The Statistics of the Trajectory of a Certain Billiard in a Flat Two-Torus

We consider a billiard in the punctured torus obtained by removing a small disk of radius >0 from the flat torus ², with trajectory starting from the center of the puncture. In this case the phase space is given by the range of the velocity only. Let (), and respectively R(), denote the first exit time (length of the trajectory), and respectively the number of collisions with the side cushions when ² is being identified with [0,1)². We prove that the probability measures on [0, ) associated with the random variables and R are weakly convergent as 0⁺ and explicitly compute the densities of the limits. Research partially supported by ANSTI grant C6189/2000.     

Validation of protein structural models using THz spectroscopy: a promising approach to solve three-dimensional structures

Terahertz (THz) spectroscopy is a promising technique for the study of protein structure and internal flexibility. Here, we used THz spectroscopy and molecular modeling for bovine serum albumin (BSA) structure investigation. BSA molecule was built using homology modeling methods and 30 different more relaxed models were obtained by molecular dynamics simulations of the hydrated protein. As the experimental and simulated THz spectra are linear, we compared them by comparing the slopes of the lines that fit them. Six BSA structures had slope values in the range given by the slope of the experimental spectrum $\pm $  0.2 and a total of sixteen BSA structures had slope values in the 0.6 interval near the experimental slope value. BSA average structures were calculated over the six and the sixteen identified BSA molecules. Based on the similarity with the crystal structure of BSA, we validated the average structure calculated over the sixteen BSA conformations. The comparison with the crystal structure showed that the structure validated using THz spectroscopy is a coarse model of BSA, as its root-mean-square deviation relative to the crystal structure is 1.9 Å. The regions from our model that present the highest deviation from the crystal structure are exterior loops. The results presented here show that using THz spectroscopy and molecular modeling is a promising approach to determine the structure of proteins.     

Soft X-ray resonant magnetic scattering studies on Fe/CoO exchange bias system

We have used soft X-ray resonant magnetic scattering (XRMS) to search for the presence of an effective ferromagnetic moment belonging to the antiferromagnetic (AF) layer which is in close contact with a ferromagnetic (F) layer. Taking advantage of the element specificity of the XRMS technique, we have measured hysteresis loops of both Fe and CoO layers of a CoO(40 Å)/Fe (150 Å) exchange bias bilayer. From these measurements we have concluded that the proximity of the F layer induces a magnetic moment in the AF layer. The F moment of the AF layer has two components: one is frozen and does not follow the applied magnetic field and the other one follows in phase the ferromagnetic magnetization of the F layer. The temperature dependence of the F components belonging to the AF layer is shown and discussed.     

Artin's L-functions and one-dimensional characters

Let K/Q be a finite Galois extension with the Galois group G, let χ₁,…,χr be the irreducible non-trivial characters of G, and let A be the C-algebra generated by the Artin L-functions L(s,χ₁),…,L(s,χr). Let B be the subalgebra of A generated by the L-functions corresponding to induced characters of non-trivial one-dimensional characters of subgroups of G. We prove: (1) B is of Krull dimension r and has the same quotient field as A; (2) B=A iff G is M-group; (3) the integral closure of B in A equals A iff G is quasi-M-group.     

Cyclic Hilbert Spaces and Connes’ Embedding Problem

Let M be a II ₁-factor with trace τ, the finite dimensional subspaces of L ²(M, τ) are not just common Hilbert spaces, but they have an additional structure. We introduce the notion of a cyclic linear space by taking these additional properties as axioms. In Sect. 3 we formulate the following problem: “does every cyclic Hilbert space embed into L ²(M, τ), for some M?”. An affirmative answer would imply the existence of an algorithm to check Connes’ embedding Conjecture. In Sect. 4 we make a first step towards the answer of the previous question.     

Qualitative and quantitative analysis of gallic acid in Alchemilla vulgaris, Allium ursinum, Acorus calamus and Solidago virga-aurea by chip-electrospray ionization mass spectrometry and high performance liquid chromatography

This study presents the results obtained from qualitative and quantitative analysis of gallic acid from hydro-alcoholic extracts (methanol, ethanol) of plants from Plantae regnum. Plant qualitative analysis was performed using a novel mass spectrometric (MS) method based on fully automated chip-nanoelectrospray ionization (nanoESI) high capacity ion trap (HCT) while quantitative analysis was carried out by high performance liquid chromatography (HPLC). These methods were applied to Alchemilla vulgaris — common lady’s-mantle (aerial part), Allium ursinum — bear’s garlic (leaves), Acorus calamus — common sweet flag (roots), Solidago virga-aurea — goldenrod (aerial part). Obtained results indicated that methanol extracts (96%, 80%) have a gallic acid content ranging between 0.0011–0.0576 mg mL⁻¹ extract while the ethanol extracts (96%, 60%) exhibit a gallic acid concentration that varies between 0.0010–0.0182 mg mL⁻¹ extract.      

