Christian Svensson

DYNAMICAL SYSTEMS AND COMMUTANTS IN CROSSED PRODUCTS

In this paper, we describe the commutant of an arbitrary subalgebra A of the algebra of functions on a set X in a crossed product of A with the integers, where the latter act on A by a composition automorphism defined via a bijection of X. The resulting conditions which are necessary and sufficient for A to be maximal abelian in the crossed product are subsequently applied to situations where these conditions can be shown to be equivalent to a condition in topological dynamics. As a further step, using the Gelfand transform, we obtain for a commutative completely regular semi-simple Banach algebra a topological dynamical condition on its character space which is equivalent to the algebra being maximal abelian in a crossed product with the integers.

Connections Between Dynamical Systems and Crossed Products of Banach Algebras by ℤ

Starting with a complex commutative semi-simple regular Banach algebra A and an automorphism σ of A, we form the crossed product of A by the integers, where the latter act on A via iterations of σ. The automorphism induces a topological dynamical system on the character space Δ(A) of A in a natural way. We prove an equivalence between the property that every nonzero ideal in the crossed product has non-zero intersection with the subalgebra A, maximal commutativity of A in the crossed product, and density of the non-periodic points of the induced system on the character space. We also prove that every non-trivial ideal in the crossed product always intersects the commutant of A non-trivially. Furthermore, under the assumption that A is unital and such that Δ(A) consists of infinitely many points, we show equivalence between simplicity of the crossed product and minimality of the induced system, and between primeness of the crossed product and topological transitivity of the system.

γ-Al2O3-based nanocomposite adsorbents for arsenic(V) removal: Assessing performance, toxicity and particle leakage.

The generation and development of effective adsorption materials for arsenic removal are urgently needed due to acute arsenic contamination of water sources in many regions around the world. In the search for these new adsorbents, the application of nanomaterials or nanocomposites, and especially the use of nanoparticles (NPs), has proven increasingly attractive. While the adsorptive performance of a range of nanocomposite and nanomaterial-based systems has been extensively reviewed in previously-published literature, the stability of these systems in terms of NP release, i.e. the ability of the nanomaterial or nanocomposite to retain incorporated NPs, is less well understood. Here we examine the performance of nanocomposites comprised of aluminium oxide nanoparticles (AluNPs) incorporated in macroporous polyacrylamide-based cryogels (n-Alu-cryo, where n indicates the percentage of AluNPs in the polymer material (n=0-6%, w/v)) for As(V) adsorption, and evaluate AluNP leakage before and after the use of these materials. A range of techniques is utilised and assessed (SEM, TEM, mass weight change, PIXE and in vitro toxicity studies). The 4-Alu-cryo nanocomposite was shown to be optimal for minimising AluNP losses while maximising As(V) removal. From the same nanocomposite we were further able to show that NP losses were not detectable at the AluNP concentrations used in the study. Toxicity tests revealed that no cytotoxic effects could be observed. The cryogel-AluNPs composites were not only effective in As(V) removal but also in immobilising the AluNPs. More challenging flow-through conditions for the evaluation of NP leakage could be included as a next step in a continued study assessing particle loss and subsequent toxicity.

Gas-borne particles with tunable and highly controlled characteristics for nanotoxicology studies.

Abstract For nanotoxicology investigations of air-borne particles to provide relevant results it is ever so important that the particle exposure of, for example cells, closely resembles the “real” exposure situation, that the dosimetry is well defined, and that the characteristics of the deposited nanoparticles are known in detail. By synthesizing the particles in the gas-phase and directly depositing them on lung cells the particle deposition conditions in the lung is closely mimicked. In this work we present a setup for generation of gas-borne nanoparticles of a variety of different materials with highly controlled and tunable particle characteristics, and demonstrate the method by generation of gold particles. Particle size, number concentration and mass of individual particles of the population are measured on-line by means of differential mobility analyzers (DMA) and an aerosol particle mass analyzer (APM), whereas primary particle size and internal structure are investigated by transmission electron microscopy. A method for estimating the surface area dose from the DMA-APM measurements is applied and we further demonstrate that for the setup used, a deposition time of around 1 h is needed for deposition onto cells in an air–liquid interface chamber, using electrostatic deposition, to reach a toxicological relevant surface area dose.

Analysis of nanoparticle–protein coronas formed in vitro between nanosized welding particles and nasal lavage proteins

Abstract Welding fumes include agglomerated particles built up of primary nanoparticles. Particles inhaled through the nose will to some extent be deposited in the protein-rich nasal mucosa, and a protein corona will be formed around the particles. The aim was to identify the protein corona formed between nasal lavage proteins and four types of particles with different parameters. Two of the particles were formed and collected during welding and two were manufactured iron oxides. When nasal lavage proteins were added to the particles, differences were observed in the sizes of the aggregates that were formed. Measurements showed that the amount of protein bound to particles correlated with the relative size increase of the aggregates, suggesting that the surface area was associated with the binding capacity. However, differences in aggregate sizes were detected when nasal proteins were added to UFWF and Fe2O3 particles (having similar agglomerated size) suggesting that yet parameters other than size determine the binding. Relative quantitative mass spectrometric and gel-based analyses showed differences in the protein content of the coronas. High-affinity proteins were further assessed for network interactions. Additional experiments showed that the inhibitory function of secretory leukocyte peptidase inhibitor, a highly abundant nasal protein, was influenced by particle binding suggesting that an understanding of protein function following particle binding is necessary to properly evaluate pathophysiological events. Our results underscore the importance of including particles collected from real working environments when studying the toxic effects of particles because these effects might be mediated by the protein corona.

Algebraic curves for commuting elements in the

In this paper we extend the eliminant construction of Burchnall and Chaundy for commuting differential operators in the Heisenberg algebra to the q-deformed Heisenberg algebra and show that it again provides annihilating curves for commuting elements, provided q satisfies a natural condition. As a side result we obtain estimates on the dimensions of the eigenspaces of elements of this algebra in its faithful module of Laurent series.

q

An ongoing discussion whether traditional toxicological methods are sufficient to evaluate the risks associated with nanoparticle inhalation has led to the emergence of Air-Liquid interface toxicology. As a step in this process, this study explores the evolution of particle characteristics as they move from the airborne state into physiological solution. Airborne gold nanoparticles (AuNP) are generated using an evaporation-condensation technique. Spherical and agglomerate AuNPs are deposited into physiological solutions of increasing biological complexity. The AuNP size is characterized in air as mobility diameter and in liquid as hydrodynamic diameter. AuNP:Protein aggregation in physiological solutions is determined using dynamic light scattering, particle tracking analysis, and UV absorption spectroscopy. AuNPs deposited into homocysteine buffer form large gold-aggregates. Spherical AuNPs deposited in solutions of albumin were trapped at the Air-Liquid interface but was readily suspended in the solutions with a size close to that of the airborne particles, indicating that AuNP:Protein complex formation is promoted. Deposition into serum and lung fluid resulted in larger complexes, reflecting the formation of a more complex protein corona. UV absorption spectroscopy indicated no further aggregation of the AuNPs after deposition in solution. The corona of the deposited AuNPs shows differences compared to AuNPs generated in suspension. Deposition of AuNPs from the aerosol phase into biological fluids offers a method to study the protein corona formed, upon inhalation and deposition in the lungs in a more realistic way compared to particle liquid suspensions. This is important since the protein corona together with key particle properties (e.g. size, shape and surface reactivity) to a large extent may determine the nanoparticle effects and possible translocation to other organs.