Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions

This paper is aimed to show the essential role played by the theory of quasi-analytic functions in the study of the determinacy of the moment problem on finite and infinite-dimensional spaces. In particular, the quasi-analytic criterion of self-adjointness of operators and their commutativity are crucial to establish whether or not a measure is uniquely determined by its moments. Our main goal is to point out that this is a common feature of the determinacy question in both the finite and the infinite-dimensional moment problem, by reviewing some of the most known determinacy results from this perspective. We also collect some properties of independent interest concerning the characterization of quasi-analytic classes associated to log-convex sequences.Comment: 28 pages, Stochastic and Infinite Dimensional Analysis, Chapter 9, Trends in Mathematics, Birkh\"auser Basel, 201

Inversion of Randomly Corrugated Surfaces Structure from Atom Scattering Data

The Sudden Approximation is applied to invert structural data on randomly corrugated surfaces from inert atom scattering intensities. Several expressions relating experimental observables to surface statistical features are derived. The results suggest that atom (and in particular He) scattering can be used profitably to study hitherto unexplored forms of complex surface disorder.Comment: 10 pages, no figures. Related papers available at http://neon.cchem.berkeley.edu/~dan

The scattering from generalized Cantor fractals

We consider a fractal with a variable fractal dimension, which is a generalization of the well known triadic Cantor set. In contrast with the usual Cantor set, the fractal dimension is controlled using a scaling factor, and can vary from zero to one in one dimension and from zero to three in three dimensions. The intensity profile of small-angle scattering from the generalized Cantor fractal in three dimensions is calculated. The system is generated by a set of iterative rules, each iteration corresponding to a certain fractal generation. Small-angle scattering is considered from monodispersive sets, which are randomly oriented and placed. The scattering intensities represent minima and maxima superimposed on a power law decay, with the exponent equal to the fractal dimension of the scatterer, but the minima and maxima are damped with increasing polydispersity of the fractal sets. It is shown that for a finite generation of the fractal, the exponent changes at sufficiently large wave vectors from the fractal dimension to four, the value given by the usual Porod law. It is shown that the number of particles of which the fractal is composed can be estimated from the value of the boundary between the fractal and Porod regions. The radius of gyration of the fractal is calculated analytically.Comment: 8 pages, 4 figures, accepted for publication in J. Appl. Crys

Black carbon measurements in the boundary layer over western and northern Europe

Europe is a densely populated region that is a significant global source of black carbon (BC) aerosol, but there is a lack of information regarding the physical properties and spatial/vertical distribution of rBC in the region. We present the first aircraft observations of sub-micron refractory BC (rBC) aerosol concentrations and physical properties measured by a single particle soot photometer (SP2) in the lower troposphere over Europe. The observations spanned a region roughly bounded by 50° to 60° N and from 15° W to 30° E. The measurements, made between April and September 2008, showed that average rBC mass concentrations ranged from about 300 ng m−3 near urban areas to approximately 50 ng m−3 in remote continental regions, lower than previous surface-based measurements. rBC represented between 0.5 and 3% of the sub-micron aerosol mass. Black carbon mass size distributions were log-normally distributed and peaked at approximately 180 nm, but shifted to smaller diameters (~160 nm) near source regions. rBC was correlated with carbon monoxide (CO) but had different ratios to CO depending on location and air mass. Light absorption coefficients were measured by particle soot absorption photometers on two separate aircraft and showed similar geographic patterns to rBC mass measured by the SP2. We summarize the rBC and light absorption measurements as a function of longitude and air mass age and also provide profiles of rBC mass concentrations and size distribution statistics. Our results will help evaluate model-predicted regional rBC concentrations and properties and determine regional and global climate impacts from rBC due to atmospheric heating and surface dimming

