Maps that are roots of power series

We introduce a class of polynomial maps that we call polynomial roots of powerseries, and show that automorphisms with this property generate the automorphism group in any dimension. In particular we determine generically which polynomial maps that preserve the origin are roots of powerseries. We study the one-dimensional case in greater depth. Funded by Veni-grant of council for the physical sciences, Netherlands Organisation for scientific research (NWO).     

Phase equilibria in binary mixtures of ethane and hexadecane

This paper reports experimental results of a study of the phase behaviour of binary mixtures of ethane + hexadecane. In the near-critical region of ethane liquid + vapour and solid hexadecane + liquid two-phase boundaries have been measured. Also the three-phase equilibrium solid hexadecane + liquid + vapour has been determined experimentally. The experimental data cover the complete mole fraction range. Pressures up to 18 MPa were applied and the investigation was performed in a temperature region from about 260 K up to 450 K.     

Mössbauer studies of medium-carbon,high-chromium martensitic steels

⁵⁷Fe Mössbauer effect spectroscopy is employed to determine the relationship between the microstructure and the mechanical properties of martensitic steels with base composition Fe-10wt%Cr-0,26wt%C. The microstructure consists predominantly of two phases: martensite and austenite. The effect of low concentrations of both Mn and Ni on the structure and the mechanical properties of these steels is studied. The results indicate that Mn and Ni additions are equally effective in increasing the fraction of retained austenite. The austenite is an important phase since it is considered to be beneficial to the toughness of steel. However, we find that the impact toughness first decreases and then increases as a function of the fraction of austenite.     

Cellular structures in solid fuel combustion

The objective of this contribution is to investigate whether the mechanism of the thermal diffusion instability in gaseous flames causing cellular flame structures also occurs during the combustion of porous solid fuel. Based on conservation for mass and energy, the relevant set of differential equations was derived. Assuming thermal equilibrium between fuel and oxidiser, a global energy equation was valid for both solid and gaseous phase. The resulting set of differential equations was discretised by the Collocation method to arrive at a system of algebraic equations. In order to investigate into cellular flame structures, an infinitesimal disturbance was superimposed onto the plane conversion front. Carrying out a linear instability analysis, yielded eigenvalues dependent on the wave number of the disturbance. A critical wave number exists below which the real part of the eigenvalues is positive, thus, indicating a regime of instability. Within this region, eigenvalues with a not-vanishing imaginary part of the eigen value existed causing cellular flame structures. However, the growth rate of disturbances was found to be small, which may explain the difficulty to investigate this phenomena experimentally.     

Anion–π Interactions in Salts with Polyhalide Anions: Trapping of I42−

The directionality of interaction of electron‐deficient π systems with spherical anions (e.g,. halides) can be controlled by secondary effects like NH or CH hydrogen bonding. In this study a series of pentafluorophenyl‐substituted salts with polyhalide anions is investigated. The compounds are obtained by aerobic oxidation of the corresponding halide upon crystallization. Solid‐state structures reveal that in bromide 2 , directing NH–anion interactions position the bromide ion in an η¹‐type fashion over but not in the center of the aromatic ring. The same directing forces are effective in corresponding tribromide salt 3 . In the crystal, the bromide ion is paneled by four electron‐deficient aromatic ring systems. In addition, compounds 4 and 6 , which have triiodide and the rare tetraiodide dianion as anions, are described. Computational studies reveal that the latter is highly unstable. In the present case it is stabilized by the crystal lattice, for example, by interaction with electron‐deficient π systems.     

Loss analysis and increasing of the fabrication tolerance of resonant coupling by tapering the mode beating section

The film mode matching method was used to analyze the inter waveguide coupling losses in a passive asymmetric twin waveguide caused by waveguide width and refractive index variation for both resonant and adiabatic coupling at a wavelength of 1,550 nm. The reasons for power losses are shown. It is demonstrated that tapering the mode beating section of the resonant coupler can increase the fabrication tolerance of resonant coupling without increasing the coupling length.