Autocorrelation function formulations and the turbulence dissipation rate: Application to dispersion models

The classical statistical diffusion theory and the binomial autocorrelation function are used to obtain a new formulation for the turbulence dissipation rate ε. The approach employs the Maclaurin series expansion of a logarithm function contained in the dispersion parameter formulation. The numerical coefficient of this new relation for ε is 100% larger than the numerical coefficient of the classical relation derived from the exponential autocorrelation function. A similar approach shows that the dispersion parameter obtained from the even exponential autocorrelation function does not result in a relation for ε and, therefore, is not suitable for application in dispersion models. In addition, a statistical comparison to experimental ground-level concentration data demonstrates that this newly derived relation for ε as well as other formulations for the turbulence dissipation rate are suitable for application in Lagrangian stochastic dispersion models. Therefore, the analysis shows that there is an uncertainty regarding the turbulence dissipation rate function form and the autocorrelation function form.     

On the operations of sequences in rings and binomial type sequences

Given a commutative ring with identity R, many different and interesting operations can be defined over the set \(H_R\) of sequences of elements in R. These operations can also give \(H_R\) the structure of a ring. We study some of these operations, focusing on the binomial convolution product and the operation induced by the composition of exponential generating functions. We provide new relations between these operations and their invertible elements. We also study automorphisms of the Hurwitz series ring, highlighting that some well-known transforms of sequences (such as the Stirling transform) are special cases of these automorphisms. Moreover, we introduce a novel isomorphism between \(H_R\) equipped with the componentwise sum and the set of the sequences starting with 1 equipped with the binomial convolution product. Finally, thanks to this isomorphism, we find a new method for characterizing and generating all the binomial type sequences.

     

On a characterization of orthogonality with respect to particular sequences of random variables in <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>

This note deals with the orthogonality between sequences of random variables. The main idea of the note is to apply the results on equidistant systems of points in a Hilbert space to the case of the space L ²(Ω, F, ℙ) of real square integrable random variables. The main result gives a necessary and sufficient condition for a particular sequence of random variables (elements of which are taken from sets of equidistant elements of L ²(Ω, F, ℙ) to be orthogonal to some other sequence in L ²(Ω, F, ℙ). The result obtained is interesting from the point of view of the time series analysis, since it can be applied to a class of sequences random variables that exhibit a monotonically increasing variance. An application to ergodic theorem is also provided.     

Carnot efficiency: Why?

In 1824, Carnot proposed a cycle operating on reversibility principles. He proved that there exists an upper limit of the efficiency of this cycle and this limit is also the upper limit for any real process. The irreversibility related to the finite-time and the finite-size constraints are fundamental for the optimization of any real thermodynamic system. It has been pointed out how fundamental is the interaction between any open system and its surroundings. The meaning of the Carnot efficiency is that even in the ideal condition, when there is no dissipation, there exists something that does not allow the system to convert all the energies absorbed in work. The aim of this paper is to show why this happens, starting from a variational approach of thermodynamics.     

Nanostructured silver thin films deposited by pulsed laser ablation

Nanostructured thin films were deposited by excimer laser ablation of silver targets in controlled atmospheres of He and Ar. The film structural properties were investigated by means of scanning electron microscope and transmission electron microscope imaging. The film growth mechanism was identified as the result of coalescence of nanometric clusters formed during plume flight. Cluster formation involves plume confinement as a consequence of the increased collisional rate among plasma species. Fast photography imaging of the laser-generated silver plasma allowed to identify plasma confinement, shock wave formation and plasma stopping.     

Besov regularization,thresholding and wavelets for smoothing data

Smoothing of data is a problem very important for many applications ranging from 1-D signals (e.g., speech) to 2-D and 3-D signals (e.g., images). Many methods exist in the literature for facing the problem; in the present paper we point our attention on regularization. We shall treat regularization methods in a general framework which is well suited for wavelet analysis; in particular we shall investigate on the relation existing between thresholding methods and regularization. We shall also introduce a new regularization method (Besov regularization), which includes some known regularization and thresholding methods as particular cases. Numerical experiments based on some test problems will be performed in order to compare the performance of some methods of smoothing data.

AMS (MOS) Subject Classifications: 65R30, 41A60.     

