A Relationship Among Gentzen's Proof-Reduction,Kirby-Paris' Hydra Game and Buchholz's Hydra Game

We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game (Section 1 and Appendix). Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game (which is two-dimensional but without labels), by a simple and natural interpretation (Section 2). Jervell proposed another type of a combinatorial game, by abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show (Section 3) that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φ_ω (0) (while that of PA or of Kirby-Paris' Game is φ₁ (0) = ?₀) in the Veblen hierarchy of ordinals.     

Synthesis of bis(alk-3-en-1-ynyl)benzene with either E- or Z-configuration via a one-pot three-component coupling reaction and its optical properties

A convenient, efficient and stereoselective synthesis of a range of bis(alk-3-en-1-ynyl)benzenes with E- and Z-configuration is described. The protocol involves Cu-mediated cross-coupling reaction of (E)- and (Z)-alk-1-enyldisiamylboranes with (trimethylsilyl)ethynyl bromide and Pd/Cu-catalyzed cross-coupling reaction with diiodobenzene. The sequential cross-coupling reaction proceeds readily under extremely mild conditions in a one-pot manner to afford bis(alk-3-en-1-ynyl)benzenes in good to excellent yields. The optical properties of the products are also described.     

A Novel Synthesis of α-Tellanyl α,β-Unsaturated Aldehydes Using α-Tellanyl β-Alkoxyalkenyl Lithiums

Abstract

β-Ethoxy-α-phenyltellanylvinyl lithiums were successfully generated in situ from phenyltellanylacetaldehyde diethyl acetal with lithium 2,2,6,6-tetrame-thylpiperidide (LTMP) and underwent methylation or nucleophilic addition with aldehydes and ketones. The successive dehydration of the allylic alcohols with trimethylsilyl trifluoromethanesulfonate (TMSOTf) gave α-phenyltellanyl α,β-unsaturated aldehydes, which transformed to some useful compounds.     

Precise measurement of positronium hyperfine splitting using the Zeeman effect

Positronium is an ideal system for the research of the quantum electrodynamics (QED) in bound state. The hyperfine splitting (HFS) of positronium, Δ_HFS, gives a good test of the bound state calculations and probes new physics beyond the Standard Model. A new method of QED calculations has revealed the discrepancy by 15 ppm (3.9σ) of Δ_HFS between the QED prediction and the experimental average. There would be possibility of new physics or common systematic uncertainties in the previous all experiments. We describe a new experiment to reduce possible systematic uncertainties and will provide an independent check of the discrepancy. We are now taking data and the current result of Δ_HFS?=?203.395 1 ±0.002 4 (stat., 12 ppm) ±0.001 9 (sys., 9.5 ppm) GHz has been obtained so far. A measurement with a precision of O(ppm) is expected within a year.     

High pressure organic chemistry; XV. Non-catalyzed cleavage reaction of ethers with acyl halides

Abstract

A variety of cyclic and acyclic ethers are efficiently reacted with acyl chlorides or acyl bromides to afford the ether-cleaved compounds of ω-chloro-or ω-bromoesters under high pressure conditions. The reactivity of ethers is found to be roughly depend on the basicity of the ether oxygen atom.     

Optimum Temporal Pulse Shape of Launched Light for Optical Time Domain Reflectometry Type Sensors Using Brillouin Backscattering

We investigated numerically the relationship between the temporal shape of an optical pulse launched into an optical fiber and the power spectrum of the Brillouin backscattered light it produces. We analyzed the measurement error of the peak-power frequency of the Brillouin backscattered light power spectra obtained from the launched light with various pulse shapes. In this investigation and analysis, we characterized the pulse shape by the width, leading-trailing time, and steepness. Regardless of the launched pulse shape, the peak-power frequency-measurement error increases as the pulse width shortens. For identical launched pulse widths, a triangular pulse generates the Brillouin backscattered-light power spectrum with both the narrowest profile and the largest peak power, and consequently provides the minimum error when we measure the peak-power frequency. This shows that a temporally triangular pulse is the best for the launched light.     

Physics in plasmonic and Mie scattered near-field for efficient surface-enhanced Raman scattering template

We describe the physics of the SERS based on the optical near-field intensity enhancement on the metallic (plasmonic) and the nonmetallic (Mie scattering) nanostructured substrates with two-dimensional (2D) periodic nanohole arrays. The calculation by the Finite-Difference Time-Domain (FDTD) method revealed that the optical intensity enhancement increases with the increase of the thickness of a gold film coating on the nonmetallic (dielectric) nanostructured Si, GaAs, and SiC substrates. The resonance spectrum shifts with the changes in the geometrical structure of the void diameter and inter-void distance. It was clarified that the optical intensity enhancement obtained with the gold-coated substrate is equivalent to that with a gold substrate at 70-nm thick gold coating on the dielectric substrates in this structure. The resonance spectral bandwidth for Mie scattering and plasmonic near-fields is different. Therefore, if the Stokes line of the Raman scattering is located within the resonance bandwidth, the SERS signal is enhanced proportionally to the fourth power of the electric near-field. However, if the Stokes shift is located out of the resonance bandwidth, the SERS signal enhancement is only proportional to the square of the scattered near-field.     

Raman spectroscopy of SWNTs produced by a XeCl excimer laser ablation at high temperatures

Synthesis of single-wall carbon nanotubes (SWNTs) was carried out by an ablation method using a XeCl excimer laser. It was irradiated onto a graphite target containing Co and Ni at the temperatures of 1073, 1173, 1273, 1373, 1473, 1523 and 1623 K under the atmosphere (0.1 MPa) of Ar gas with the flow rate of 12 ml/min. The measurement by a scanning/transmission electron microscope and Raman spectroscopy found the formation of SWNTs with the diameter of about 1.3 nm and the length of about 2 μm in ablated carbonaceous soot. The ratio of peak intensity of 1590 cm⁻¹ (G band) to that of 1335 cm⁻¹ (D band) in the high frequency Raman spectra increased with increasing the ambient temperature. The radial breathing mode (RBM) in the low frequency Raman spectra shows that the mean diameter of SWNTs increased with increasing the ambient temperature.     

Extended string field theory for massless higher-spin fields

We propose a new gauge field theory which is an extension of ordinary string field theory by assembling multiple state spaces of the bosonic string. The theory includes higher-spin fields in its massless spectrum together with the infinite tower of massive fields. From the theory, we can easily extract the minimal gauge-invariant quadratic action for tensor fields with any symmetry. As examples, we explicitly derive the gauge-invariant actions for some simple mixed symmetric tensor fields. We also construct covariantly gauge-fixed action by extending the method developed for string field theory.     

Temperature dependence of aluminum nitride reflectance spectra in vacuum ultraviolet region

Temperature dependence of optical reflectance spectra in vacuum ultraviolet region for aluminum nitride has been measured on high-quality single crystal with synchrotron radiation. The dominant structure due to the interband transition is observed at photon energy around 7.7 eV. With decreasing temperature, the energy position of the dominant structure in the reflectance spectra shifts towards higher energy. The experimental data has been fitted to the Bose-Einstein expression and the obtained parameter related to the strength of the electron-phonon interactions is much smaller than that for the peak at 6.2 eV, suggesting that the higher-lying interband transition energy decreases more slowly with increasing temperature in aluminum nitride (AlN).