Composition operators on Hardy spaces on Lavrentiev domains

For any simply connected domain , we prove that a Littlewood type inequality is necessary for boundedness of composition operators on , , whenever the symbols are finitely-valent. Moreover, the corresponding ``little-oh' condition is also necessary for the compactness. Nevertheless, it is shown that such an inequality is not sufficient for characterizing bounded composition operators even induced by univalent symbols. Furthermore, such inequality is no longer necessary if we drop the extra assumption on the symbol of being finitely-valent. In particular, this solves a question posed by Shapiro and Smith (2003). Finally, we show a striking link between the geometry of the underlying domain and the symbol inducing the composition operator in , and in this sense, we relate both facts characterizing bounded and compact composition operators whenever is a Lavrentiev domain.

     

Hausdorff dimension and conformal measures of Feigenbaum Julia sets

We show that contrary to anticipation suggested by the dictionary between rational maps and Kleinian groups and by the ``hairiness phenomenon', there exist many Feigenbaum Julia sets whose Hausdorff dimension is strictly smaller than two. We also prove that for any Feigenbaum Julia set, the Poincaré critical exponent is equal to the hyperbolic dimension . Moreover, if , then . In the stationary case, the last statement can be reversed: if , then . We also give a new construction of conformal measures on that implies that they exist for any , and analyze their scaling and dissipativity/conservativity properties.

     

On-Surface Synthesis and Real-Space Visualization of Aromatic P3N3

On-surface synthesis is at the verge of emerging as the method of choice for the generation and visualization of unstable or unconventional molecules, which could not be obtained via traditional synthetic methods. A case in point is the on-surface synthesis of the structurally elusive cyclotriphosphazene (P₃N₃), an inorganic aromatic analogue of benzene. Here, we report the preparation of this fleetingly existing species on Cu(111) and Au(111) surfaces at 5.2 K through molecular manipulation with unprecedented precision, i.e., voltage pulse-induced sextuple dechlorination of an ultra-small (about 6 Å) hexachlorophosphazene P₃N₃Cl₆ precursor by the tip of a scanning probe microscope. Real-space atomic-level imaging of cyclotriphosphazene reveals its planar D_3h-symmetric ring structure. Furthermore, this demasking strategy has been expanded to generate cyclotriphosphazene from a hexaazide precursor P₃N₂₁ via a different stimulation method (photolysis) for complementary measurements by matrix isolation infrared and ultraviolet spectroscopy.     

An electrochemical study into the interaction between complement-derived peptides and DOPC mono- and bilayers

Electrochemical methods employing the hanging mercury drop electrode were used to study the interaction between variants of the complement-derived antimicrobial peptide CNY21 (CNYITELRRQH ARASHLGLAR) and dioleoyl phosphatidylcholine (DOPC) monolayers. Capacitance potential and impedance measurements showed that the CNY21 analogues investigated interact with DOPC monolayers coating the mercury drop. Increasing the peptide hydrophobicity by substituting the two histidine residues with leucine resulted in a deeper peptide penetration into the hydrophobic region of the DOPC monolayer, indicated by an increase in the dielectric constant of the lipid monolayer (Deltaepsilon = 2.0 after 15 min interaction). Increasing the peptide net charge from +3 to +5 by replacing the histidines by lysines, on the other hand, arrests the peptide in the lipid head group region. Reduction of electroactive ions (Tl+, Pb2+, Cd2+, and Eu3+) at the monolayer-coated electrode was employed to further characterize the types of defects induced by the peptides. All peptides studied permeabilize the monolayer to Tl+ to an appreciable extent, but this effect is more pronounced for the more hydrophobic peptide (CNY21L), which also allows penetration of larger ions and ions of higher valency. The results for the various ions indicate that charge repulsion rather than ion size is the determining factor for cation penetration through peptide-induced defects in the DOPC monolayer. The effects obtained for monolayers were compared to results obtained with bilayers from liposome leakage and circular dichroism studies for unilamellar DOPC vesicles, and in situ ellipsometry for supported DOPC bilayers. Trends in peptide-induced liposome leakage were similar to peptide effects on electrochemical impedance and permeability of electroactive ions for the monolayer system, demonstrating that formation of transmembrane pores alone does not constitute the mechanism of action for the peptides investigated. Instead, our results point to the importance of local packing defects in the lipid membrane in close proximity to the adsorbed peptide molecules.     

Perchlorination of Coronene Enhances its Propensity for Self‐Assembly on Graphene

Providing a quantitative understanding of the thermodynamics involved in molecular adsorption and self‐assembly at a nanostructured carbon material is of fundamental importance and finds outstanding applications in the graphene era. Here, we study the effect of edge perchlorination of coronene, which is a prototypical polyaromatic hydrocarbon, on the binding affinity for the basal planes of graphite. First, by comparing the desorption barrier of hydrogenated versus perchlorinated coronene measured by temperature‐programmed desorption, we quantify the enhancement of the strength of physisorption at the single‐molecule level though chlorine substitution. Then, by a thermodynamic analysis of the corresponding monolayers based on force‐field calculations and statistical mechanics, we show that perchlorination decreases the free energy of self‐assembly, not only enthalpically (by enhancing the strength of surface binding), but also entropically (by decreasing the surface concentration). The functional advantage of a chemically modulated 2D self‐assembly is demonstrated in the context of the molecule‐assisted liquid‐phase exfoliation of graphite into graphene.     

