A graph-theoretic approach to a partial order of knots and links

AbstractWe say that a link L1 is an s-major of a link L2 if any diagram of L1 can be transformed into a diagram of L2 by changing some crossings and smoothing some crossings. This relation is a partial ordering on the set of all prime alternating links. We determine this partial order for all prime alternating knots and links with the crossing number less than or equal to six. The proofs are given by graph-theoretic methods

Site-dependent Local Spin Susceptibility and Low-energy Excitation in a Weyl Semimetal WTe2_2

Site-dependent local spin susceptibility is investigated with $^{125}$Te nuclear magnetic resonance in a Weyl semimetal WTe$_2$. The nuclear spin-lattice relaxation rate $1/T_1T$ shows a dependence of the square of temperature $T$ at high temperatures, followed by a constant behavior below 50 K. The temperature dependence features Weyl fermions appearing around the linearly crossing bands. The Knight shift $K$ scales to the square root of $1/T_1T$, corroborating a predominant spin contribution in low-lying excitation. The observed dependence of $K$ and $1/T_1T$ on the four Te sites shows the site-dependent electron correlation and density of states. The angular profile of the NMR spectrum gives the anisotropic hyperfine coupling tensor, consistent with $5p$ hole occupations on Te sites.Comment: 6 pages, 5 figure

Electrochemical Glycosylation as an Enabling Tool for the Stereoselective Synthesis of Cyclic Oligosaccharides

Electrochemical glycosylation of a linear oligosaccharide with a protecting-group-free primary hydroxyl group afforded cyclic oligo-saccharides, up to hexasaccharides, in high yields. Precursors of the cyclic oligosaccharides were prepared by automated electro-chemical assembly-a method for the automated electrochemical solution-phase synthesis of oligosaccharides. We demonstrated that electrochemical glycosylation is useful not only for intermolecular glycosylation but also for intramolecular glycosylation to synthesize cyclic oligosaccharides

Electrochemical performance of Sn4P3 negative electrode for Na-ion batteries in ether-substituted ionic liquid electrolyte

We have previously disclosed that the ionic-liquid electrolyte sodium bis(fluorosulfonyl)amide (NaFSA)/1-methyl-1-propylpyrrolidinium bis(fluorosulfonyl)amide (Py13-FSA) can significantly improve the cycling stability of Sn4P3 negative electrodes for Na-ion batteries (NIBs). However, the strong electrostatic interaction between Na+ and FSA− in the electrolyte leads to high viscosity and low conductivity. In this study, we have tried to improve the conductivity of the electrolyte and enhance the rate capability of the Sn4P3 electrode by introducing an ether group in the side-chain of the ionic liquid cation to reduce said electrostatic interaction. Ether-substituted ionic liquid 1-methoxymethyl-1-methylpyrrolidinium (PyMOM)-FSA showed higher conductivity than Py13-FSA and the Sn4P3 electrode exhibited a higher rate capability. The differential capacity vs. potential plots suggest that the reaction between Na+ and Sn or P is promoted in the ether-substituted ionic liquid electrolyte. These results demonstrate that introduction of an ether moiety is an effective approach to improve the rate capability of the Sn4P3 electrode in NIBs

Direct Extraction of Polysaccharides from Moso Bamboo (Phylostachys heterocycla) Chips Using a Mixed Solvent System of an Amino Acid Ionic Liquid with Polar Aprotic Solvent

The cellulose-dissolving ability and some physical properties of mixed solvents of an amino acid IL, N-methyl-N-(2-methoxyethyl)pyrolidin-1-ium 2,6-diaminohexanoate ([P1ME][Lys]), with polar aprotic solvents, such as 1,3-dimethylimidazolidinone (DMI), N,N-dimethylformamide (DMF), dimethylsulfoxide (DMSO), and acetonitrile (CH3CN), have been investigated. The viscosity was significantly reduced by the increasing content of polar aprotic solvents, and a 1:1 mixture (molar ratio) of [P1ME][Lys] with DMF showed 91.5 cP which corresponded to less than 1/10 compared to that of the pure IL at 25 °C (1058 cP). The β values of the mixed solvents, which have the IL contents over 0.1, exhibited β-values similar to that of the pure IL. On the other hand, the π-value was dependent on the ratio of the IL content, and the pure IL had the highest π-value. We found that the mixed solvent of [P1ME][Lys] with DMF (1:1) easily dissolved the cellulose and the mixed solvent could be used to extract cellulose from moso bamboo (Phylostachys heterocycla) powder. The efficiency of the extraction of cellulose from the bamboo powder was significantly increased when a 1:1 mixture of the IL with a polar aprotic solvent was used as the extracting solvent at 60 °C; the extraction ratio of the 1:1 mixture (IL: DMF) reached twice that of the pure IL. We thus obtained cellulose in 18% (w/w) yield from the bamboo powder

Effect of Annealing Temperature of Ni-P/Si on its Lithiation and Delithiation Properties

Annealed Ni–P–coated Si (Ni–P/Si) anodes for lithium-ion batteries have shown a superior cycle life with discharge capacity of 1000 mA h g−1 over 1100 cycles in some ionic-liquid electrolytes. However, the annealing temperature has yet to be optimized for Ni–P/Si electrodes. We investigated the electrochemical performance of Ni–P/Si electrode annealed at various temperatures in this study. The Ni–P/Si electrodes annealed at 800 ± 20 °C exhibited a superior cycle life with a reversible capacity of 1000 mA h g−1 over 1000 cycles, whereas the capacity of the electrodes annealed at temperatures of 750 °C and 850 °C faded at approximately 500 cycles. At 800 °C, a newly formed NiSi2 phase was theorized to significantly contribute to improving adhesion between the Ni–P coating layer and the Si particles. The Ni–P coating particles tended to aggregate at 850 °C, leading to a reduction in the coating effect, that is, a decline in their reactivity with Li+, acceleration of electrode disintegration, and a reduction in electrical conductivity. On the other hand, Ni–P/Si electrodes annealed at 850 °C exhibited a superior rate performance. The amount of available NiSi2 which ultimately contributed to higher reactivity with Li should increase

Lattice QCD Constraints on Hybrid and Quark Stars

A QCD-motivated dynamical-quasiparticle model with parameters adjusted to reproduce the lattice-QCD equation of state is extrapolated from region of high temperatures and moderate baryonic densities to the domain of high baryonic densities and zero temperature. The resulting equation of state matched with realistic hadronic equations of state predicts a phase transition into the quark phase at higher densities than those reachable in neutron star interiors. This excludes the possibility of the existence of hybrid (hadron-quark) stars. Pure quark stars are possible and have low masses, small radii and very high central densities. Similar results are obtained for a simple bag model with massive quarks, fitted to reproduce the same lattice results. Self-bound quark matter is also excluded within these models. Uncertainties in the present extrapolation re discussed. Comparison with standard bag models is made.Comment: 13 p., 8 figs., 7 tables, Version accepted by Phys. Rev.

Piperidinium-Based Ionic Liquids as an Electrolyte Solvent for Li-Ion Batteries: Effect of Number and Position of Oxygen Atom in Cation Side Chain on Electrolyte Property

ArticleJournal of The Electrochemical Society. 167(7): 174101 (2019)journal articl