On nonstability of the linear recurrence of order one

We show that, under some assumptions, the linear recurrence (or difference equation) of order one in a Banach space is nonstable in the Hyers-Ulam sense. Our results are also connected with the notion of shadowing in dynamical systems and computer sciences.     

Conformation of hydrogen‐bonded dimeric o‐methyl‐substituted benzoic acids

Molecules of 2,4‐dimethylbenzoic acid, C₉H₁₀O₂, form typical centrosymmetric hydrogen‐bonded dimers. The carboxyl group is twisted with respect to the benzene ring and the methyl group in the ortho position shows evasive in‐plane splaying. The relation between the in‐plane splaying and the twist angle of the carboxyl group for various ortho‐substituted dimeric derivatives of benzoic acid is presented. It shows how the steric strains are released depending on the numbers and positions of the substituents.     

Synthesis and physicochemical properties of the Al(III), Ga(III) and In(III) complexes with chrysin

New solid compounds of Al(III), Ga(III) and In(III) with chrysin were obtained. Their composition and some physicochemical properties were studied by thermogravimetric analysis, UV-vis, infrared and solid state ¹³C NMR spectroscopies. Upon heating the hydrated compounds M(C₁₅H₉O₄)₃·nH₂O decomposed to the oxides. The structure of the compounds was elucidated on the basis of obtained results.     

Formation of dilithiated bis-(1H-pyrazol-1-yl)alkanes and their application in the synthesis of diboronic acids

Bis-(1H-pyrazol-1-yl)alkanes were deprotonated at the pyrazole 5-positions on treatment with LDA in THF at low temperature. These dianions reacted with tert-butylisocyanate as the electrophile to install a tert-butylamide group at the pyrazole 5-position. The obtained amides were next converted into the respective diboronic acids by Br–Li exchange with t-BuLi in THF at low temperature, followed by the use of triethyl borate as the electrophile. The X-ray analysis of the obtained diboronic acids revealed the presence of a variety of structural motifs, which stabilize the structure by hydrogen bond formation. The stabilization pattern differs greatly with a minor modification of the linker connecting the pyrazole rings.     

Quantification of UV-induced erythema and pigmentation using computer-assisted digital image evaluation

Photography has been used in human skin research for some time. With the advent of digital photography in recent years, its use has increased. However, the focus has now turned from documentation to actual analysis and quantification of skin color changes. The advantages of digital photography outweigh any shortcomings as long as consistent, standardized procedures are followed and quality control is implemented. We present a simple procedure to standardize images and discuss a computer-assisted digital image evaluation (CADIE) technique to quantify skin color changes following UV exposure. The CADIE approach is illustrated with examples from two different studies on UV responses in human skin. Using the Commission Internationale de l'Eclairage L*a*b* color coordinate system in combination with a personal computer and image-editing software, we analyzed digital images obtained in these two studies. We demonstrate the feasibility of using digital photography for objective evaluation of UV erythema in different racial/ethnic groups and for measuring pigmentation changes caused by repeated exposures over a period of several weeks. Our results indicate how objective assessment using CADIE can be an adjunct to visual and optical observation in clinical and scientific evaluations.     

Cyclopentadienylaluminum donor-acceptor complexes - Molecular and supramolecular structure

Lewis acid-base complexes of cyclopentadienylaluminum derivatives Me_xCp_3−x Al (x = 0-2) and trimethylaluminum with selected aromatic amines (L): dmap = 4-dimethylaminopyridine, py-Me = 4-methylpyridyne, were synthesized and characterized by ¹H, ¹³C, ²⁷Al NMR: Cp₃Al · dmap (1), Cp₃Al · py-Me (2), MeCp₂Al · dmap (3), MeCp₂Al · py-Me (4), Me₂CpAl · dmap (5), Me₂CpAl · py-Me (6), Me₃Al · py-Me (7). ¹H NMR studies of 3-6 revealed small amounts of the ligand redistribution products. The crystal structures of 1, 2 and 3 were determined by single X-ray diffraction studies. The compounds 1, 2 and 3 are monomeric with Cp ligands bonded to the aluminum center in η¹(σ), η¹(π) manner. The change of Cp-Al bond character from η¹(π) to η¹(σ) was found to reasonable correlate with the aromaticity of Cp⁻ ligand described by HOMA index. Analysis of close intra- and intermolecular contacts showed presence of CH?π interactions leading to the formation of 2-D supramolecular networks. It was found that these interactions impact on the coordination sphere of aluminum and the conformation of Cp ring.     

Ultrafast photoinduced charge separation dynamics in polythiophene/SnO2 nanocomposites

We present a study of photoinduced interfacial electron transfer (ET) dynamics of SnO2 nanocrystalline thin films sensitized by polythiophene derivatives (regioregular poly(3-hexylthiophene) (P3HT) and regiorandom poly(3-undecyl-2,2'-bithiophene) (P3UBT)). ET dynamics were measured by following the dynamics of injected electrons in SnO2 and polarons in the conjugated polymer using ultrafast mid-IR transient absorption spectroscopy. The rate of electron transfer from P3HT and P3UBT to SnO2 films was determined to occur on sub-picosecond time scale (120 +/- 20 fs). In P3HT/SnO2 composite, interchain charge transfer was found to compete with and reduce the quantum efficiency of interfacial electron transfer at high polymer loading. This interchain charge separation processes can be reduced in non-regioregular polymer or at low polymer loading levels.     

Analysis of human breath with micro extraction techniques and continuous monitoring of carbon dioxide concentration

The detection of volatile organic compounds (VOCs) in human breath can be useful for the clinical routine diagnosis of several diseases in a non-invasive manner. Traditional methods of breath analysis have some major technical problems and limitations. Membrane extraction with a sorbent interface (MESI), however, has many advantages over current methods, including good selectivity and sensitivity, and is well suited for breath analysis. The aim of this project was to develop a simple and reproducible sampling device and method based on the MESI system for breath analysis. The feasibility and validity of the MESI system was tested with real human breath samples. Internal standard calibration methods were used for the quantitative analysis of various breath samples. Calibration curves for some main components (target analytes such as acetone and pentane) were determined in the research. The optimized stripping-side and feeding-side gas velocities were determined. The use of breath CO₂ as an internal standard for the analysis of breath VOCs is an effective method to solve the difficulties associated with variations in the target analyte concentrations in a sample, which are attributed to mass losses and different breathing patterns of different subjects. In this study, the concentration of breath acetone was successfully expressed normalized to CO₂ as in the alveolar air. Breath acetone of healthy males and females profiled at different times of the day was plotted using the MESI system, and results were consistent with the literature. This technique can be used for monitoring breath acetone concentrations of diabetic patients and for applications with other biomarker monitoring.