Radiation Curing of Coatings

Abstract

Printing inks, paints, and other coatings are applied as a liquid or paste but must change to a solid and nontacky state before the painted or coated article can be used. The change is known as curing or drying. Sometimes it occurs by physical means, the evaporation of a solvent or dispersion medium for example, and sometimes by chemical changes such as polymerization and cross-linking. These chemical processes connect the many relatively small molecules of the original liquid or paste into a large molecular network or insoluble solid, which may be either rigid or rubbery in consistency depending upon the requirements of a particular application. Among traditional materials, gravure inks and many lacquers dry by solvent evaporation while paints and inks based upon linseed oil “dry” by chemical cross-linking promoted by oxygen in the air. Considerable time is usually required for curing in both methods, and the evaporation of solvents can result in air pollution and potential fire hazards. There is also a tendency of the media to dry upon presses, brushes, sprayers, and other application equipment. The long cure time requirement raises difficulties in modern production lines; the other factors have become more acute since the rapid rise of petroleum prices and the advent of air pollution legislation.     

A Combined Experimental and Computational Study of Chrysanthemin as a Pigment for Dye-Sensitized Solar Cells

The theoretical study of chrysanthemin (cyanidin 3-glucoside) as a pigment for TiO₂-based dye-sensitized solar cells (DSSCs) was performed with the GAUSSSIAN 09 simulation. The electronic spectra of neutral and anionic chrysanthemin molecules were calculated by density functional theory with B3LYP functional and DGDZVP basis set. A better energy level alignment was found for partially deprotonated molecules of chrysanthemin, with the excited photoelectron having enough energy in order to be transferred to the conduction band of TiO₂ semiconductor in DSSCs. In addition, we used the raw aqueous extracts of roselle (Hibiscus sabdariffa) calyces as the source of chrysanthemin and the extracts with various pH values were tested in DSSCs. The extracts and photosensitized semiconductor layers were characterized by UV-Vis spectroscopy, and DSSCs based on raw extracts were characterized by current density-voltage measurements.     

Isoflavonoid-Antibiotic Thin Films Fabricated by MAPLE with Improved Resistance to Microbial Colonization

Staphylococcus aureus (Gram-positive) and Pseudomonas aeruginosa (Gram-negative) bacteria represent major infectious threats in the hospital environment due to their wide distribution, opportunistic behavior, and increasing antibiotic resistance. This study reports on the deposition of polyvinylpyrrolidone/antibiotic/isoflavonoid thin films by the matrix-assisted pulsed laser evaporation (MAPLE) method as anti-adhesion barrier coatings, on biomedical surfaces for improved resistance to microbial colonization. The thin films were characterized by Fourier transform infrared spectroscopy, infrared microscopy, and scanning electron microscopy. In vitro biological assay tests were performed to evaluate the influence of the thin films on the development of biofilms formed by Gram-positive and Gram-negative bacterial strains. In vitro biocompatibility tests were assessed on human endothelial cells examined for up to five days of incubation, via qualitative and quantitative methods. The results of this study revealed that the laser-fabricated coatings are biocompatible and resistant to microbial colonization and biofilm formation, making them successful candidates for biomedical devices and contact surfaces that would otherwise be amenable to contact transmission.     

Supramolecular Structure - A Key Parameter for Cellulose Biodegradation

Summary: Three different cellulosic substrata, like microcrystalline cellulose, cotton cellulose and spruce dissolving pulp, were chosen for biodegradation. The kinetics of the enzymatic hydrolysis of these celluloses by Trichoderma reesei, has been investigated. The experiments proved the fact that both the morphological structure and the crystalline one are crucial to the process and the ratio of the reactions. In addition, in order to obtain the most accessible cellulose substratum it was studied the biodegradation of cellulose allomorphs of spruce dissolving pulp. The insoluble cellulose fraction remaining after enzymatic hydrolysis was examined by X-ray diffraction method and it was established the degree of crystallinity and the average crystallite size. The enzymatic degradation is also proved by the decrease in the degree of polymerization of hydrolyzed samples.