The PCF Trichotomy Theorem does not hold for short sequences

Abstract. The PCF Trichotomy Theorem deals with sequences of ordinal functions on an infinite modulo some ideal I. If a -increasing sequence of ordinal functions has regular length which is larger than , then by the Trichotomy Theorem the sequence satisfies one of three structural conditions. It was of some interest to find out if the Trichotomy Theorem could hold also for sequences of length . It is shown that this is not the case. Received: 17 January 1998     

Voice Prosthesis Coated with Sustained Release Varnish Containing Clotrimazole Shows Long-Term Protection against Candida albicans: An In Vitro Study

Fungal biofilm formation on voice prosthesis (VP) is a major health problem that requires repeated replacement of the prosthesis. Candida albicans is one of the pathogens that frequently inhabits the VP. We proposed that coating VPs with sustained-release varnish (SRV) containing clotrimazole (CTZ) might prevent fungal biofilm formation. The long-term antifungal activities of SRV-CTZ- versus SRV-placebo-coated VPs was tested daily by measuring the inhibition zone of C. albicans seeded on agar plates or by measuring the fungal viability of C. albicans in suspension. The extent of biofilm formation on coated VPs was analyzed by confocal microscopy and scanning electron microscopy. We observed that SRV-CTZ-coated VPs formed a significant bacterial inhibition zone around the VPs and prevented the growth of C. albicans in suspension during the entire testing period of 60 days. Fungal biofilms were formed on placebo-coated VPs, while no significant biofilms were observed on SRV-CTZ-coated VPs. HPLC analysis shows that CTZ is continuously released during the whole test period of 60 days at a concentration above the minimal fungistatic concentration. In conclusion, coating VPs with an SRV-CTZ film is a potential effective method for prevention of fungal infections and biofilm formation on VPs.     

Aggregation and deposition kinetics of fullerene (C60) nanoparticles

The aggregation and deposition kinetics of fullerene C60 nanoparticles have been investigated over a wide range of monovalent and divalent electrolyte concentrations by employing time-resolved dynamic light scattering (DLS) and quartz crystal microbalance (QCM), respectively. Aggregation kinetics of the fullerene nanoparticles exhibited reaction-limited (slow) and diffusion-limited (fast) regimes in the presence of both electrolytes, having critical coagulation concentrations (CCC) of 120 and 4.8 mM for the monovalent (NaCl) and divalent (CaCl2) salts, respectively. The measured stability ratios of the aggregating fullerene nanoparticles were in very good agreement with Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, with a derived Hamaker constant of 6.7 x 10-21 J for the fullerene nanoparticles in aqueous medium. For the deposition kinetics studies, the rate of fullerene nanoparticle deposition increased with increasing electrolyte concentrations, as was indicated in the aggregation kinetics results. However, at electrolyte concentrations approaching or exceeding the CCC, the rate of deposition dropped sharply due to significant concurrent aggregation of the fullerene nanoparticles. The deposition of the fullerene nanoparticles was further shown to be mostly irreversible, with immediate detachment of the nanoparticles observed only when exposed to a solution of high pH.     

Convexity numbers of closed sets in

For 2$"> let be the -ideal in generated by all sets which do not contain equidistant points in the usual metric on . For each 2$"> a set is constructed in so that the -ideal which is generated by the convex subsets of restricted to the convexity radical is isomorphic to . Thus is equal to the least number of convex subsets required to cover -- the convexity number of .

For every non-increasing function \aleph_0\}$"> we construct a model of set theory in which for each . When is strictly decreasing up to , uncountable cardinals are simultaneously realized as convexity numbers of closed subsets of . It is conjectured that , but never more than , different uncountable cardinals can occur simultaneously as convexity numbers of closed subsets of . This conjecture is true for and .     

Van der Waerden spaces

A topological space is van der Waerden if for every sequence in there exists a converging subsequence so that contains arbitrarily long finite arithmetic progressions. Not every sequentially compact space is van der Waerden. The product of two van der Waerden spaces is van der Waerden.

The following condition on a Hausdorff space is sufficent for to be van der Waerden:

The closure of every countable set in is compact and first-countable.

