Average unit cell approach to diffraction analysis of some aperiodic structures — decorated fibonacci chain

The average unit cell approach has been successfully used to construct the probability distributions of atomic distances from the reference lattice points and to calculate the diffraction patterns for decorated Fibonacci chains with non-Fibonacci type of decoration. General method able to distinguish between various quasilattice decorations has been elaborated and tested for decorated Fibonacci chains. Financial support from the Polish Committee for Sci. Research under grant No. 2 P03B 041 16 is acknowledged. Presented at the DI-CRM Workshop held in Prague, 18–21 June 2000.     

A novel hydroxy functionalized polyester obtained by ring opening copolymerization of L‐lactide with a pyrolysis product of cellulose

A hydroxylactone ((1R,5S)‐1‐hydroxy‐3,6‐dioxabicyclo [3.2.1] octan‐2‐one, abbreviated as LAC) obtained from catalytic pyrolysis of cellulose was investigated as a monomer in the synthesis of polyesters by ring‐opening polymerization (ROP) with L ‐lactide. Although stannous octoate resulted inactive, ROP initiated by zirconium (IV) acetylacetonate afforded novel copolyesters from LAC and lactide mixtures in the bulk at 110 °C. Copolymers were obtained with different LAC content (from 19 to 45%) with a random microstructure as established by detailed NMR analysis. FTIR spectrometry confirmed the presence in the polymer chain of the OH groups originally present in LAC, which do not react during polymerization due to steric hindrance and inter/intramolecular hydrogen bonding. Reaction with trichloroacetylisocyanide proved that OH groups of the polyesters can be readily derivatized. The application of LAC as a comonomer enables the insertion of the alcohol functionality in polylactide avoiding protection/deprotection steps and potentially expanding the realm of biomaterials affordable from carbohydrate feedstock. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 247–257, 2009     

Applications of small iridium-based mercury electrodes to high concentrations of depolarizers

Voltammetric and microscopic data on the analytical properties of small iridium-based (127- μm diameter) mercury film electrodes are presented. A method of estimating and controlling the size of the deposit is described. The voltammetric behaviour of electrodes with mercury deposits varying from a film to a near-hemisphere is discussed for linear-scan, differential- and normal- pulse voltammetry. The systems Pb²⁺/Pb, Fe³⁺/Fe²⁺ and Co²⁺/Co, are used to show that, by changing the size of the deposit, either time-dependent or almost time-independent (steady-state) voltammograms can be obtained under the same instrumental conditions. Possible applications to the determination of high concentrations of depolarizers are outlined; voltammetric data for the determination of lead in the range 10–120 mM are presented. The evaluation of diffusion coefficients is discussed.     

Detection of Anomalous Diffusion with Deep Residual Networks

Identification of the diffusion type of molecules in living cells is crucial to deduct their driving forces and hence to get insight into the characteristics of the cells. In this paper, deep residual networks have been used to classify the trajectories of molecules. We started from the well known ResNet architecture, developed for image classification, and carried out a series of numerical experiments to adapt it to detection of diffusion modes. We managed to find a model that has a better accuracy than the initial network, but contains only a small fraction of its parameters. The reduced size significantly shortened the training time of the model. Moreover, the resulting network has less tendency to overfitting and generalizes better to unseen data.     

Preparation and evaluation of solid-phase microextraction fibres based on functionalized latex nanoparticle coatings for trace analysis of inorganic anions

The use of a functionalized latex nanoparticle coating as a new sorbent phase for solid-phase microextraction (SPME) was examined. By means of electrostatic absorption onto ionized silanol groups, a fused-silica rod was coated with polymeric nanoparticles functionalized with quaternary ammonium groups. Optimum conditions for the preparation of the coated fibre are presented. The fibre was used for the extraction of a mixture of seven anions from water samples which are analysed by coupling the SPME fibre to an ion chromatographic system via a special interface. The results obtained proved the suitability of this novel coating as a new SPME fibre. A linear calibration for the target analytes was achieved over the concentration range from 5 μg L⁻¹ to 5 mg L⁻¹ (r² > 0.988), while limits of detection for these ions were all below 3.7 μg L⁻¹ (S/N = 3). The reproducibility of a single fibre (n = 4) under similar conditions was between 7 and 12%, while the fibre to fibre reproducibility (n = 5) was between 8.9 and 14%.     

On variable discounting in dynamic programming: applications to resource extraction and other economic models

This paper generalizes the classical discounted utility model introduced in Samuelson (Rev. Econ. Stud. 4:155–161, 1937) by replacing a constant discount rate with a function. The existence of recursive utilities and their constructions are based on Matkowski’s extension of the Banach Contraction Principle. The derived utilities go beyond the class of recursive utilities studied in the literature and enable a discussion on subtle issues concerning time preferences in the theory of finance, economics or psychology. Moreover, our main results are applied to the theory of optimal economic growth related with resource extraction models with unbounded utility function of consumption.     

On homogeneous Lagrange means

Let \(f\) be a real differentiable function in an open interval \(I\) with one-to-one derivative. We observe that if the Lagrange mean \(L^{[f]}\) of a generator \(f\) is conditionally positively homogeneous, then \(f\) must be of the class \(C^{\infty }\) and the function $$\begin{aligned} g(x):=xf^{\prime }\left( x\right) -f\left( x\right) ,\quad \quad x\in I, \end{aligned}$$ is also a generator of \(L^{[f]}\) i.e. that \(L^{[g]}=L^{[f]}.\) We show that this fact and a result on equality of two Lagrange means allow easily to determine all positively homogeneous Lagrange means.     

Proton hydration in aqueous solution: Fourier transform infrared studies of HDO spectra

This paper attempts to elucidate the number and nature of the hydration spheres around the proton in an aqueous solution. This phenomenon was studied in aqueous solutions of selected acids by means of Fourier transform infrared spectroscopy of semiheavy water (HDO), isotopically diluted in H(2)O. The quantitative version of difference spectrum procedure was applied for the first time to investigate such systems. It allowed removal of bulk water contribution and separation of the spectra of solute-affected HDO. The obtained spectral data were confronted with ab initio calculated structures of small gas-phase and polarizable continuum model (PCM) solvated aqueous clusters, H+(H2O)n, n=2-8, in order to help in establishing the structural and energetic states of the consecutive hydration spheres of the hydrated proton. This was achieved by comparison of the calculated optimal geometries with the interatomic distances derived from HDO band positions. The structure of proton hydration shells outside the first hydration sphere essentially follows the model structure of other hydrated cations, previously revealed by affected HDO spectra. The first hydration sphere complex in diluted aqueous solutions was identified as an asymmetric variant of the regular Zundel cation [The Hydrogen Bond: Recent Developments in Theory and Experiments, edited by P. Schuster, G. Zundel, and C. Sandorfy (North-Holland, Amsterdam, 1976), Vol. II, p. 683], intermediate between the ideal Zundel and Eigen structures [E. Wicke et al., Z. Phys. Chem. Neue Folge 1, 340 (1954)]. Evidence was found for the existence of strong and short hydrogen bonds, with oxygen-oxygen distance derived from the experimental affected spectra equal 2.435 A on average and in the PCM calculations about 2.41-2.44 A. It was also evidenced for the first time that the proton possesses four well-defined hydration spheres, which were characterized in terms of hydrogen bonds' lengths and arrangements. Additionally, an outer hydration layer, shared with the anion, as well as loosely bound water molecules interacting with free electron pairs of the central complex were detected in the affected spectra.