Transparent and colourless ionic liquids with refractive index over 1.60 were synthesised by combining 1-benzyl-3-methylimidazolium or hexyltriphenylphosphonium cations with suitable anions. There is a positive relation between their refractive index and Kamlet-Taft parameters, especially dipolarity/polarisability, suggested as a potential parameter to design ionic liquids with high refractive ...

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A. M. Alexeev,1 R. R. Hartmann,2 and M. E. Portnoi1,3,* 1School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom 2De La Salle University-Manila, 2401 Taft Avenue, 1004 Manila, Philippines 3International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal, RN, Brazil (Received 28 April 2015; revised manuscript received 31 October 2015; published...

We give the classification of (co-)path Hopf algebras and semi-path Hopf algebras with pointed module structures. This leads to the classification of multiple crown algebras and multiple Taft algebras as well as pointed Yetter-Drinfeld kG-modules and their corresponding Nichols algebras. Moreover, we characterize quantum enveloping algebras in terms of semi-path Hopf algebras.

We give the classification of (co-)path Hopf algebras and semi-path Hopf algebras with pointed module structures. This leads to the classification of multiple crown algebras and multiple Taft algebras as well as pointed Yetter-Drinfeld kG-modules and their corresponding Nichols algebras. Moreover, we characterize quantum enveloping algebras in terms of semi-path Hopf algebras.

In the paper, we describe Drinfel'd double structure of $n$-rank Taft algebra and all its simple modules, then endow $R$-matrices with some application to knot invariants. The invariants get is a generalization Jones polynomial, in particular, it recovers polynomial rank $1$ case, while $2$ one-parameter specialization two-parameter unframed Dubrovnik higher case composite ($n$-power) polynomial.

As President of the United States from 1909 to 1913, William Howard Taft's minimum body mass index was 42 kg/m(2). This article presents evidence that he suffered from obstructive sleep apnea, manifested by excessive daytime somnolence, snoring, systemic hypertension and, perhaps, cognitive and psychosocial impairment. As president, Taft's hypersomnolence was severe and obvious, but never promp...