Error estimates for distributed parameter identification in parabolic problems with output least squares and Crank-Nicolson method

The identification problem of a functional coefficient in a parabolic equation is considered. For this purpose an output least squares method is introduced, and estimates of the rate of convergence for the Crank-Nicolson time discretization scheme are proved, the equation being approximated with the finite element Galerkin method with respect to space variables.     

Photoinduced electron transfer in Langmuir-Blodgett monolayers of porphyrin-fullerene dyads

A series of electron donor-acceptor (DA) dyads, composed of a porphyrin donor and a fullerene acceptor covalently linked with two molecular chains, were used to fabricate solid molecular films with the Langmuir-Blodgett (LB) technique. By means of the LB technique, the DA molecules can be oriented perpendicular to the plane of the substrate. In DHD6ee and its zinc derivative hydrophilic groups are attached to the phenyl moieties in the porphyrin end of the molecule; while in the other three dyads, TBD6a, TBD6hp, and TBD4hp, the hydrophilic groups are in the fullerene end of the molecule. This makes it possible to alternate the orientation of the molecules in two opposite directions with respect to the air-water interface and to fabricate molecular assemblies in which the direction of the primary photoinduced vectorial electron transfer can be controlled both by the deposition direction of the LB monolayer and by the selection of the used DA molecule. This was proved by the time-resolved Maxwell displacement charge measurements. The spectroscopic properties of the DA films were studied with the steady-state absorption and fluorescence methods. In addition, the time correlated single photon counting technique was used to determine the fluorescence properties of the dyad films.     

1H NMR spectral analysis and conformational behavior of n‐alkanes in different chemical environments

Alkyl chains are common structural units, for example in lipids, and their ¹H NMR spectral parameters offer valuable information about their conformational behavior in solvent environment. Even the spectra of short n‐alkanes are complex, which is obviously a reason why their accurate spectral analyses have not been reported before. The present study reports the quantum mechanical analysis of ¹H NMR spectra of n‐butane, n‐pentane, n‐hexane, and n‐heptane. The spectral parameters were used to characterize the conformational behavior of n‐alkanes. The temperature dependence analysis of coupling constants suggests that the enthalpy difference between the gauche (g) and trans (t) conformations (ΔH_g) of n‐butane in chloroform is 2.55–2.85 kJ mol^?1. The difference between the trans–gauche (tg) and all‐trans (tt) conformers of n‐pentane (ΔH_tg) seems to be 0.1–0.2 kJ mol^?1 higher. The coupling constant information shows that the t_n conformations become more favored with longer chains, although not only for energetic reasons but also partly because the g⁺g^‐ arrangements become sterically unfavorable, which decreases the number of favorable g_n‐type conformations. The analysis of the ¹H NMR spectra of n‐pentane and n‐hexane in solvents representing different chemical environments indicates that polar and spherical dimethyl sulfoxide favors clearly the g conformations, whereas n‐hexane‐d₁₄ favors slightly the extended t_n conformation. In addition to the intrinsic scientific importance for NMR spectral parameter prediction and molecular modeling in solution, the results provide some insights to behavior of hydrocarbon chains and their spectra in different chemical environments. Copyright © 2012 John Wiley & Sons, Ltd.     

Comparing the quality and predictiveness between 3D QSAR models obtained from manual and automated alignment

A set of 113 flexible cyclic urea inhibitors of human immunodeficiency virus protease (HIV-1 PR) was used to compare the quality and predictive power of CoMFA and CoMSIA models for manually or automatically aligned inhibitor set. Inhibitors that were aligned automatically with molecular docking were in agreement with information obtained from existing X-ray structures. Both alignment methods produced statistically significant CoMFA and CoMSIA models, with the best q(2) value being 0.649 and the best predictive r(2) being 0.754. The manual alignment gave statistically higher values, whereas the automated alignment gave more robust models for predicting the activities of an external inhibitor set. Both models utilized similar amino acids in the HIV-1 PR active site, supporting the idea that hydrogen bonds form between an inhibitor and the backbone carbonyl oxygens of Gly48 and Gly48' and also the backbone NH group of Asp30, Gly48, Asp29', and Gly48' of the enzyme. These results suggest that an automated inhibitor alignment can yield predictive 3D QSAR models that are well comparable to manual methods. Thus, an automated alignment method in creating 3D QSAR models is encouragable when a well-characterized structure of the target protein is available.     

