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.     

Penicillium camemberti and Penicillium roqueforti enhance the growth and survival of Shiga toxin-producing Escherichia coli O157 under mild acidic conditions

The effects of secondary starter molds of common mold-ripened cheeses on the Shiga toxin-producing Escherichia coli (STEC) O157 were assessed in 3 model systems. In the 1st model, 8 STEC O157 strains were incubated in the spent culture of Penicillium camemberti or Penicillium roqueforti under mild acidic conditions at 25 °C. In the spent cultures of the mold at pH 4.8 to 5.0, the lag times of STEC O157 growth were significantly shorter than those observed in fresh medium. Analyses of the spent culture of P. camemberti showed that the causative agents of the growth enhancement were produced by the mold in response to an acidic environment and were not fully inactivated in heat treatment. In the 2nd model, P. camemberti and STEC O157 were cocultured in acidified milk at 25 °C. The population of STEC O157 reached 10(8) CFU/mL in the presence of the mold, whereas the population steadily declined in the absence of the mold. Although this growth enhancement was partially attributable to alkalization by the mold, it was observed even when the pH of this model was stabilized. In the 3rd model, 2 STEC O157 strains were incubated in the spent cultures of molds at pH 4.5 at 10 °C. In the spent culture, proportions of injured cells were significantly lower and D values were significantly higher than those in control, except one STEC O157 strain in the spent culture of P. camemberti. These results showed that the molds could enhance the growth and survival of STEC O157 by changing the environment. Practical Application: This study demonstrated that molds in foods can improve the growth and survival of the Shiga toxin-producing Escherichia coli O157. Because microbial interactions are ubiquitous in food, our results provide an important insight for understanding the behavior of microorganisms in food.     

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.     

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.     

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.     

Simple and accurate methods for quantifying deformation,disruption, and development in biological tissues

When mechanical factors underlie growth, development, disease or healing, they often function through local regions of tissue where deformation is highly concentrated. Current optical techniques to estimate deformation can lack precision and accuracy in such regions due to challenges in distinguishing a region of concentrated deformation from an error in displacement tracking. Here, we present a simple and general technique for improving the accuracy and precision of strain estimation and an associated technique for distinguishing a concentrated deformation from a tracking error. The strain estimation technique improves accuracy relative to other state-of-the-art algorithms by directly estimating strain fields without first estimating displacements, resulting in a very simple method and low computational cost. The technique for identifying local elevation of strain enables for the first time the successful identification of the onset and consequences of local strain concentrating features such as cracks and tears in a highly strained tissue. We apply these new techniques to demonstrate a novel hypothesis in prenatal wound healing. More generally, the analytical methods we have developed provide a simple tool for quantifying the appearance and magnitude of localized deformation from a series of digital images across a broad range of disciplines.     

Method for evaluating detergency of hydrocarbon solvents

Translated from Khimiya i Tekhnologiya Topliv i Masel, No. 2, p. 36, February, 1988.