Positive-definite functions on infinite-dimensional groups

This paper concerns positive-definite functions on infinite-dimensional groups G. Our main results are as follows: first, we claim that if G has a σ-finite measure μ on the Borel field whose right admissible shifts form a dense subgroup G ₀, a unique (up to equivalence) unitary representation (H, T) with a cyclic vector corresponds to through a method similar to that used for the G–N–S construction. Second, we show that the result remains true, even if we go to the inductive limits of such groups, and we derive two kinds of theorems, those taking either G or G ₀ as a central object. Finally, we proceed to an important example of infinite-dimensional groups, the group of diffeomorphisms on smooth manifolds M, and see that the correspondence between positive-definite functions and unitary representations holds for under a fairy mild condition. For a technical reason, we impose condition (c) in Sect. 2 on the measure space throughout this paper. It is also a weak condition, and it is satified, if G is separable, or if μ is Radon. This research was partially supported by a Grant-in-Aid for Scientific Research (No.18540184), Japan Socieity of the Promotion of Science.     

A novel mediator-polymer-modified anode for microbial fuel cells

A high-performance anode system based on a combination of mediator-polymer-modified graphite felt and bacteria capable of reducing extracellular materials shows significant potential for practical use in microbial fuel cells (MFCs).     

Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces

We define and study Musielak-Orlicz-Sobolev spaces with zero boundary values on any metric space endowed with a Borel regular measure. We extend many classical results, including completeness, lattice properties and removable sets, to Musielak-Orlicz-Sobolev spaces on metric measure spaces. We give sufficient conditions which guarantee that a Sobolev function can be approximated by Lipschitz continuous functions vanishing outside an open set. These conditions are based on Hardy type inequalities.     

Synthesis and micromechanical properties of flexible, self-supporting polymer-SiO2 nanofilms

Large-scale, self-supporting ultrathin films composed of an elastomeric polyacrylate network interpenetrated by a silica (SiO2) network were synthesized and characterized. The organic network was first photopolymerized and the silica structure was subsequently developed in situ in the preformed organic gel. Composition and morphology of the hybrid interpenetrated network (IPN) nanofilms were characterized by infrared spectroscopy, X-ray photoelectron spectroscopy, scanning electron microscopy, and transmission electron microscopy and compared with the case of zirconia (ZrO2) hybrid IPN reported earlier. Young modulus, ultimate tensile strength, and ultimate tensile elongation were determined for different organic/inorganic molar ratios and give some insights on how the composition of the nanofilms influence their robustness and self-supporting properties.     

Investigation of intense electromagnetic transient phenomenon andPaschen curves for hydrogen and helium in subnanosecond regime

One of the major drivers of pulsed power innovation is ultrawide-band technology. Subnanosecond risetimes with nanosecond or less pulse durations place this technology in a temporal regime that corresponds to microwave frequencies. These ultrawide-band devices have pushed pulsed power technology into a parameter space where there is little published data on breakdown. This paper describes the experimental determination of the Paschen curve for two gases under the application of intense, transient, electric fields. This experiment utilized the Hindenberg series of hydrogen gas switched pulsers at the Air Force Research Laboratory located at Kirtland Air Force Base. The Paschen curves for hydrogen and helium are presented. For subnanosecond risetime pulses, there are typically very few free electrons in the discharge space generated by external radiation sources such as cosmic rays. The occurrence of cosmic ray ionization in the gap is unlikely in such a short period of time. Therefore, electric field emission plays a very important role in these discharges. However, a small number of discharges are effected by ionization from external radiation, with the resulting data lying along classic Paschen curves. As a verification of this effect, an intense continuous ultraviolet (UV) source was utilized for supplying seed electrons and the expected Paschen curves of hydrogen and helium were obtained     

Laser-induced crystalline phase transition from rutile to anatase of niobium doped TiO2

The investigation of the laser-induced crystalline phase transition of niobium doped TiO₂ single crystal is discussed in this paper. The TiO₂ single crystal was studied by using Raman spectroscopy and electron backscatter diffraction before and after irradiation by 266?nm?ns laser at the threshold intensity of 56?MW/cm². Experimental results show an evidence of anatase phase formation from rutile single crystal. Moreover, the analysis of the experimentally obtained and calculated crystallographic texture indicates that the converted TiO₂ layer has a polycrystalline structure with the preferred orientations. According to the Raman spectroscopy the amount of anatase phase increases with the number of laser pulses indicating the dose-dependent conversion process.     

