Not all Julia sets are quasi-self-similar

We show that there exist rational functions, whose Julia set fails to be quasi-self-similar.

     

Kinetics of the Oxidation of Monosaccharides with Acidic Bromate and N-Bromosuccinimide

Abstract

In earlier studies on the oxidation of monosaccharides, we measured the rates of the oxidation of three aldohexoses, two ketohexoses and three aldopentoses with V(V),¹ Ce(IV)²Cr(VI)³ and MII(VII).⁴We now report on the corresponding oxidations with bromate ion and N-bromosuccinimide (NBS) as oxidants. To our knowledge, only kinetic studies of oxidations of ribose with BrO₃-in aqueous H₂O₄ ⁵ and aldoses with NBS in 10% AcOH - H₂SO₄ ⁶ have been reported. Because oxidation of carbohydrates is subject to HSO₄- ion catalysis, HClO₄ was used, as in our earlier studies, in the present investigation to minimize the number of different catalyzing species.     

Melt‐compounded nanocomposites of titanium dioxide atomic‐layer‐deposition‐coated polyamide and polystyrene powders

Polyamide and polystyrene particles were coated with titanium dioxide films by atomic layer deposition (ALD) and then melt‐compounded to form polymer nanocomposites. The rheological properties of the ALD‐created nanocomposite materials were characterized with a melt flow indexer, a melt flow spiral mould, and a rotational rheometer. The results suggest that the melt flow properties of polyamide nanocomposites were markedly better than those of pure polyamide and polystyrene nanocomposites. Such behavior was shown to originate in an uncontrollable decrease in the polyamide molecular weight, likely affected by a high thin‐film impurity content, as shown in gel permeation chromatography (GPC) and scanning electron microscope (SEM) equipped with an energy‐dispersive spectrometer. Transmission electron microscope image showed that a thin film grew on both studied polymer particles, and that subsequent melt‐compounding was successful, producing well dispersed ribbon‐like titanium dioxide with the titanium dioxide filler content ranging from 0.06 to 1.12 wt%. Even though we used nanofillers with a high aspect ratio, they had only a minor effect on the tensile and flexural properties of the polystyrene nanocomposites. The mechanical behavior of polyamide nanocomposites was more complex because of the molecular weight degradation. Our approach here to form polymeric nanocomposites is one way to tailor ceramic nanofillers and form homogenous polymer nanocomposites with minimal work‐related risks in handling powder form nanofillers. However, further research is needed to gauge the commercial potential of ALD‐created nanocomposite materials. Copyright © 2011 John Wiley & Sons, Ltd.     

Determination of the Glass Electrode Parameters by Means of Potentiometric Titration of Acetic Acid in Aqueous Sodium or Potassium Chloride Solutions at 25°C

Single-ion activity coefficient equations are presented for the calculation of stoichiometric (molality scale) dissociation constants K _m for acetic acid in aqueous NaCl or KCl solutions at 25°C. These equations are of the Pitzer or Hückel type and apply to the case where the inert electrolyte alone determines the ionic strength of the acetic acid solution considered. K _m for a certain ionic strength can be calculated from the thermodynamic dissociation constant K _a by means of the equations for ionic activity coefficients. The data used in the estimation of the parameters for the activity coefficient equations were taken from the literature. In these data were included results of measurements on galvanic cells without a liquid junction (i.e., on cells of the Harned type). Despite the theoretical difficulties associated with the single-ion activity coefficients, K _m can be calculated for acetic acid in NaCl or KCl solutions by the Pitzer or Hückel method (the two methods give practically identical K _m values) almost within experimental error at least up to ionic strengths of about 1 mol-kg^–1. Potentiometric acetic acid titrations with base solutions (NaOH or KOH) were performed in a glass electrode cell at constant ionic strengths adjusted by NaCl or KCl. These titrations were analyzed by equation E = E _o + k(RT/F) ln[m(H⁺)], where m(H⁺) is the molality of protons, and E is the electromotive force measured. m(H⁺) was calculated for each titration point from the volume of the base solution added by using the stoichiometric dissociation constant K _m obtained by the Pitzer or Hückel method. During each base titration at a constant ionic strength, E _o and k in this equation were observed to be constants and were determined by linear regression analysis. The use of this equation in the analysis of potentiometric glass electrode data represents an improvement when compared to the common methods in use for two reasons. No activity coefficients are needed and problems associated with liquid junction potentials have been eliminated.     

