On the invariant measure for the quasi‐linear Lasota equation

The problem of the existence of the invariant measure is important considering its connections with chaotic behaviour. In the papers (Zesz. Nauk. Uniw. Jagiellońskiego, Pr. Mat. 1982; 23 :117–123; Ann. Pol. Math. 1983; XLI :129–137; J. Differential Equations 2004; 196 :448–465) the existence of invariant and ergodic measures according to the dynamical system generated by the Lasota equation was proved, i.e. the equation describing the dynamics and becoming different of the population of cells. In this paper, the existence of such measure for the quasi‐linear Lasota equation is proved. This measure is the carriage of the measure described by Dawidowicz (Zesz. Nauk. Uniw. Jagiellońskiego, Pr. Mat. 1982; 23 :117–123). Copyright © 2006 John Wiley & Sons, Ltd.     

Relevance of Reflection in Static and Dynamic Light Scattering Experiments

Using a monodisperse PMMA dispersion, it was shown that light reflection at the sample cuvette walls may greatly influence the results of both static (SLS) and dynamic (DLS) light scattering experiments. Considering SLS, this reflection phenomenon mostly causes an overestimation of the scattered intensity at high scattering angles, which may give rise to the emergence of an additional, artificial peak in the lower region of the particle size distribution. On the other hand, the influcence of reflection on DLS measurements was shown to be particularly important in the upper region of the particle size distribution. The experimentally observed phenomena were explained from the basic principles of both particle sizing methods. Finally, it was shown that the disturbing effect of reflection could be avoided by modifying either the hardware or the software of the static and dynamic light scattering technique.     

Characterization of heat-assisted magnetic probe recording on CoNi/Pt multilayers

A method of heat-assisted magnetic recording (HAMR) potentially suitable for probe-based storage systems is characterized. In this work, field emission current from a scanning tunneling microscope (STM) tip is used as the heating source. Pulse voltages of 2–7 V were applied to a CoNi/Pt multilayered film fabricated on either bare silicon or oxidized silicon substrates. Different types of Ir/Pt and W STM tips were used in the experiment. The results show that thermally recorded magnetic marks are formed with a nearly uniform mark size of 170 nm on the film fabricated on bare silicon substrate when the pulse voltage is above a threshold voltage. The mark size becomes 260 nm when they are written on the identical film fabricated on an oxidized silicon substrate. The threshold voltage depends on the material work function of the tip, with W having a threshold voltage about 1 V lower than Pt. A synthesized model, which contains the calculation of the emission current, the simulation of heat transfer during heating, and the study of magnetic domain formation, was introduced to explain experimental results. The simulation agrees well with the experiments.     

Statistics of travel time and intensity of two first arrivals of short pulses backscattered by a rough 3D surface

The time history of a pulse backscattered by a rough surface contains information about the position of the surface and the properties of the scatterers. This information is utilized successfully in a number of remote sensing techniques ranging from echo sounding of the ocean bottom to medical ultrasonics and satellite altimetry. In the current paper, statistical properties of backscattered waves are considered in a geometrical optics approximation. The probing pulse duration is assumed to be sufficiently short so that signals backscattered in the vicinity of individual specular points on a rough surface do not overlap in time. Theoretical results previously obtained for a 2D problem [I. M. Fuks and O. A. Godin, 2005, Waves in Random and Complex Media, 14, 539-562; M. I. Charnotskii and I. M. Fuks, 2005, Waves in Random and Complex Media, 15, 451-467] are extended to wave scattering by 3D rough surfaces by following a mathematical approach developed in stochastic geometry. Predictions of an asymptotic theory are verified against results of Monte-Carlo simulations. Probability density functions of travel times and intensities of the first and second arrivals of the backscattered wave are quantified in terms of statistical moments of roughness assuming normal distribution of elevations. It is found that, as in the 2D case, the travel time and the intensity are strongly correlated; on average, the earlier a signal arrives, the smaller is its intensity.     

Amidinoethylation—a new reaction—IV : The amidinoethylation of alcohols: a facile synthesis of 3-alkoxy-N,N'-substituted-propanamidines

The amidinoethylation of alcohols takes place by the addition of sodium alkoxides 2 (R¹ = Me, Et) to the CC double bond of a variety of N,N'-substituted-propenamidines 1 (Method A). This illustrates the activation of the CC double bond by the conjugated amidine function and provides a new class of Michael acceptors for alcohols. However, this activation is poorer than with other nucleophiles or Michael acceptors. The amidinoethylation makes available 3-alkoxy-N,N'-substituted-amidines not easily accessible by other classical methods. However, it is demonstrated that the general N,N'-substituted-amidine synthesis via the nitrilium salts can also apply to nitrile compounds having an alkoxygroup present on the molecule (method B). Since the cyanoethylation of alcohols (4) is a very fast and facile reaction the method B is the preferred strategy for the synthesis of 3-alkoxy-N,N'-substituted-propanamidines 3.     

Equilibria in complexes of N-heterocyclic molecules,part XII. The reaction of hydroxide and alkoxide Ions with platinum(II) complexes of 5-nitro-1,10-phenanthroline and 2,2′-bipyridyl

Summary Bis-(5-nitro-1,10-phenanthroline)platinum(II) dichloride and diperchlorate have been prepared. The reaction between the parent cation and hydroxide ion has been studied using 1 FI n.m.r. spectroscopy and found to involve attack at the ligand. The bis-(2,2-bipyridyl)platinum(II) ion has been shown to be highly reactive towards methoxide ion. The dissociation of a 2,2-bipyridyl ligand is preceded by attack at the ligand.Part XI: R. D. Gillard, t.. A. P. Kane-Maguire and P. A. Williams,Transition Met. Chem., 2, 47 (1977).On leave from the University of Baghdad, Iraq.