Fabrication of Ordered Arrays of Biodegradable Polymer Pincushions Using Self-Organized Honeycomb-Patterned Films

Nano- and micropatterned structures of tissue engineering scaffolds made of biodegradable and biocompatible polymers profoundly influence cell behavior. The present study describes a technically simple and inexpensive method to rapidly fabricate hexagonal arrays of biodegradable polymer pillars (pincushions). As precursors to these polymer pincushion arrays, highly regular porous biodegradable polymer films (self-organized honeycomb-patterned films, called honeycomb films) were prepared on a glass substrate using a simple casting technique. Scanning electron microscope observations revealed that the honeycomb film was composed of a top and bottom layer. This double-layered structure is attributable to the self-organization of hexagonally packed arrays of water droplets that form the template. When we peeled off the top layer of the honeycomb film under ambient conditions using adhesive tape, we obtained arrays of polymer pincushions on both side of the glass substrate and on the adhesive tape. Each air hole is surrounded by six pincushions, each with a diameter of 0.1-1 µm. We also studied factors that determine the morphology of the pincushions, such as the thermal and mechanical properties of the polymers used. It was shown that the heights, widths, and distances of separation between the pincushions could be controlled by the choice of polymer and the pore structure of the original honeycomb film. Such well-ordered, biologically inspired pincushion structures could find application in biomedical, photonic, and electronic materials.     

Direct Observation of Dye-Containing Amphiphilic Copolymer in the Honeycomb-Patterned Film

Honeycomb-patterned film was prepared by casting chloroform solution of hydrophobic polymer and dye-containing amphiphilic copolymer under humid conditions. The confocal laser scanning microscopy image shows that amphiphilic copolymer is localized around the pores of the honeycomb-patterned film.     

Measurement of nitrogen atomic flux for RF-MBE growth of GaN and AlN on Si substrates

Production and measurement of active nitrogen atoms (N+N*), which consist of ground state nitrogen atoms N and excited state nitrogen atoms N*, in an inductively coupled radio frequency discharge for the growth of group III nitrides and their alloys using a molecular beam epitaxy (MBE) were studied. Two discharge modes of the low brightness (LB) and the high brightness (HB) used in this study to produce excited nitrogen molecules (N₂*) and dissociated active nitrogen atoms (N+N*). The flux of (N+N*) was measured by a Langumuir-like electrode due to the self-ionization of adsorbed (N+N*) on a negatively biased electrode. The self-ionization, which emits electrons from (N+N*), forms an atom current and is confirmed using different electrodes such as Pt and CuBe and different electrode area. The atom current was calibrated by the grown GaN thickness in a VG80H MBE machine. The calibrated flux of (N+N*) per atom current in the VG80H machine is 5.5×10⁻⁴ ML/s/nA, where ML is monolayer. The atom current is useful to monitor the flux of chemically active nitrogen atoms N+N* for growth of group III nitrides and their alloys. Activity modulation migration enhanced epitaxial growth (AM-MEE) was demonstrated as an application of the measurement of atom current for the growth of the group III nitrides.     

Breath Figures of Nanoscale Bricks: A Universal Method for Creating Hierarchic Porous Materials from Inorganic Nanoparticles Stabilized with Mussel‐Inspired Copolymers

High‐performance catalysts and photovoltaics are required for building an environmentally sustainable society. Because catalytic and photovoltaic reactions occur at the interfaces between reactants and surfaces, the chemical, physical, and structural properties of interfaces have been the focus of much research. To improve the performance of these materials further, inorganic porous materials with hierarchic porous architectures have been fabricated. The breath figure technique allows preparing porous films by using water droplets as templates. In this study, a valuable preparation method for hierarchic porous inorganic materials is shown. Hierarchic porous materials are prepared from surface‐coated inorganic nanoparticles with amphiphilic copolymers having catechol moieties followed by sintering. Micron‐scale pores are prepared by using water droplets as templates, and nanoscale pores are formed between the nanoparticles. The fabrication method allows the preparation of hierarchic porous films from inorganic nanoparticles of various shapes and materials.