beginning elementary school teachers' instruction of mathematics and how it connected to their pupils' learning. The Reformed Teaching Observation Protocol (RTOP) was used to measure the extent to which beginning teachers used reformed teaching practices. As a measure of pupil learning, we utilized assessment scores specific to the mathematics unit observed and correlated them with teachers' RTOP scores. We found that beginning teachers who implemented reformed teaching practices tended to have pupils who scored higher on the district mathematics test with a statistically significant correlation of 0.56 (p < .05). Implications of these findings and others are discussed in terms of using the RTOP to improve practice at the elementary school level and for future school‐based research.     

Using block designs in crossing number bounds

The crossing number $\mathrm{\text{CR}}\left(G\right)$ of a graph $G=\left(V,E\right)$ is the smallest number of edge crossings over all drawings of $G$ in the plane. For any $k\ge 1$, the $k$‐planar crossing number of $G,{\mathrm{\text{CR}}}_k\left(G\right)$, is defined as the minimum of $\text{CR}\left(G_1\right)+\text{CR}\left(G_2\right)+?+\text{CR}\left(G_k\right)$ over all graphs $G_1,G_2,\dots ,G_k$ with ${\cup }_{i=1}^k{G}_i=G$. Pach et al [Comput. Geom.: Theory Appl. 68 (2018), pp. 2–6] showed that for every $k\ge 1$, we have ${\text{CR}}_k\left(G\right)\le (2/k^2?1/k^3)\text{CR}\left(G\right)$ and that this bound does not remain true if we replace the constant $2/k^2?1/k^3$ by any number smaller than $1/k^2$. We improve the upper bound to $(1/k^2)\left(1+o\left(1\right)\right)$ as $k\to \infty$. For the class of bipartite graphs, we show that the best constant is exactly $1/k^2$ for every $k$. The results extend to the rectilinear variant of the $k$‐planar crossing number.     

Synthesis of 2,6-disubstituted piperazines by a diastereoselective palladium-catalyzed hydroamination reaction

A highly diastereoselective intramolecular hydroamination is the key step in a modular synthesis of 2,6-disubstituted piperazines. The requisite hydroamination substrates were prepared in excellent yields by nucleophilic displacement of cyclic sulfamidates derived from amino acids. A variety of alkyl and aryl substituents at the 2-position were tolerated. The stereochemistry of the piperazines was determined to be trans by X-ray crystallography, which also showed the preferred conformation of the 2,6-disubstituted piperazine to be a twist-boat due to A(1,3) strain.     

Homology and derived p-series of groups

We give homological conditions that ensure that a group homomorphisminduces an isomorphism modulo any term of the derived p –series, in analogy to Stallings's 1963 result for the p-lowercentral series. In fact, we prove a stronger theorem that isanalogous to Dwyer's extensions of Stallings’ results.It follows that spaces that are _p-homology equivalent have isomorphicfundamental groups modulo any term of their p-derived series.Various authors have related the ranks of the successive quotientsof the p-lower central series and of the derived p-series ofthe fundamental group of a 3-manifold M to the volume of M,to whether certain subgroups of ₁(M) are free, to whether finiteindex subgroups of ₁(M) map onto non-abelian free groups, andto whether finite covers of M are ‘large’ in variousother senses.     

Recent developments in the high-resolution gas chromatography of polychlorinated biphenyls.

The capillary gas chromatography of polychlorinated biphenyls (PCBs) is reviewed. Focus is on the most recent developments in the separation and detection of PCBs rather than sample preparation methods. Included are a comprehensive look at stationary phases that have been used to separate PCBs and the relatively new work on chiral separations of PCBs. Mass spectrometry and atomic emission are presented as selective detection techniques. Suggestions for additional research are proposed where appropriate.