On the classical Maki–Thompson rumour model in continuous time

In this paper, the Maki–Thompson model is slightly refined in continuous time, and a new general solution is obtained for each dynamics of spreading of a rumour. It is derived an equation for the size of a stochastic rumour process in terms of transitions. We give new lower and upper bounds for the proportion of total ignorants who never learned a rumour and the proportion of total stiflers who either forget the rumour or cease to spread the rumour when the rumour process stops, under general initial conditions. Simulation results are presented for the analytical solutions. The model and these numerical results are capable to explain the behaviour of the dynamics of any other dynamical system having interactions similar to the ones in the stochastic rumour process and requiring numerical interpretations to understand the real phenomena better. The numerical process in the differential equations of the model is investigated by using error-estimates. The estimated error is calculated by the Runge–Kutta method and found either negligible or zero for a relatively small size of the population. This pioneering paper introduces a new mathematical method into Operations research, motivated by various areas of scientific, social and daily life, it presents numerical computations, discusses structural frontiers and invites the interested readers to future research.     

A Mass for ALF Manifolds

We prove a positive mass theorem on ALF manifolds, i.e. complete noncompact manifolds that are asymptotic to a circle fibration over a Euclidean base, with fibers of asymptotically constant length.     

Quantitative aspects of analyzing small molecules – monitoring singly or doubly charged ions? A case study of ximelagatran

Precision, reproducibility and lower limit of quantitation (LLOQ) are important characteristics of a quantitative method. We have investigated these properties for Ximelagatran (Xi), which has a high tendency to form doubly charged ions in electrospray ionization (ESI), by studying the percentage of doubly charged species formed when varying the formic acid (FA) concentration, analyte concentration, amount of organic modifier and flow rate. It was found that the percentage of [Xi + 2H]²⁺ can be controlled to be more than 90% or less than 10% by varying the amount of FA present, and that the change between these values is dramatic. Furthermore, the percentage of [Xi + 2H]²⁺ formed decreases with increased analyte concentration and increased flow rate. No apparent relationship with the amount of organic modifier was found. The results have the implication that, by carefully controlling the selected parameters, the LLOQ, precision and reproducibility can be improved. We have compared the fragmentation of the singly and doubly charged species and concluded that the [Xi + 2H]²⁺ ion is more inclined to undergo fragmentation than [Xi + H]⁺. As a consequence, unusual instrumental settings had to be used for the experiments. The fragmentation patterns are to a great extent similar, but the doubly charged species is more inclined to generate low‐mass product ions. Copyright © 2010 John Wiley & Sons, Ltd.     

Dissociative and molecular oxygen chemisorption channels on reduced rutile TiO2(110): An STM and TPD study

High-resolution scanning tunneling microscopy (STM) and temperature-programmed desorption (TPD) were used to study the interaction of O₂ with reduced TiO₂(110)–(1 × 1) crystals. STM is the technique of choice to unravel the relation between vacancy and non-vacancy assisted O₂ dissociation channels as a function of temperature. It is revealed that the vacancy-assisted, first O₂ dissociation channel is preferred at low temperature (~ 120 K), whereas the non-vacancy assisted, second O₂ dissociation channel operates at temperatures higher than 150 K–180 K. Based on the STM results on the two dissociative O₂ interaction channels and the TPD data, a new comprehensive model of the O₂ chemisorption on reduced TiO₂(110) is proposed. The model explains the relations between the two dissociative and the molecular O₂ interaction channels. The experimental data are interpreted by considering the available charge in the near-surface region of reduced TiO₂(110) crystals, the kinetics of the two O₂ dissociation channels as well as the kinetics of the diffusion and reaction of Ti interstitials.     

Oligocarbamate molecular transporters: design,synthesis, and biological evaluation of a new class of transporters for drug delivery

Molecular transporters have the ability to deliver drugs and probe molecules into cells and tissues irrespective of their physical properties. We now report the design, synthesis, and biological evaluation of a new family of molecular transporters, guanidinylated oligocarbamates that enable exceptionally efficient uptake into cells and tissues. The synthesis features a solid-phase stepwise oligomerization to obtain the oligocarbamates and a single step perguanidinylation for the facile introduction of up to nine guanidinium groups. The oligocarbamate 9-mer is found to be among the most efficient transporters known, entering cells faster than even d-Arg9 and HIV-1 Tat49-57. Significantly, this new family of transporters also enables uptake into the formidable skin barrier of a probe molecule that by itself does not penetrate skin.     

Contents of Volume 68 (2002)

Volume Contents

Contents of Volume 68 (2002)     

Universality class of criticality in the restricted primitive model electrolyte

The 1:1 equisized hard-sphere electrolyte or restricted primitive model has been simulated via grand-canonical fine-discretization Monte Carlo. Newly devised unbiased finite-size extrapolation methods using loci in the temperature-density or (T,rho) plane of isothermal rho(2-k) vs pressure inflections, of Q identical with(2)/ maxima, and of canonical and C(V) criticality, yield estimates of (T(c),rho(c)) to +/-(0.04,3)%. Extrapolated exponents and Q ratio are (gamma,nu,Q(c)) = [1.24(3), 0.63(3); 0.624(2)], which support Ising (n = 1) behavior with (1.23(9), 0.630(3); 0.623(6)), but exclude classical, XY (n = 2), self-avoiding walk (n = 0), and n = 1 criticality with potentials varphi(r)>Phi/r(4.9) when r-->infinity.     

On the verification of the applicability of the orthotropic plate wave theory to paper

In the literature one basic work can be found that describes an attempt to verify the applicability of the orthotropic plate wave theory to paper. In the present study we have repeated the key experiment and also modified the original experimental set-up to be able to make new complementary measurements. The performed verification attempt is based on a key experiment in which an ultrasonic resonance method is used. When it is applied to paper, a second resonance can be observed in addition to the one that originates from the asymmetric A0 mode. The result of the verification experiment is conclusive only if the source of this second resonance is the symmetric S0 mode. Our results show that the second resonance is not generated by the S0 mode. Instead, they indicate that the source is a longitudinal wave propagating in the thickness direction of the paper. We therefore conclude that the applicability of the orthotropic plate wave theory to paper cannot be verified by performing the key experiment that is described in the literature.     

Digestion method for silver accumulated in micro-organisms

Silver is accumulated to high concentrations in certain microbial strains. Here a bomb digestion method is proposed, using HNO3 and HCl, for the extraction and digestion of silver and silver compounds from the organic matrix. The method is applicable for the quantitative determination of silver by inductively coupled plasma atomic emission spectroscopy.