A Family of Maximum Entropy Densities Matching Call Option Prices

Abstract

We investigate the position of the Buchen–Kelly density (Peter W. Buchen and Michael Kelly. The maximum entropy distribution of an asset inferred from option prices. Journal of Financial and Quantitative Analysis, 31(1), 143–159, March 1996.) in the family of entropy maximizing densities from Neri and Schneider (Maximum entropy distributions inferred from option portfolios on an asset. Finance and Stochastics, 16(2), 293–318, April 2012.), which all match European call option prices for a given maturity observed in the market. Using the Legendre transform, which links the entropy function and the cumulant generating function, we show that it is both the unique continuous density in this family and the one with the greatest entropy. We present a fast root-finding algorithm that can be used to calculate the Buchen–Kelly density and give upper boundaries for three different discrepancies that can be used as convergence criteria. Given the call prices, arbitrage-free digital prices at the same strikes can only move within upper and lower boundaries given by left and right call spreads. As the number of call prices increases, these bounds become tighter, and we give two examples where the densities converge to the Buchen–Kelly density in the sense of relative entropy. The method presented here can also be used to interpolate between call option prices, and we compare it to a method proposed by Kahalé (An arbitrage-free interpolation of volatilities. Risk, 17(5), 102–106, May 2004). Orozco Rodriguez and Santosa (Estimation of asset distributions from option prices: Analysis and regularization. SIAM Journal on Financial Mathematics, 3(1), 374–401, 2012.) have produced examples in which the Buchen–Kelly algorithm becomes numerically unstable, and we use these as test cases to show that the algorithm given here remains stable and leads to good results.     

Structural and optical properties of pulsed laser deposited ZnO thin films

Nanocrystalline ZnO thin films were grown by means of pulsed laser deposition. The ablation process was carried out at relatively low background oxygen gas pressure (10 Pa) and by varying the substrate temperature up to 600 °C. Information on the structural and morphological properties of the deposited thin films have been obtained by means of X-ray photoelectron, Raman spectroscopies, X-ray diffraction (XRD) and atomic force microscopy (AFM). The results showed that all the deposited films are sub-stoichiometric in oxygen and with a hexagonal wurtzite crystalline structure, characterized by features of some tens of nanometers in size. An improvement of the films' crystalline quality was observed for the deposition temperature of 300 °C while the further increase of the deposition temperature up to 600 °C induces a worsening of the material's structural properties with the development of a large amount of nanoparticle's clusters. The analysis of the XRD patterns shows a growth crystallographic preferential direction as a function of the deposition temperature, in agreement with the appearance of the only E₂ optical phonon mode in the Raman spectra. Such findings are compatible with the changes observed in the photoluminescent (PL) optical response and was related to the modification of the ZnO thin film structural quality.     

Correlation between carbon nanotube microstructure and their catalytic efficiency towards the p-coumaric acid degradation

Pristine and annealed multi-walled C nanotubes are preliminarily tested as catalysts towards the degradation of p-coumaric acid with better performances than the widely used activated carbon. In order to clarify the origin of their different catalytic efficiency, the samples are analysed by means of high-resolution transmission electron microscopy, X-ray photoemission, reflection electron energy loss and micro-Raman spectroscopy. Chemical composition, mass density, bonding configurations and threefold- to fourfold-coordinated carbon bonding ratios are determined. The comparative discussion of the results obtained leads to attribute the higher catalytic activity of the pristine nanotubes to their larger sp²/sp³ carbon bonding fraction and greater amount of oxygen containing functional groups.     

Antimicrobial Effect and Cytotoxic Evaluation of Mg-Doped Hydroxyapatite Functionalized with Au-Nano Rods

Hydroxyapatite (HA) is the main inorganic mineral that constitutes bone matrix and represents the most used biomaterial for bone regeneration. Over the years, it has been demonstrated that HA exhibits good biocompatibility, osteoconductivity, and osteoinductivity both in vitro and in vivo, and can be prepared by synthetic and natural sources via easy fabrication strategies. However, its low antibacterial property and its fragile nature restricts its usage for bone graft applications. In this study we functionalized a MgHA scaffold with gold nanorods (AuNRs) and evaluated its antibacterial effect against S. aureus and E. coli in both suspension and adhesion and its cytotoxicity over time (1 to 24 days). Results show that the AuNRs nano-functionalization improves the antibacterial activity with 100% bacterial reduction after 24 h. The toxicity study, however, indicates a 4.38-fold cell number decrease at 24 days. Although further optimization on nano-functionalization process are needed for cytotoxicity, these data indicated that Au-NRs nano-functionalization is a very promising method for improving the antibacterial properties of HA.