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.     

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.     

Cyclophosphamides from aminosugars and aminonucleosides

Condensation of bis-(2-chloroethyl)phosphoramidic dichloride with 3′-amino-3′-deoxy-N,N-dimethyladenosine afforded the 2′,3′-cyclicphosphorodiamidate (III). By an improved synthesis, methyl 3-amino-3-deoxy-β-D-ribofuranoside was obtained as a model compound for conversion to the analogous 2,3-cyclicphosphorodiamidate (XII). Existence of the latter as two diastereomers due to phosphorus asymmetry was shown by nmr analysis, using comparison with the 5-(O-p-nitrobenzoate) (XIII) as a basis for assignments.     

Correlation hole and physical properties: A model calculation

The correlation hole of Coulson and Nielson and its extension to momentum space by Banyard and Reed is studied by using an exactly solvable model. For this model all relevant quantities pertaining to the correlation hole have been calculated exactly. We use this model to study the relationship between the fit to the correlation hole for an approximate wave function and the closeness of the approximate energies to the exact ones. We show that, although in general the better the fit the closer are the approximate physical quantities to the exact ones, there are exceptions where that is not the case. Also, we present a convenient method for the calculation of the two particle distribution in momentum space and generalize the concept of the correlation hole by defining it in the pseudophase space of position and momentum.     

Chemo-enzymatic synthesis of 4-methylumbelliferyl beta-(1-->4)-D-xylooligosides: new substrates for beta-D-xylanase assays

Transglycosylation catalyzed by a beta-D-xylosidase from Aspergillus sp. was used to synthesize a set of 4-methylumbelliferyl (MU) beta-1-->4-D-xylooligosides having the common structure [beta-D-Xyl-(1-->4)]2-5-beta-D-Xyl-MU. MU xylobioside synthesized chemically by the condensation of protected MU beta-D-xylopyranoside with ethyl 2,3,4-tri-O-acetyl-1-thio-beta-D-xylopyranoside was used as a substrate for transglycosylation with the beta-D-xylosidase from Aspergillus sp. to produce higher MU xylooligosides. The structures of oligosaccharides obtained were established by 1H and 13C NMR spectroscopy and electrospray tandem mass spectrometry. MU beta-D-xylooligosides synthesized were tested as fluorogenic substrates for the GH-10 family beta-D-xylanase from Aspergillus orizae and the GH-11 family beta-D-xylanase I from Trichoderma reesei. Both xylanases released the aglycone from MU xylobioside and the corresponding trioside. With substrates having d.p. 4 and 5, the enzymes manifested endolytic activities, splitting off MU, MUX, and MUX2 primarily.