On circular–linear one-factorizations of the complete graph

In Korchmáros et al. (2018)one-factorizations of the complete graph $K_n$ are constructed for $n=q+1$ with any odd prime power $q$ such that either $q\equiv 1(mod4)$ or $q=2^h?1$. The arithmetic restriction $n=q+1$ is due to the fact that the vertices of $K_n$ in the construction are the points of a conic $\Omega$ in the finite plane of order $q$. Here we work on the Euclidean plane and describe an analogous construction where the role of $\Omega$ is taken by a regular $n$-gon. This allows us to remove the above constraints and construct one-factorizations of $K_n$ for every even $n\ge 6$.     

Edge proximity and matching extension in projective planar graphs

A graph $G$ with at least $2m+2$ vertices is said to be distance $d$ $m$-extendable if, for any matching $M$ of $G$ with $m$ edges in which the edges lie at distance at least $d$ pairwise, there exists a perfect matching of $G$ containing $M$. In this paper we prove that every 5-connected triangulation on the projective plane of even order is distance 3 7-extendable and distance 4 $m$-extendable for any $m$.     

Design of robust differential microphone arrays with the Jacobi–Anger expansion

Due to their small size, differential microphone arrays (DMAs) are very attractive. Moreover, they have been effective in combating noise and reverberation. Recently, a new class of DMAs of different orders have been developed with the MacLaurin’s series and the frequency-independent patterns. However, the MacLaurin’s series does not approximate well the exponential function, which appears in the general definition of the beampattern, when the intersensor spacing is not small enough. To circumvent this problem, we propose in this paper to approximate the exponential function with the Jacobi–Anger expansion. Based on this approximation and the frequency-independent Chebyshev patterns, we derive first-, second-, and third-order DMAs. Furthermore, in order to improve the robustness of DMAs against white noise amplification, we propose to use more microphones combined with minimum-norm filters. It is also shown that the Jacobi–Anger expansion is optimal from a mean-squared error perspective. Simulations are carried out to evaluate the performance of the proposed DMAs.     

Fe3O4@C Nanotubes Grown on Carbon Fabric as a Free-Standing Anode for High-Performance Li-Ion Batteries

Recently, Li-ion batteries (LIBs) have attracted extensive attention owing to their wide applications in portable and flexible electronic devices. Such a huge market for LIBs has caused an ever-increasing demand for excellent mechanical flexibility, outstanding cycling life, and electrodes with superior rate capability. Herein, an anode of self-supported Fe₃O₄@C nanotubes grown on carbon fabric cloth (CFC) is designed rationally and fabricated through an in situ etching and deposition route combined with an annealing process. These carbon-coated nanotube structured Fe₃O₄ arrays with large surface area and enough void space can not only moderate the volume variation during repeated Li⁺ insertion/extraction, but also facilitate Li⁺/electrons transportation and electrolyte penetration. This novel structure endows the Fe₃O₄@C nanotube arrays stable cycle performance (a large reversible capacity of 900 mA h g⁻¹ up to 100 cycles at 0.5 A g⁻¹) and outstanding rate capability (reversible capacities of 1030, 985, 908, and 755 mA h g⁻¹ at 0.15, 0.3, 0.75, and 1.5 A g⁻¹, respectively). Fe₃O₄@C nanotube arrays still achieve a capacity of 665 mA h g⁻¹ after 50 cycles at 0.1 A g⁻¹ in Fe₃O₄@C//LiCoO₂ full cells.     

Some useful integer arrays for the teaching of generalization skills

Teachers of first-year college mathematics and engineering courses must often spend considerable time reviewing material originally taught in high school. Instead of this being a mere exercise in repetition, this article suggests that such a review can enrich and revitalize by unifying some of the subjects that need to be re-taught. In the example presented, the subjects in question are absolute values, graphs and solutions of equations, and domains of definition. These are unified by the problem of finding an analytic expression for a square and triangle and their interiors. In the course of the development, basic notions such as the additive property of areas and convexity are introduced. The approach presented in the article was tried with secondary school teachers participating in professional development workshops and with students at a technical college; the teachers and students responded enthusiastically to the material.     

Proposition of a compensated pixelwise calibration for photonic infrared cameras and comparison to classic calibration procedures: Case of thermoelastic stress analysis

In this paper, we propose a compensated pixelwise calibration that integrates the effects of the camera housing temperature. The results of this calibration are compared on black body images to classic two points Non Uniformity Correction based calibrations, compensated or not. It is shown that the proposed approach leads to a significant improvement in the thermal resolution with a reduction in the mean error as well as the standard deviation. The approach is finally challenged on a real case measurement focusing on thermoelasticity. The gain in terms of accuracy measurement is highlighted by comparing the proposed calibration to classic calibrations and the scope of interest of this new calibration is discussed.     

Plasma generation in silicon-based inductive grid arrays

Selective illumination of a silicon wafer can be used for the construction of non-permanent inductive grids. A numerical model is used for the calculation of plasma density distribution in silicon as a function of time. Some indicative results on the microwave properties of the device are presented.     

Single molecule study of DNA collision with elliptical nanoposts conveyed by hydrodynamics

Periodic arrays of micro‐ or nanopillars constitute solid‐state matrices with excellent properties for DNA size separation. Nanofabrication technologies offer many solutions to tailor the geometry of obstacle arrays, yet most studies have been conducted with cylinders arranged in hexagonal lattices. In this report, we investigate the dynamics of single DNA collision with elliptical nanoposts using hydrodynamic actuation. Our data show that the asymmetry of the obstacles has minor effect on unhooking dynamics, and thus confirm recent predictions obtained by Brownian dynamics simulations. In addition, we show that the disengagement dynamics are correctly predicted by models of electrophoresis, and propose that this consistency is associated to the confinement in slit‐like channels. We finally conclude that elliptical posts are expected to marginally improve the performances of separation devices.     

Photoinduced alignment of polymer liquid crystals containing azobenzene moieties in the side group VII. On He-Ne laser beam irradiation

Photoinduced alignment in a polymer liquid crystal prepared from 6-{1-[4-(2-cyano-4-nitrophenylazo)phenyl]piperazino}hexyl acrylate and 4'-[6-(methacryloyloxy)hexyloxy]-4-cyanobiphenyl was investigated for the first time on irradiation with a polarized He-Ne laser beam at 633 nm. The azobenzene moieties as well as the inert cyanobiphenyl mesogenic units were aligned with the molecular long axis perpendicular to the polarization direction of the irradiation light. Alignment induced on short irradiation was reversible, while that induced under prolonged irradiation was irreversible due to the occurrence of crosslinking which might be caused by photoinduced decomposition of the azobenzene moieties during the photoirradiation process.