Prediction of reverberation time using the residual minimization method

In many practical situations the assumption of sound field dispersion needed for the application of the Sabine’s theory is not fulfilled. In general, sound field is sufficiently dispersed if there are no large differences in the dimensions of the room, limiting partitions are not parallel, or the sound absorbing material is uniformly distributed. In practice, very few of these requirements are satisfied. As a result, a number of other formulas describing reverberation time have been created, for example Fitzroy’s or Neubauer’s formulas. However, these methods in many cases differ significantly from the actual measurements. The paper presents a method used to estimate reverberation time as well as its applicability potential involving laboratory models and auditorium rooms. The proposed method can be classified into a group of learning methods and involves the use of statistical methods which allow for approximation with the use of the least squares method.     

Investigation studies involving sound absorbing parameters of roadside screen panels subjected to aging in simulated conditions

The paper presents the results of investigation studies involving the impact of atmospheric factors on sound-absorbing parameters of roadside acoustic screen panels. The research studies comprised the aging test consisting of 1000 cycles in simulated conditions, sound absorption measurements and surface morphology tests, using the SEM scanning method. The simulation of aging consisted of 100 or 150 cycles at a time. Then, the panels were investigated in the reverberation chamber to define their sound-absorbing properties. The process was repeated until 1000 cycles were completed. Basing on the carried out tests, a statistical linear model was worked out which was used to estimate the value of a single number sound absorption coefficient after successive aging cycles. The optimality of the model was demonstrated by means of a statistical test confirming normal distribution of random residuals. For the research studies, we employed an innovative structural design of panels for which aging characteristics were obtained. Basing on the obtained results and on the statistical analysis, the prospects to maintain acoustic properties of the panels during their service life was estimated.     

Nonsymmetric and symmetric fractional calculi on arbitrary nonempty closed sets

We introduce a nabla, a delta, and a symmetric fractional calculus on arbitrary nonempty closed subsets of the real numbers. These fractional calculi provide a study of differentiation and integration of non‐integer order on discrete, continuous, and hybrid settings. Main properties of the new fractional operators are investigated and some fundamental results presented, illustrating the interplay between discrete and continuous behaviors. Copyright © 2015 John Wiley & Sons, Ltd.     

How realistic is the pore size distribution calculated from adsorption isotherms if activated carbon is composed of fullerene-like fragments?

A plausible model for the structure of non-graphitizing carbon is one which consists of curved, fullerene-like fragments grouped together in a random arrangement. Although this model was proposed several years ago, there have been no attempts to calculate the properties of such a structure. Here, we determine the density, pore size distribution and adsorption properties of a model porous carbon constructed from fullerene-like elements. Using the method proposed recently by Bhattacharya and Gubbins (BG), which was tested in this study for ideal and defective carbon slits, the pore size distributions (PSDs) of the initial model and two related carbon models are calculated. The obtained PSD curves show that two structures are micro-mesoporous (with different ratio of micro/mesopores) and the third is strictly microporous. Using the grand canonical Monte Carlo (GCMC) method, adsorption isotherms of Ar (87 K) are simulated for all the structures. Finally PSD curves are calculated using the Horvath-Kawazoe, non-local density functional theory (NLDFT), Nguyen and Do, and Barrett-Joyner-Halenda (BJH) approaches, and compared with those predicted by the BG method. This is the first study in which different methods of calculation of PSDs for carbons from adsorption data can be really verified, since absolute (i.e. true) PSDs are obtained using the BG method. This is also the first study reporting the results of computer simulations of adsorption on fullerene-like carbon models.     

Spectroscopic and electrochemical studies of cocaine–opioid interactions

The drugs of abuse cocaine (C), heroin (H), and morphine (M) have been studied to enable understanding of the occurrence of cocaine–opioid interactions at a molecular level. Electrochemical, Raman, and NMR studies of the free drugs and their mixtures were used to study drug–drug interactions. The results were analyzed using data obtained from quantum-mechanical calculations. For the cocaine–morphine mixture (C–MH), formation of a binary complex was detected; this involved the 3-phenolic group and the heterocyclic oxygen of morphine and the carbonyl oxygen and the methyl protons of cocaine’s methyl ester group. NMR studies conducted simultaneously also revealed C–MH binding geometry consistent with theoretical predictions and with electrochemical and vibrational spectroscopy results. These results provide evidence for the occurrence of a cocaine–morphine interaction, both in the solid state and in solution, particularly for the hydrochloride form. A slight interaction, in solution, was also detected by NMR for the cocaine–heroin mixture. Figure "Schematic representation of the proposed model for cocaine:morphine salt interaction"