Momentum‐based approximation of incompressible multiphase fluid flows

We introduce a time stepping technique using the momentum as dependent variable to solve incompressible multiphase problems. The main advantage of this approach is that the mass matrix is time‐independent making this technique suitable for spectral methods. A level set method is applied to reconstruct the fluid properties such as density. We also introduce a stabilization method using an entropy‐viscosity technique and a compression technique to limit the flattening of the level set function. We extend our algorithm to immiscible conducting fluids by coupling the incompressible Navier‐Stokes and the Maxwell equations. We validate the proposed algorithm against analytical and manufactured solutions. Results on test cases such as Newton's bucket problem and a variation thereof are provided. Surface tension effects are tested on benchmark problems involving bubbles. A numerical simulation of a phenomenon related to the industrial production of aluminium is presented at the end of the paper.     

The Prevalence of Voice Disorders Among Day Care Center Teachers Compared with Nurses: A Questionnaire and Clinical Study

The acceptance of voice disorders by day care center teachers as an occupational disease is not an invariably established practice. This is due to the lack of reliable evidence of a higher risk for voice disorders in this profession. To find out the risk of voice disorders, an epidemiological study was conducted among day care center teachers (n = 262), using hospital nurses (n = 108) as a control group. Symptoms were charted by a questionnaire. In a clinical examination made by a laryngologist, the voice quality was assessed and the laryngeal status noted. Teachers at day care centers had significantly more voice disorders than did nurses. Vocal nodules and laryngitis findings appeared significantly more frequently among day care center teachers than among those in the control group. The results prove voice disorders to be more frequent among day care center teachers than among control group subjects, and also that the main cause for this may be a higher vocal loading among day care center teachers than among control group subjects.     

Experimental aspects of ultrasonically enhanced cross-flow membrane filtration of industrial wastewater

Ultrasound based on-line cleaning for membrane filtration of industrial wastewater was studied. An ultrasonic transducer was assembled in the membrane module in order to get an efficient cleaning of membranes in fouling conditions. The focus of the studies was on the effects of the ultrasound propagation direction and frequency as well as the transmembrane pressure. The more open the membrane was the easier the membrane became plugged by wastewater colloids, when the ultrasound propagation direction was from the feed flow side of the membrane. If the membrane was tight enough, the ultrasound irradiated from the feed side of the membrane increased the flux significantly. However, in the circumstances studied, the power intensity needed during filtration was so high that the membranes eroded gradually at some spots of the membrane surface. It was discovered that the ultrasonic field produced by the used transducers was uneven in pressurised conditions. On the other hand, the ultrasound treatment at atmospheric pressure during an intermission pause in filtration turned out to be an efficient and, at the same time, a gentle method in membrane cleaning. The input power of 120 W (power intensity of 1.1 W/cm2) for a few seconds was sufficient for cleaning. The flux improvement was significant when using a frequency of 27 kHz but only minor when using 200 kHz.     

Nonlinear magnetohydrodynamics in axisymmetric heterogeneous domains using a Fourier/finite element technique and an interior penalty method

The Maxwell equations in the MHD limit in heterogeneous axisymmetric domains composed of conducting and non-conducting regions are solved by using a mixed Fourier/Lagrange finite element technique. Finite elements are used in the meridian plane and Fourier modes are used in the azimuthal direction. Parallelization is made with respect to the Fourier modes. Continuity conditions across interfaces are enforced using an interior penalty technique. The performance of the method is illustrated on kinematic and full dynamo configurations.     

Filtering the histories of a partially observed marked point process

We consider a situation in which the evolution of an ‘underlying’ marked point process is of interest, but where this process is not directly observable. Instead, we assume that another marked point process, which is fully determined by the underlying process, can be observed. The problem is then the estimation, at any given time t, of the underlying development so far, given the corresponding observations. The solution, in the sense of a conditional distribution of the underlying pre-t history, is shown to satisfy a recursive filter formula. Sufficient conditions for the uniqueness of the solution are given. Two non-trivial examples are considered in detail.