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.     

Unified Interactive Multiple Objective Programming: An Open Architecture For Accommodating New Procedures

It has previously been shown that nine of the most prominent procedures of interactive multiple objective programming can be considered as special cases of a common procedure called the unified algorithm. In this paper, we show how four additional procedures can be similarly included in the unified approach. Also, the paper presents a procedure-switching matrix that depicts the possibilities for switching from one procedure to another, one iteration to the next, in the unified algorithm if so directed by a user.     

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.     

DISCREPANCIES IN THE MEASUREMENT OF SPECTRAL SOURCES

Abstract— Comparison of spectroradiometric and meter measurements of a series of ultraviolet radiation sources indicates that a wide divergence between readings can occur. We found that with a xenon are filtered as a solar simulator producing UV-A (320–400 nm) and UV-B (290–320 nm) radiation, the meter can either over-or underestimate the emission of the source when different cutoff filters are used. The most severe discrepancy appears with the UV-B meter reading, although the UV-A reading can also be problematic. Meters should be calibrated against the specific sources they will be used to measure.     

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.