Algebraic curves admitting the same Galois closure for two projections

A criterion for the existence of a plane model of an algebraic curve such that the Galois closures of projections from two points are the same is presented. As an application, it is proved that the Hermitian curve in positive characteristic coincides with the Galois closures of projections of some plane curve from some two non-uniform points.Comment: 6 page

The Chernoff Modification of the Fisher Exact Test for the Difference of Two Binomial Probabilities

To test the difference of two binomial probabilities, we will apply the Fisher exact test modified by Chernoff (2002), which will be called CMF test. The key idea is to use the P-value of Fisher exact test as a test statistic and this makes it possible to apply the Fisher exact test for more general problems. The numerical comparison with the likelihood ratio test and the Bayes test are also conducted and we find that the performance of CMF test is close to that of the likelihood ratio test and it is satisfactory in various situations. We also give a Kullback-Leibler information number of the margins to for the testing problems which justify the stability of P-values of CMF test.Fisher Exact Test, Binomial Probabilities, Chernoff Modification, Test of Difference of Probabilities

Clonal spread of antimicrobial-resistant Escherichia coli isolates among pups in two kennels

Although the dog breeding industry is common in many countries, the presence of antimicrobial resistant bacteria among pups in kennels has been infrequently investigated. This study was conducted to better understand the epidemiology of antimicrobial-resistant Escherichia coli isolates from kennel pups not treated with antimicrobials. We investigated susceptibilities to 11 antimicrobials, and prevalence of extended-spectrum β-lactamase (ESBL) in 86 faecal E. coli isolates from 43 pups in two kennels. Genetic relatedness among all isolates was assessed using pulsed-field gel electrophoresis (PFGE). Susceptibility tests revealed that 76% of the isolates were resistant to one or more of tested antimicrobials, with resistance to dihydrostreptomycin most frequently encountered (66.3%) followed by ampicillin (60.5%), trimethoprim-sulfamethoxazole (41.9%), oxytetracycline (26.7%), and chloramphenicol (26.7%). Multidrug resistance, defined as resistance against two or more classes of antimicrobials, was observed in 52 (60.5%) isolates. Three pups in one kennel harboured SHV-12 ESBL-producing isolates. A comparison between the two kennels showed that frequencies of resistance against seven antimicrobials and the variation in resistant phenotypes differed significantly. Analysis by PFGE revealed that clone sharing rates among pups of the same litters were not significantly different in both kennels (64.0% vs. 88.9%), whereas the rates among pups from different litters were significantly different between the two kennels (72.0% vs. 33.3%, P < 0.05). The pups in the two kennels had antimicrobial-resistant E. coli clones, including multidrug-resistant and ESBL-producing clones. It is likely that resistant and susceptible bacteria can clonally spread among the same and/or different litters thus affecting the resistance prevalence

Layered Double Hydroxide (LDH)-based Monolith with Interconnected Hierarchical Channels: Enhanced Sorption Affinity for Anionic Species

Monolithic layered double hydroxides (LDHs) with interconnected channels have been expected to enhance sorption rate as well as increase accumulation of anions. Although powder molding can form easy-handled LDH compacts, interconnected channel formation therein has not been achieved. Herein, we demonstrate cm-scale monolithic LDH-based composites with interconnected hierarchical channels via a spontaneous sol−gel reaction. The synthesis was performed on Mg−Al hydrotalcite-type LDHs starting from metal chlorides aqueous/ethanolic solution with poly(ethylene oxide) incorporated. Addition of propylene oxide triggers sol−gel reaction to form monolithic xerogels with a formula of [Mg0.66Al0.33(OH)2Cl0.33·2.92H2O]·3.1Al(OH)3. LDH crystals together with aluminum hydroxide crystals homogeneously build up gel skeletons with well-defined hierarchical channels. The interconnected channels in μm range (macrochannel) are formed as a phase-separated structure, whereas the channels in nm range (nanochannel) are as interstices of primary particles. The channel architectures are preserved in the course of rehydration process, affording enhanced sorption affinity for anion species in the process. Both of macro and mesochannels as well as high charge density of the obtained LDHs (Mg/Al=2.0) contribute enhanced anion sorption in the monolithic xerogels. The materials obtained here opens up applications of high performance adsorbent and ion-storage free from diffusion limitation.The present work is partially supported by Grant-in-Aid for Scientific Research (B) (No. 22360276), and Grant-in-Aid for Young Scientists (B) (No. 24750206) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), administrated by Japan Society for the Promotion of Science (JSPS). Y. T. is also partially supported financially by a research grant from The Murata Scientific Foundation

Eulerian polynomials and polynomial congruences

We prove that the Eulerian polynomial satisfies certain polynomial congruences. Furthermore, these congruences characterize the Eulerian polynomial