Generalized Pólya–Szegö type inequalities for some non-commutative geometric means

In this paper, we shall show generalized Pólya–Szegö type inequalities of n positive invertible operators on a Hilbert space for any integer $n?3$ in terms of the following two typical non-commutative geometric means, that is, one is the higher order weighted geometric mean due to Lawson–Lim which is an extension of the Ando–Li–Mathias geometric mean, and the other is the weighted chaotic geometric mean. Among others, the Specht ratio plays an important role in our discussion, which is the upper bound of a ratio type reverse of the weighted arithmetic–geometric mean inequality.     

Rapid speciation and quantification of selenium compounds by HPLC-ICP MS using multiple standards labelled with different isotopes

Speciation analysis using high-performance liquid chromatography–inductively coupled plasma mass spectrometry (HPLC-ICP MS) is now commonly used to investigate metabolic and toxicological aspects of some metals and metalloids. We have developed a rapid method for simultaneous identification and quantification of metabolites of selenium (Se) compounds using multiple standards labelled with different isotopes. A mixture of the labelled standards was spiked in a selenised garlic extract and the sample was subjected to speciation analysis by HPLC-ICP MS. The selenised garlic contains γ-glutamyl-methylselenocysteine, methylselenocysteine, and selenomethionine and the concentrations of those Se compounds were 723.8, 414.8, and 310.7 ng Se ml^?1, respectively. The isotopically labelled standards were also applied to the speciation of Se in rat urine. Selenate, methylselenonic acid, selenosugar, and trimethyselenium ions were found to be excreted by the present speciation procedure. Multiple standards labelled with different stable isotopes enable high-throughput identification and quantitative measurements of Se metabolites.     

Effect of restart at signals on traffic flow through a series of signals

We study the effect of restart at signals on the vehicular traffic controlled by a series of signals. The Nagel–Schreckenberg model (NS model) and Fukui–Ishibashi model (FI model) are applied to the vehicular motion. In the FI model, the step-by-step acceleration is not taken into account but the acceleration effect is included in the NS model. It is shown that the difference between both models results in the restart effect at signals. The extended version of the NS model with signals is formulated by the difference equation. The restart at signals has an effective effect on the traffic flow. The fundamental diagram changes highly by the restart effect. The dependences of mean speed on the cycle time are shown.     

Rationality of Bershadsky-Polyakov Vertex Algebras

We prove the conjecture of Kac-Wakimoto on the rationality of exceptional W-algebras for the first non-trivial series, namely, for the Bershadsky-Polyakov vertex algebras ${W_3^{(2)}}$ W 3 ( 2 ) at level k =  p/2?3 with ${p = 3, 5, 7, 9, \dots}$ p = 3 , 5 , 7 , 9 , ? . This gives new examples of rational conformal field theories.     

Nonselective excitation of pulsed ELDOR using multi-frequency microwaves

The use of a polychromatic microwave pulse to expand the pumping bandwidth in pulsed electron-electron double resonance (PELDOR) was investigated. The pumping pulse was applied in resonance with the broad (～100 mT) electron paramagnetic resonance (EPR) signal of the manganese cluster of photosystem II in the S2 state. The observation pulses were in resonance with the narrow EPR signal of the tyrosine radical, YD·. It was found that in the case of the polychromatic pumping pulse containing five harmonics with the microwave frequencies between 8.5 and 10.5 GHz the PELDOR effect corresponding to the dipole interaction between the Mn cluster and YD· was about 2.9 times larger than that achieved with a monochromatic pulse. In addition to the dipolar modulation, the nuclear modulation effects were observed. The effects could be suppressed by averaging the PELDOR trace over the time interval between the observation microwave pulses. The polychromatic excitation technique described will be useful for improving the PELDOR sensitivity in the measurements of long distances in biological samples, where the pair consists of a radical with a narrow EPR spectrum and slow phase relaxation, and a metal center that has a broad EPR spectrum and a short phase relaxation time.     

Design of highly nonlinear octagonal photonic crystal fiber with near-zero flattened dispersion at 1.31μm waveband

This paper presents a highly nonlinear octagonal photonic crystal fiber (HN-OPCF) with a Ge-doped core for dental optical coherence tomography (OCT) applications. The simulation results show that a nonlinear coefficient of 56.3W⁻¹ km⁻¹ and the flattened dispersion of less than −1:0 ps/(nm·km) are obtained in 75 nm waveband (1265–1340 nm). Owing to its high nonlinear coefficient and flattened dispersion, the HN-OPCF is expected to be suitable for supercontinuum generation, which is very important in OCT applications. The numerical simulation results demonstrate that the proposed HN-OPCF can generate wideband supercontinuum.     

Oxidation of an Internal-Edge-Substituted [5]Helicene-Derived Phosphine Synchronously Enhances Circularly Polarized Luminescence

Small chiral organic molecules with CD properties are in high demanded due to their potential use in promising electronic and biological applications. Herein, we reveal a system in which the oxidation of a phosphino group to the corresponding phosphine oxide on the inner rim of a helicene derivative induces a CPL response. Laterally π-extended 7,8-dihydro[5]helicenes bearing phosphine and phosphine oxide groups on their inner helical rims (i. e., the C1 position) were synthesized, and their helical structures were unambiguously determined by X-ray crystallography. The photophysical (UV/visible and emission) and chiroptical properties of these compounds were investigated in various solvents. Despite their structural similarities, phosphine oxide showed a significantly better CPL response than phosphine, with a high dissymmetry factor for emission (|g_lum|=(1.3–1.9)×10⁻³) that can be attributed to structural changes in the interior of the helicene helix.     

Catalytic Asymmetric Hydrogenation of Dehydroamino Acid Esters with Biscarbamate Protection and Its Application to the Synthesis of xCT Inhibitors

Catalytic asymmetric hydrogenation of dehydroamino acid esters with biscarbamate protection was examined for the first time to prepare optically active amino acids. The new method was successfully applied to the synthesis of new cystine–glutamate exchanger inhibitors.     

Enantioselective Friedel–Crafts Alkylation Reaction of Heteroarenes with N-Unprotected Trifluoromethyl Ketimines by Means of Chiral Phosphoric Acid

An enantioselective Friedel–Crafts alkylation reaction of pyrroles and indoles with N-unprotected trifluoromethyl ketimines by use of chiral phosphoric acid provided α-trifluoromethylated primary amines bearing chiral tetrasubstituted carbon centers in high yields and with high to excellent enantioselectivities. The present reaction is unique to N-unprotected trifluoromethyl ketimines. No reaction took place with N-p-methoxyphenyl (PMP)-substituted ketimine. Corresponding α-trifluoromethylated amines were transformed without loss of enantioselectivity.