On extensions of rational modules

Given a topological algebra A, we investigate when the categories of all rational A-modules and of finite-dimensional rational modules are closed under extensions inside the category of A-modules. We give a complete characterization of these two properties, in terms of a topological and a homological condition, for complete algebras. We also give connections to other important notions in coalgebra theory such as coreflexive coalgebras. In particular, we are able to generalize many previously known partial results and answer some questions in this direction, and obtain large classes of coalgebras for which rational modules are closed under extensions as well as various examples where this is not true.     

Study of Self‐Assembly of the Lignin Model Compound on Cellulose Model Substrate

Herein we report a topographical study of the supramolecular organization of enzymatically polymerized lignin model compound – dehydrogenative polymer (DHP) of coniferyl alcohol – on cellulose substrate, using the Environmental Scanning Electron Microscopic (ESEM) technique. A comparison of deposits obtained by bulk polymerization in solution and direct polymerization in the presence of cellulose substrate shows distinct differences in supramolecular organization. DHP polymerized in solution expresses a 3‐D structure with short‐range ordered motifs, while the polymer formed in the presence of cellulose substrate arranges in a single layer compact structure consisting of several domains. Such structures could be described as a two‐dimensional hexagonal close packed lattice(HCPL), with the dimension of unit cell in 1 μm range. The domains have a quite regular structure with few lattice defects, forming a good example of two‐dimensional colloidal crystal. The growth of DHP globules and their assembly into supramolecular structures are interpreted in terms of cooperative electrostatic interaction of polymer precursors, with a framework of cellulose OH groups and interfacial interactions (hydrophilic/hydrophobic) in the course of the structure growth. The results strongly suggest that the carbohydrate matrix in plant cells can serve as a template for lignin structure formation in the plant cell wall.

Self‐assembled lignin model compound on cellulose substrate.     

Infrared reflection-absorption spectroscopy and polarization-modulated infrared reflection-absorption spectroscopy studies of the aequorin langmuir monolayer

The Langmuir monolayer of aequorin and apoaequorin was studied by infrared reflection-absorption spectroscopy (IRRAS) and polarization-modulated IRRAS techniques. The alpha-helices in the aequorin Langmuir monolayer were parallel to the air-water interface at zero surface pressure. When the surface pressure increased to 15 mN.(m-1), the alpha-helices became tilted and the turns became parallel to the air-water interface. As for apoaequorin, the alpha-helices were also parallel to the air-water interface at 0 mN.m(-1). However, the alpha-helix became tilted and the turns became parallel to the air-water interface quickly at 5 mN.m(-1). With further compression of the apoaequorin Langmuir monolayer, the orientation remained the same. The different behaviors of aequorin and apoaequorin at the air-water interface were explained by the fact that aequorin formed dimers at the air-water interface but apoaequorin was a monomer. It is more difficult for a dimer to be tilted by the compression of the Langmuir monolayer.     

Coupled purely nonlinear oscillators: normal modes and exact solutions for free and forced responses

Nonlinear Dynamics - This article is concerned first with free vibrations in a chain of two-mass oscillators with purely nonlinear springs whose power of nonlinearity can be any real number higher...     

Normal modes of a double pendulum at low energy levels

Nonlinear Dynamics - This study is concerned with a double pendulum and its regular behaviour associated with low energy levels and the influence of the associated initial conditions on the...     

Deconvolution of fluorescence spectra: contribution to the structural analysis of complex molecules

Fluorescence spectroscopy is a sensitive analytical tool in the studies of both simple and complex molecular structures. In complex molecules, however, determining the number and position of components may give a specific insight into the structure, complementary to the other analytical techniques. We applied log–normal model to analyze fluorescence of simple monofluorophore molecule. In order to analyze spectra where both fluorophores and Raman emission bands were present, we developed a method obtained by combination of the symmetric, Gaussian, for Raman and asymmetric, log–normal model, for fluorescence, applicable to the molecules of different complexity. Technically, for each sample we varied excitation wavelength with 5 nm step and recorded the corresponding emission spectra. They were subsequently used for component analysis. Position of each component was plotted against the excitation wavelength. Applying this approach we could identify minimal number of components having stable positions, while their approximate probability density (APD) in a spectral series was correlated with the probable number of fluorophores in the molecule. The method was tested on molecules containing different number of fluorophores: monomers involved in the synthesis of plant polymer lignin—coniferyl alcohol (one fluorophore), ferulic acid (two fluorophores) and on lignin model compound produced from these monomers (many fluorophores). All investigated species belong to benzene-substituted class of compounds, and it is reasonable to assume that they have similar fluorescence band contour. We also report the results of environmental scanning electron microscopy (ESEM) studies showing multilayered dehydrogenative polymer (DHP) structure, in order to show complexity of the polymer. Our results present complementarity of these two approaches in the structural studies of the lignin model compound.     