TMTHSI,a superior 7-membered ring alkyne containing reagent for strain-promoted azide–alkyne cycloaddition reactions

We describe the development of TMTH-SulfoxImine (TMTHSI) as a superior click reagent. This reagent combines a great reactivity, with small size and low hydrophobicity and compares outstandingly with existing click reagents. TMTHSI can be conveniently functionalized with a variety of linkers allowing attachment of a diversity of small molecules and (peptide, nucleic acid) biologics.

TMTHSI was developed as new reagent for strain-promoted azide–alkyne cycloaddition reactions, enabling connection of a diversity of small to large molecular constructs.     

Linear viscoelastic models: Part I. Relaxation modulus and melt calibration

Constitutive models for the linear viscoelasticity of polymers are presented for the relation between the relaxation modulus and the molecular weight distribution (MWD). We also compute the MWD from a simulated relaxation modulus curve by first obtaining the rheologically effective distribution (RED) as a function of time, and converting this into the MWD by melt calibration; that is, the relation between timescale and the molecular weight. This procedure has similarities with the widely used universal calibration with solved polymers. The main principles of our technique are applied here to familiar relaxation modulus data, for which we present two models: (1) an analytical model derived from control theory, which is known capable of modelling partially observed system and (2) a practical characteristic model for obtaining usable results. No relaxation time or spectrum procedures are used to model the process of linear viscoelastic relaxation. The use of relative calculations and melt calibration dispenses with the need to know the real chain structures such as branching and entangled chain dynamics, and the model remains useful for future investigations of polymer chain structures and dynamics, such as using tube theory.     

Theoretical studies of aluminoxane chains, rings, cages, and nanostructures

Alumina nanostructures and three families of aluminoxanes, linear, cyclic, and cagelike structures, have structures that resemble their isovalent electronic hydrocarbon analogues. Specific examples of each family are the counterparts of fullerene, allene, benzene, and cubane, respectively. The aluminoxanes and alumina nanostructures are related to each other; the latter can be regarded as a hydrogen- or alkyl-free form of aluminoxane. By exploiting this relationship, the relative stabilities of the three families of aluminoxanes, alumina nanostructures, and alumina crystal lattices have been estimated. According to ab initio calculations, aluminoxane cages, which take the form of a truncated octahedron and related polyhedra, are favored. The stability of the preferred cage, T-symmetric Al28O28H28, is practically equal to that of the alpha-alumina crystal lattice.     

Coherent fluorescence emission by using hybrid photonic–plasmonic crystals

The spatial and temporal coherence of the fluorescence emission controlled by a quasi‐two‐dimensional hybrid photonic–plasmonic crystal structure covered with a thin fluorescent‐molecular‐doped dielectric film is investigated experimentally. A simple theoretical model to describe how a confined quasi‐two‐dimensional optical mode may induce coherent fluorescence emission is also presented. Concerning the spatial coherence, it is experimentally observed that the coherence area in the plane of the light source is in excess of 49 μm², which results in enhanced directional fluorescence emission. Concerning temporal coherence, the obtained coherence time is 4 times longer than that of the normal fluorescence emission in vacuum. Moreover, a Young's double‐slit interference experiment is performed to directly confirm the spatially coherent emission. This smoking gun proof of spatial coherence is reported here for the first time for the optical‐mode‐modified emission.     

Generalized Gaussian bridges

A generalized bridge is a stochastic process that is conditioned on N$N$ linear functionals of its path. We consider two types of representations: orthogonal and canonical. The orthogonal representation is constructed from the entire path of the process. Thus, the future knowledge of the path is needed. In the canonical representation the filtrations of the bridge and the underlying process coincide. The canonical representation is provided for prediction-invertible Gaussian processes. All martingales are trivially prediction-invertible. A typical non-semimartingale example of a prediction-invertible Gaussian process is the fractional Brownian motion. We apply the canonical bridges to insider trading.