A Hausdorff space that satisfies satisfies, in fact, a stronger property: for every sequence in :

There exists so that is converging, and contains arbitrarily long finite arithmetic progressions and sets of the form for arbitrarily large finite sets .

There are nonmetrizable and noncompact spaces which satisfy . In particular, every sequence of ordinal numbers and every bounded sequence of real monotone functions on satisfy .

     

Novel porous polyurethane films

Polyurethane films treated in a two-stage process with aqueous bromine and ammonia solutions underwent significant modifications in crystalline and surface structure as well as in mechanical and physical properties. Bromine was sorbed on the film, and formed several charge transfer complexes with the soft and hard segments of the polyurethane as well as bridges between adjacent chains. In the second stage, ammonia reacted with the sorbed bromine producing gaseous nitrogen and ammonium bromide. The expansion of the gas resulted in a repacking of the polymeric chains and the formation of a porous structure. The bromine concentrations used and the times of contact between the films and the bromine were 0.02–0.06 normal and 1–10 min, respectively. The contact angle of the films decreased, depending on treatment conditions, from 73 to 20. The water vapor permeability increased three-fold. The treatment appeared to bring about a crystallization in the hard as well as in the soft segments of the PU as shown by differential scanning calorimetry measurements. Possible applications of the treated films for wound dressing are discussed. © 1998 John Wiley & Sons, Ltd.     

SWNT-MWNT hybrid filter attains high viral removal and bacterial inactivation

We describe the concept and demonstrate the efficacy of a novel SWNT-MWNT hybrid filter for the removal and inactivation of microbial pathogens from water. The filter is composed of a thin SWNT layer (0.05 mg cm(-2)) on top of a thicker MWNT layer (0.27 mg cm(-2)) supported by a microporous support membrane. The SWNT-MWNT filter exhibits high log removal of several model viruses (MS2, PRD1, and T4 bacteriophages) by depth filtration, which predominantly takes place in the thicker and more uniform MWNT layer. The filter removes all bacteria by a sieving mechanism, with the top SWNT layer providing high levels of inactivation of model bacteria (Escherichia coli K12 and Staphylococcus epidermidis), as well as microbes from river water and treated wastewater effluent. The dual-layer SWNT-MWNT filter lays the framework for new possibilities in point-of-use water filtration.     

Force field‐dependant structural divergence revealed during long time simulations of Calbindin d9k

The structural and the dynamic features of the Calbindin (CaB) protein in its holo and apo states are compared using molecular dynamics simulations under nine different force fields (FFs) (G43a1, G53a6, Opls‐AA, Amber94, Amber99, Amber99p, AmberGS, AmberGSs, and Amber99sb). The results show that most FFs reproduce reasonably well the majority of the experimentally derived features of the CaB protein. However, in several cases, there are significant differences in secondary structure properties, root mean square deviations (RMSDs), root mean square fluctuations (RMSFs), and S² order parameters among the various FFs. What is more, in certain cases, these parameters differed from the experimentally derived values. Some of these deviations became noticeable only after 50 ns. A comparison with experimental data indicates that, for CaB, the Amber94 shows overall best agreement with the measured values, whereas several others seem to deviate from both crystal and nuclear magnetic resonance data. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Biocidal activity of plasma modified electrospun polysulfone mats functionalized with polyethyleneimine-capped silver nanoparticles

The incorporation of silver nanoparticles (AgNPs) into polymeric nanofibers has attracted a great deal of attention due to the strong antimicrobial activity that the resulting fibers exhibit. However, bactericidal efficacy of AgNP-coated electrospun fibrous mats has not yet been demonstrated. In this study, polysulfone (PSf) fibers were electrospun and surface-modified using an oxygen plasma treatment, which allowed for facile irreversible deposition of cationically charged polyethyleneimine (PEI)-AgNPs via electrostatic interactions. The PSf-AgNP mats were characterized for relative silver concentration as a function of plasma treatment time using ICP-MS and changes in contact angle. Plasma treatment of 60 s was the shortest time required for maximum loss of bacteria (Escherichia coli) viability. Time-dependent bacterial cytotoxicity studies indicate that the optimized PSf-AgNP mats exhibit a high level of inactivation against both gram negative bacteria, Escherichia coli, and gram positive bacteria, Bacillus anthracis and Staphylococcus aureus.