The unique solution of the Karcher equation and the self-adjointness of the Karcher mean

Lawson and Lim showed that the Karcher equation for positive invertible operators on a Hilbert space has a unique solution using the method of the implicit function theorem of a Banach space. In this paper, in the framework of the operator inequality, we show the equivalence of the unique solution of the Karcher equation and the self-adjointness of the Karcher mean. For this, we reform the notion of the operator power means of negative order by virtue of the Tsallis relative operator entropy of negative order.     

Tuning of the internal energy and isomer distribution in small protonated water clusters H(+)(H2O)(4-8): an application of the inert gas messenger technique

Infrared spectroscopy of gas-phase hydrated clusters provides us much information on structures and dynamics of water networks. However, interpretation of spectra is often difficult because of high internal energy (vibrational temperature) of clusters and coexistence of many isomers. Here we report an approach to vary these factors by using the inert gas (so-called "messenger")-mediated cooling technique. Protonated water clusters with a messenger (M), H(+)(H(2)O)(4-8)·M (M = Ne, Ar, (H(2))(2)), are formed in a molecular beam and probed with infrared photodissociation spectroscopy in the OH stretch region. Observed spectra are compared with each other and with bare H(+)(H(2)O)(n). They show clear messenger dependence in their bandwidths and relative band intensities, reflecting different internal energy and isomer distribution, respectively. It is shown that the internal energy follows the order H(+)(H(2)O)(n) > H(+)(H(2)O)(n)·(H(2))(2) > H(+)(H(2)O)(n)·Ar > H(+)(H(2)O)(n)·Ne, while the isomer-selectivity, which changes the isomer distribution in the bare system, follows the order H(+)(H(2)O)(n)·Ar > H(+)(H(2)O)(n)·(H(2))(2) > H(+)(H(2)O)(n)·Ne ~ (H(+)(H(2)O)(n)). Although the origin of the isomer-selectivity is unclear, comparison among spectra measured with different messengers is very powerful in spectral analyses and makes it possible to easily assign spectral features of each isomer.     

Size-dependent metamorphosis of electron binding motif in cluster anions of primary amide molecules

Electron binding motifs in cluster anions of primary amides, (acetamide)(n)(-) and (propionamide)(n)(-), were studied with photoelectron spectroscopy. For both the amides, two band series due to distinct isomeric species in the multipole-bound states were found in the low electron binding energy region (<~0.4 eV) of the photoelectron spectra at the excitation wavelength of 1064 nm. In the case of acetamide, the isomer of higher band peak energies is predominant for 6≤ n ≤ 8, but it vanishes completely for n ≥ 9 to be replaced with the lower energy isomer. The same spectral behavior was seen for propionamide exhibiting an exception at n = 7. The isomers appearing in the lower and higher energy sides were attributed to the straight and folded forms of ladder-like hydrogen bond network structures, respectively, on the basis of density functional calculations. In the folded forms, the excess electron is held in the space between two terminal amide molecules of the ladder-like networks. Referring to calculations of potential energy curves with respect to the folding coordinate of the ladder-like networks, it is inferred that the major isomer alternation between n = 8 and 9 originates from an increase of stiffness of the molecular ladders depending on the cluster sizes. In photoelectron spectra at the 355 nm excitation, the valence anion state having a band peak around 2.5 eV was observed to emerge with threshold sizes of n = 13 and 9 for acetamide and propionamide, respectively. Static and dynamical effects of alkyl groups on the electron binding motifs are discussed in comparison with the previous study on formamide cluster anions.     

Formation of Pickering emulsions stabilized via interaction between nanoparticles dispersed in aqueous phase and polymer end groups dissolved in oil phase

The influence of end groups of a polymer dissolved in an oil phase on the formation of a Pickering-type hydroxyapatite (HAp) nanoparticle-stabilized emulsion and on the morphology of HAp nanoparticle-coated microspheres prepared by evaporating solvent from the emulsion was investigated. Polystyrene (PS) molecules with varying end groups and molecular weights were used as model polymers. Although HAp nanoparticles alone could not function as a particulate emulsifier for stabilizing dichloromethane (oil) droplets, oil droplets could be stabilized with the aid of carboxyl end groups of the polymers dissolved in the oil phase. Lower-molecular-weight PS molecules containing carboxyl end groups formed small droplets and deflated microspheres, due to the higher concentration of carboxyl groups on the droplet/microsphere surface and hence stronger adsorption of the nanoparticles at the water/oil interface. In addition, Pickering-type suspension polymerization of styrene droplets stabilized by PS molecules containing carboxyl end groups successfully led to the formation of spherical HAp-coated microspheres.     

