The gonality of smooth curves with plane models

The Hausdorff measure with fractional index is used in order to define a functional on measurable sets of the plane. A fractal set, constructed using the well-known Von Koch set, is involved in the definition. This functional is proved to arise as the limit of a sequence of classical functionals defined on sets of finite perimeter. Thus it is shown that a natural extension of the ordinary functionals of the calculus of variations leads both to fractal sets and to the fractional Hausdorff measure.     

A theorem on paths in planar graphs

C. Thomassen extended Tutte's theorem on cycles in planar graphs in the paper “A Theorem on Paths in Planar Graphs”. This note corrects a flaw in his proof.     

Preparation and Characterization of Nano-structured Ceramic Powders Synthesized by Emulsion Combustion Method

The emulsion combustion method (ECM), a novel powder production process, was originally developed to synthesize nano-structured metal-oxide powders. Metal ions in the aqueous droplets were rapidly oxidized by the combustion of the surrounding flammable liquid. The ECM achieved a small reaction field and a short reaction period to fabricate the submicron-sized hollow ceramic particles with extremely thin wall and chemically homogeneous ceramic powder. Alumina, zirconia, zirconia–ceria solid solutions and barium titanate were synthesized by the ECM process. Alumina and zirconia powders were characterized to be metastable in crystalline phase and hollow structure. The wall thickness of alumina was about 10nm. The zirconia–ceria powders were found to be single-phase solid solutions for a wide composition range. These powders were characterized as equiaxed-shape, submicron-sized chemically homogeneous materials. The powder formation mechanism was investigated through the synthesis of barium titanate powder with different metal sources.     

Photoelectron emission and XPS studies of real iron surfaces subjected to scratching in air,water, and organic liquids

The influence of temperature and surface overlayer on the photoelectron emission from scratched real iron surfaces was investigated using thermally assisted photoelectron emission (TAPE) and X‐ray photoelectron spectroscopy (XPS) measurements. The scratching was conducted with a diamond cutter in seven atmospheres. The intensity of TAPE as a function of temperature, called glow curve, was measured in the range 25–339 °C using a Geiger counter under ultraviolet irradiation at 210 nm. The temperature was scanned in two cycles (Up1 and Down1, and Up2 and Down2). The XPS measurements were carried out at 25 °C and after TAPE measurements at 200 and 339 °C. The photoelectron emission intensity at 40 °C in the Up1 scan increased in the order of air < water ≈ methanol ≈ cyclohexane < ethanol < benzene < acetone, and then each glow curve exhibited a gradual increase with temperature through a broad peak. It was found that the dependence of the emission intensity in the Up1 scan on the oxygen component ratio, Z_O = O^2?/(OH^? + O^2?) and the percentage of the Fe metal and FeOOH components of the Fe3p spectra for the atmospheres greatly differed. Additionally, the glow curve in the Up1 scan was completely different from that in the other scans. It was proposed that the photoelectron emission in the Up1 scan originates from not only the base metal but also the surface overlayer having trapped electrons and is strongly influenced by the acid–base interaction of the surface hydroxyl groups with the liquids molecules. Copyright © 2016 John Wiley & Sons, Ltd.     

A characterization of double coverings of curves

The gonality sequence \({(d_{r})_{r}}\) of a curve X of genus g which doubly covers a curve of genus h satisfies \({d_{r} = 2(r + h)}\) for all \({r = h, h + 1, \ldots, g - 3h}\) provided that \({g \gg h}\). In this paper we explore if this striking feature of \({(d_{r})_{r}}\) actually characterizes such a covering.     

Usefulness of Mesoporous Silica as a Template for the Preparation of Bundles of Bi Nanowires with Precisely Controlled Diameter Below 10 nm

The reduction of the diameter of Bi nanowires below 10 nm has been an important target because of the theoretical prediction with regard to significant enhancement in thermoelectric performance by size reduction. In this study, we have demonstrated the usefulness of mesoporous silica with tunable pore size as a template for the preparation of thin Bi nanowires with diameters below 10 nm. Bi was deposited within the templates through a liquid phase deposition using hexane and 1,1,3,3‐tetramethyldisiloxane as a solvent and reducing agent, respectively. Bundles of thin Bi nanowires with non‐crystalline frameworks were successfully obtained after the template removal. The diameter was precisely controlled between about 6 nm and 9 nm. The judicious choices of mesoporous silica and deposition conditions are critical for the successful preparation. The reliable formation of such thin Bi nanowires reported here opens up exciting new possibilities.     

Synthesis of cyclopentadienones catalyzed by methylidynetricobalt nonacarbonyl

Easily prepared and air-stable methylidynetricobalt nonacarbonyl could be used as a catalyst for the intramolecular [2 + 2 + 1]-cocyclization of diynes and carbon monoxide producing cyclopentadienones.     

The optimization for cyclization reaction of 2-(2-carbomethoxyethynyl)aniline derivatives and formal synthesis of pyrroloquinoline quinone and its analogue utilizing a sequential coupling-cyclization reaction

The reaction conditions for the Pd-catalyzed cyclization reaction of 2-(2-carbomethoxyethynyl)aniline derivatives were investigated. The amounts of Pd(PPh₃)₄, methyl propiolate, and ZnBr₂ could be significantly reduced compared with those reported in our preliminary publication by careful tuning of the solvent and the reaction temperature. In addition to the above results, formal syntheses of pyrroloquinoline quinone (PQQ) and its analogue from 2-amino-5-nitrophenol using a Pd-complex-catalyzed sequential coupling-cyclization reaction between methyl propiolate and 2-iodoaniline derivatives are described.     

Re-entrant volume phase transition of hydrogel membrane of microcapsule

Re-entrant volume phase transition of hydrogel wall membrane of microcapsules (MC) was first observed using MC suspensions consisting of poly (L-lysine-alt-terephthalic acid) wall and aqueous inner and outer solutions with different pHs. To analyze the dynamics of the re-entrant phase transition, we extended the theory for the swelling and the shrinking dynamics of the microcapsule gel [T. Narita, T. Yamamoto, D. Suzuki, T. Dobashi, Langmuir 19 (2004) 4051]. In the theory, the microcapsule size and the force constant for the driving force which gives rise to the size relaxation were chosen as the thermodynamic variables. The time course of the cross-sectional area of the microcapsules fitted well to the theoretical equations, and the time constants determined as the fitting parameters were discussed in terms of the force constant relaxation and the size relaxation.