On the remainder term of Gauss–Radau quadratures for analytic functions

For analytic functions the remainder term of Gauss–Radau quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours with foci at the points ±1$\pm 1$ and a sum of semi-axes ?>1$?>1$ for the Chebyshev weight function of the second kind. Starting from explicit expressions of the corresponding kernels the location of their maximum modulus on ellipses is determined. The corresponding Gautschi's conjecture from [On the remainder term for analytic functions of Gauss–Lobatto and Gauss–Radau quadratures, Rocky Mountain J. Math. 21 (1991), 209–226] is proved.     

On the behavior of parametrically excited purely nonlinear oscillators

In this study, parametrically excited purely nonlinear oscillators are considered. Instabilities associated with 2:1, 3:1, and 4:1 subharmonics resonances are analyzed by assuming the solution for motion in the form of a Jacobi elliptic function, the elliptic parameter, and the frequency of which are calculated based on the energy conservation law of the corresponding conservative system. Chirikov??s overlap criterion is used to obtain the approximate critical value of the amplitude of the parametric excitation that causes the transition from local irregular behavior (seen as chaotic) to global chaos. The analytical results derived are compared with numerically results.     

Intermittent single-molecule interfacial electron transfer dynamics

We report on single-molecule studies of photosensitized interfacial electron transfer (ET) processes in Coumarin 343 (C343)-TiO(2) nanoparticles (NP) and Cresyl Violet (CV(+))-TiO(2) NP systems, using time-correlated single-photon counting coupled with scanning confocal fluorescence microscopy. Fluorescence intensity trajectories of individual dye molecules adsorbed on a semiconductor NP surface showed fluorescence fluctuations and blinking, with time constants distributed from milliseconds to seconds. The fluorescence fluctuation dynamics were found to be inhomogeneous from molecule to molecule and from time to time, showing significant static and dynamic disorders in the interfacial ET reaction dynamics. We attribute fluorescence fluctuations to the interfacial ET reaction rate fluctuations, associating redox reactivity intermittency with the fluctuations of molecule-TiO(2) electronic and Franck-Condon coupling. Intermittent interfacial ET dynamics of individual molecules could be characteristic of a surface chemical reaction strongly involved with and regulated by molecule-surface interactions. The intermittent interfacial reaction dynamics that likely occur among single molecules in other interfacial and surface chemical processes can typically be observed by single-molecule studies but not by conventional ensemble-averaged experiments.     

Surface chemistry of lipid raft and amyloid Aβ (1-40) Langmuir monolayer

Lipid rafts being rich in cholesterol and sphingolipids are considered to provide ordered lipid environment in the neuronal membranes, where it is hypothesized that the cleavage of amyloid precursor protein (APP) to Aβ (1-40) and Aβ (1-42) takes place. It is highly likely that the interaction of lipid raft components like cholesterol, sphingomylein or GM1 leads to nucleation of Aβ and results in aggregation or accumulation of amyloid plaques. One has investigated surface pressure-area isotherms of the lipid raft and Aβ (1-40) Langmuir monolayer. The compression-decompression cycles and the stability of the lipid raft Langmuir monolayer are crucial parameters for the investigation of interaction of Aβ (1-40) with the lipid raft Langmuir monolayer. It was revealed that GM1 provides instability to the lipid raft Langmuir monolayer. Adsorption of Aβ (1-40) onto the lipid raft Langmuir monolayer containing neutral (POPC) or negatively charged phospholipid (DPPG) was examined. The adsorption isotherms revealed that the concentration of cholesterol was important for adsorption of Aβ (1-40) onto the lipid raft Langmuir monolayer containing POPC whereas for the lipid raft Langmuir monolayer containing DPPG:cholesterol or GM1 did not play any role. In situ UV-vis absorption spectroscopy supported the interpretation of results for the adsorption isotherms.