A comment on pure-strategy Nash equilibria in competitive diffusion games

In [N. Alon, M. Feldman, A.D. Procaccia, M. Tennenholtz, A note on competitive diffusion through social networks, Inform. Process. Lett. 110 (2010) 221–225], the authors introduced a game-theoretic model of diffusion process through a network. They showed a relation between the diameter of a given network and existence of pure Nash equilibria in the game. Theorem 1 of their paper says that a pure Nash equilibrium exists if the diameter is at most two. However, we have an example which does not admit a pure Nash equilibrium even if the diameter is two. Hence we correct the statement of Theorem 1 of their paper.     

Formation of Tetravalent Fe Ions in LaFeO3 Perovskite Through Mechanochemical Modification by Ball Milling

Mechanochemical modification of previously synthesized LaFeO₃ perovskite‐type oxide by a high‐energy ball milling was investigated to introduce Fe⁴⁺ ions or transform some Fe³⁺ into Fe⁴⁺ in LaFeO₃. X‐ray absorption fine structure studies revealed that the formation of Fe⁴⁺ ions into LaFeO₃ perovskite has been achieved at first time by ball milling at room temperature without any additives or replacement of La³⁺ ions by some divalent cations. The structural model of Fe⁴⁺ containing LaFeO₃ could be described as with a modified perovskite having equal amounts of La and Fe vacancies, which is supported by a good correlation between the results of Fe K‐edge XANES spectra and O₂‐TPD. The synthesis of Fe⁴⁺‐containing LaFeO₃ perovskite by ball milling was able to produce the O₂ adsorption capacity of nonsubstituted perovskite‐type oxide.     

Accuracy of the difference scheme of solving the eigenvalue problem for the Laplacian

The finite-difference approximation of the eigenvalue problem with the Dirichlet boundary conditions for the Laplacian in a two-dimensional domain of complex form is analyzed for accuracy and the error of eigenfunctions from the class W₂²( W) W_2^2\left( \Omega \right) in the mesh norm of W₂¹( w) W_2^1\left( \omega \right) is estimated.     

Space charge behavior in polymer film based on increment of capacitance under AC high field

Polymer materials have excellent dielectric and insulation properties; however, those properties in AC high field region have not been known well. Recently we established an evaluation method of high‐field AC dissipation current waveform of polymer materials 1 . AC dissipation current waveforms of polyethylene and polypropylene films show nonlinear distortion in AC high‐field region. This nonlinearity was thought to be related to the behavior of AC space charge formation in the sample near electrodes. The properties of space charge formed under AC high field at power frequency seem to differ from those formed under DC high field. The measurement of AC space charge distribution is not so easy due to the resolution limit of the space charge measurement. We studied the dielectric properties of biaxially oriented polypropylene (BOPP) film under AC high field up to 120 °C. It was found that tan δ, AC dissipation current (Ixr), and unbalanced component of capacitive current (ΔIxc) increased when the temperature became higher. In particular, ΔIxc increased above some threshold field and was considered to be due to the AC space charge formation. This AC space charge layer near electrode is thought to be formed due to carrier injection under AC high‐field application. Usually, the carrier mobility becomes smaller on lowering the temperature. Most of the carriers injected from the electrode are trapped near the electrode in the sample film. But in the high‐temperature region, the carrier mobility becomes larger and the carrier injection starts to increase from lower field. Many more carriers are injected from the electrode. It is thought that some of the injected carriers are trapped inside the sample film; the others go through the sample to the opposite side. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 141(2): 8–16, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10018     

Formation mechanism of monodispersed spherical core-shell ceria/polymer hybrid nanoparticles

Very unique core-shell ceria (cerium oxide)/polymer hybrid nanoparticles that have monodispersed spherical structures and are easily dispersed in water or alcohol without the need for a dispersant were reported recently. The formation mechanism of the unique nanoparticles, however, was not clear. In order to clarify the formation mechanism, these nanoparticles were prepared using a polyol method (reflux heating) under varied conditions of temperature, time, and concentration and molecular weight of added polymer (poly(vinylpyrrolidone)). The size of the resultant nanoparticles was strongly and complicatedly dependent on the set temperature used during reflux heating and the poly(vinylpyrrolidone) molecular weight. Furthermore, the size of the nanoparticles increased by a 2-step process as the reflux heating time increased. The IR spectral changes with increasing reflux time indicated the increase in the number of cross-linked polymers in the shell. From these results, the formation mechanism was discussed and proposed.     

Synthesis of Succinic Gemini Surfactants and the Effect of Stereochemistry on Their Monolayer Behaviors

In this work, succinic gemini surfactants, dl‐ and meso‐2,3‐bis(alkyl)succinic acids (alkyl: C₆H₁₃–C₁₃H₂₇), were successfully synthesized by oxidative coupling of enolates of fatty acid tert‐butyl esters with copper(II) bromide followed by treatment with CF₃COOH. Focusing on the influence of stereochemistry (dl‐ and meso‐) of succinic geminis, their monolayer behaviors at the air–water interface were explored using surface pressure–area (Π–A) isotherms, the compression modulus of monolayers (ε_s), and Brewster angle microscope (BAM) analysis. meso‐2,3‐Bis(undecyl)succinic acid showed a unique isotherm where the surface pressure drastically decreased at A = ~0.56 nm² (Π = 21.9 mN m^?1) regardless of compression rates and subphase temperatures, while dl‐isomer showed the common isotherm of gas → liquid‐expanded → liquid‐condensed phase transitions. BAM analysis on meso‐2,3‐bis(undecyl)succinic acid films at the air–water interface showed that small islands of aggregates appear just after the maximum pressure (A = ~0.56 nm²), and on further compression needle‐shaped assemblies appear that can grow in size. It was reasonably concluded that hydrophobic interactions can operate more effectively in meso‐isomers than in dl‐isomers, and that meso‐molecules can “jump up” to cause a transition from monolayer to bilayer. This is the first finding of the “jumping‐up” phenomenon of gemini surfactants having meso‐stereochemistry.     

The growth of carbon coating layers on iron particles and the effect of alloying the iron with silicon

Magnetic fine particles of metallic Fe coated with graphitic carbon layers were synthesized by annealing Fe₂O₃ particles with carbon powders at 1673 K in nitrogen atmosphere. For comparison, SiC was added to Fe₂O₃. X-ray diffraction measurement showed that the lattice constants of Fe changed depending on the Si contents. Mössbauer spectroscopy confirmed that Fe-Si alloys were formed by the Si addition and that the iron carbide disappeared. Electron microscope images revealed that the thickness of carbon coating layers increased from 24 nm to 36 nm as a result of the Si addition. Soaking tests showed that the corrosion resistance of the carbon-coated Fe particles was improved by the addition of Si. The results suggest that Si caused C to leave the Fe cores and move to the surface to form a carbon coating.     

Approximation theorems for operator exponential and cosine functions

An integral approximation error is estimated for an operator exponential function, and the unimprovability of the estimate with respect to order is investigated. The smoothness of the initial vector in terms of the order of accuracy of the Cayley transform method is substantiated for approximations of operator exponential and cosine functions.