Fractal Analysis of Protein Potential Energy Landscapes

The fractal properties of the total potential energy V as a function of time t are studied for a number of systems, including realistic models of proteins (PPT, BPTI and myoglobin). The fractal dimension of V(t), characterized by the exponent \gamma, is almost independent of temperature and increases with time, more slowly the larger the protein. Perhaps the most striking observation of this study is the apparent universality of the fractal dimension, which depends only weakly on the type of molecular system. We explain this behavior by assuming that fractality is caused by a self-generated dynamical noise, a consequence of intermode coupling due to anharmonicity. Global topological features of the potential energy landscape are found to have little effect on the observed fractal behavior.Comment: 17 pages, single spaced, including 12 figure

Detection of antibacterial activity of essential oil components by TLC-bioautography using luminescent bacteria

The aim of the present study was the chemical characterization of some medically relevant essential oils (tea tree, clove, cinnamon bark, thyme and eucalyptus) and the investigation of antibacterial effect of the components of these oils by use of a direct bioautographic method. Thin layer chromatography (TLC) was combined with biological detection in this process. The chemical composition of the oils was determined by gas chromatography (GC) and gas chromatography-mass spectrometry (GC-MS). Eucalyptol (84.2%) was the main component of the essential oil of eucalyptus, eugenol (83.7%) of clove oil, and trans-cinnamic aldehyde (73.2%), thymol (49.9%) and terpinen-4-ol (45.8%) of cinnamon bark, thyme and tea tree oils, respectively. Antibacterial activity of the separated components of these oils, as well as their pure main components (eucalyptol, eugenol, trans-cinnamic aldehyde and thymol) was observed against the Gram-negative luminescence tagged plant pathogenic bacterium Pseudomonas syringae pv. maculicola (Psmlux) and the Gram-negative, naturally luminescent marine bacterium Vibrio fischeri. On the whole, the antibacterial activity of the essential oils could be related to their main components, but the minor constituents may be involved in this process. Trans-cinnamic aldehyde and eugenol were the most active compounds in TLC-bioautography. The sensitivity of TLC-bioautographic method can be improved with using luminescent test bacteria. This method is more cost-effective and provides more reliable results in comparison with conventional microbiological methods, e.g. disc-diffusion technique

Identification and Mode of Action of a Plant Natural Product Targeting Human Fungal Pathogens.

<i>Candida albicans</i> is a major cause of fungal diseases in humans, and its resistance to available drugs is of concern. In an attempt to identify novel antifungal agents, we initiated a small-scale screening of a library of 199 natural plant compounds (i.e., natural products [NPs]). <i>In vitro</i> susceptibility profiling experiments identified 33 NPs with activity against <i>C. albicans</i> (MIC <sub>50</sub> s ≤ 32 μg/ml). Among the selected NPs, the sterol alkaloid tomatidine was further investigated. Tomatidine originates from the tomato ( <i>Solanum lycopersicum</i> ) and exhibited high levels of fungistatic activity against <i>Candida</i> species (MIC <sub>50</sub> s ≤ 1 μg/ml) but no cytotoxicity against mammalian cells. Genome-wide transcriptional analysis of tomatidine-treated <i>C. albicans</i> cells revealed a major alteration (upregulation) in the expression of ergosterol genes, suggesting that the ergosterol pathway is targeted by this NP. Consistent with this transcriptional response, analysis of the sterol content of tomatidine-treated cells showed not only inhibition of Erg6 (C-24 sterol methyltransferase) activity but also of Erg4 (C-24 sterol reductase) activity. A forward genetic approach in <i>Saccharomyces cerevisiae</i> coupled with whole-genome sequencing identified 2 nonsynonymous mutations in <i>ERG6</i> (amino acids D249G and G132D) responsible for tomatidine resistance. Our results therefore unambiguously identified Erg6, a C-24 sterol methyltransferase absent in mammals, to be the main direct target of tomatidine. We tested the <i>in vivo</i> efficacy of tomatidine in a mouse model of <i>C. albicans</i> systemic infection. Treatment with a nanocrystal pharmacological formulation successfully decreased the fungal burden in infected kidneys compared to the fungal burden achieved by the use of placebo and thus confirmed the potential of tomatidine as a therapeutic agent