Modification of the glass surface property in PDMS-glass hybrid microfluidic devices

This paper presents a simple method to change the hydrophilic nature of the glass surface in a poly(dimethylsiloxane) (PDMS)-glass hybrid microfluidic device to hydrophobic by an extra-heating step during the fabrication process. Glass substrates bonded to a native or oxygen plasma-treated PDMS chip having microchambers (12.5 mm diameter, 110 μm height) were heated at 200°C for 3 h, and then the hydrophobicity of the glass surfaces on the substrate was evaluated by measuring the contact angle of water. By the extra-heating process, the glass surfaces became hydrophobic, and its contact angle was around 109°, which is nearly the same as native PDMS surfaces. To demonstrate the usefulness of this surface modification method, a PDMS-glass hybrid microfluidic device equipped with microcapillary vent structures for pneumatic manipulation of droplets was fabricated. The feasibility of the microcapillary vent structures on the device with the hydrophobic glass surfaces are confirmed in practical use through leakage tests of the vent structures and liquid handling for the electrophoretic separation of DNA molecules.     

Electronic States near the Fermi Level in the Antiferromagnetic and Ferromagnetic Spinels of Zn 1− x Cu x Cr 2 Se 4 ; 0.0 ≤ x ≤ 1.0

The electronic states of normal-type spinels in Zn 1 m x Cu x Cr 2 Se 4 have been studied by X-ray absorption spectroscopy near the K-edge of Zn, Cu, Cr and Se ions. It is found that characteristic white lines occur near the X-ray absorption threshold for Zn and Se ions, but not for Cu and Cr ions. It is also found that the white lines show a slight energy shift, which depends on the Cu concentration. The energy shifts mean that Fermi level gradually approaches the top region of the valence band of Se 2 m , on increasing the Cu ions. The substitution of Zn 2+ with Cu 1+ ions increases the number of positive carriers, holes. The holes occupying the top region of the valence band strongly correlate with Cr 4+ , which forms an empty orbital in the 3d-band of Cr 3+ and exchanges the valence electrons with Cr 3+ . It is interpreted that the ferromagnetism in Zn 1 m x Cu x Cr 2 Se 4 is made by double-exchange interaction between Cr 3+ and Cr 4+ ions and that holes contribute to the electronic conductivity of Zn 1 m x Cu x Cr 2 Se 4 .     

Decay Pion Spectroscopy of Electro-Produced Hypernuclei

The investigation of light hypernuclei is quite important for understanding the basic YN interaction and the mechanism of hypernuclear structure. We started the commissioning of the decay pion spectroscopy of light hypernuclei at MAMI-C in 2011. In order to realize the K⁺ tagging efficiently, some detectors on KAOS spectrometer were upgraded or newly installed. The existing and well-studied spectrometers, SpekA, SpekC were used as pion spectrometers. The analysis is ongoing to estimate the detectors performance and develop the spectrometers for future experiments with higher beam intensity. The preliminary results of the particle identification are presented in this article.     

Thermal Conductivity Measurement of Gases by the Transient Short-Hot-Wire Method

Measurements of the thermal conductivity of helium and hydrogen are performed using the transient short-hot-wire method. The short hot wire is made of platinum and has a diameter of about 10 μm and a length of about 15 mm. It is attached by spot welding to platinum terminals with a diameter of 1.5 mm. The probe is inserted into the sample vessel that has a volume of 35 cm³ and an inner diameter of 30 mm. The thermal conductivity is evaluated by comparing a numerical solution of the heat conduction in and around the short wire with the experimentally obtained temperature rise of the wire. The measured thermal conductivities show good reproducibility. Also, the measured thermal conductivities agree with the reference equations within a deviation of ± 1%.     

Remaining of ϵ-iron structure at atmospheric pressure and superlattice formation by shearing at high pressure

Transmission X-ray diffraction pattern of iron sheared at high pressure show rings whose interplanar spacings correspond to those of ?-iron and their integral multiple, in spite of the fact that it has been kept at atmospheric pressure for ～3 months from the shearing. This and other related phenomena suggest that the pattern corresponds to the remains of the ?-iron structure in which superlattice formed. The volume of the specimen at atmospheric pressure after elapsing ～3 months at atmospheric pressure from the shearing was 86% of that before the shearing.