Geometric properties of root vectors for equation of nonhomogeneous damped string: transformation operators method

The spectral decomposition theorem for a class of nonselfadjoint operators in a Hilbert space is obtained in the paper. These operators are the dynamics generators for the systems governed by 1–dim hyperbolic equations with spatially nonhomogeneous coefficients containing first order damping terms and subject to linear nonselfadjoint boundary conditions. These equations and boundary conditions describe, in particular, a spatially nonhomogeneous string subject to a distributed viscous damping and also damped at the boundary points. The main result leading to the spectral decomposition is the fact that the generalized eigenvectors (root vectors) of the above operators form Riesz bases in the corresponding energy spaces. The proofs are based on the transformation operators method. The classical concept of transformation operators is extended to the equation of damped string. Originally, this concept was developed by I. M. Gelfand, B. M. Levitan and V. A. Marchenko for 1–dim Schrödinger equation in connection with the inverse scattering problem. In the classical case, the transformation operator maps the exponential function (stationary wave function of the free particle) into the Jost solution of the perturbed Schrödinger equation. For the equation of a nonhomogeneous damped string, it is natural to introduce two transformation operators (outgoing and incoming transformation operators). The terminology is motivated by an analog with the Lax—Phillips scattering theory. The transformation operators method is used to reduce the Riesz bases property problem for the generalized eigenvectors to the similar problem for a system of nonharmonic exponentials whose complex frequencies are precisely the eigenvalues of our operators. The latter problem is solved based on the spectral asymptotics and known facts about exponential families. The main result presented in the paper means that the generator of a finite string with damping both in the equation and in the boundary conditions is a Riesz spectral operator. The latter result provides a class of nontrivial examples of non—selfadjoint operators which admit an analog of the spectral decomposition. The result also has significant applications in the control theory of distributed parameter systems.     

Temperature-induced crystallization in concentrated suspensions of multiarm star polymers: a molecular dynamics study

In this work, we study temperature-induced crystallization in dense suspensions of multiarm star polymers. This is a continuation of a previous study, which identified and studied the emergence of "glassy" amorphous states, in accordance with experimental observations. We performed molecular dynamics simulations on two types of star polymers: 128-arm stars and 64-arm stars dissolved in n-decane in the temperature range of 20-60 degrees C. These supramolecules are modeled as "soft spheres" interacting via a theoretically developed potential of mean field. Both systems attain a crystalline structure with the characteristics of a face-centered-cubic (fcc) crystal beyond a certain temperature. Kinetics is sensitive on initial configuration. Interestingly, kinetic trapping in "temporary" energy wells leads to highly crystalline structures, yet less ordered than their genuine equilibrium fcc structure. This complication illustrates the difficulty in reaching the equilibrium state, which is crystalline at high temperatures. A structural analysis of the final conformations is presented. The effect of size dispersity and star functionality of soft spheres on microstructure is also examined. Both factors influence crystallization and their effect is quantified by our study.     

Ligand exchange capillary electrophoresis by cyclodextrin derivatives, a powerful tool for enantiomeric separations

Five pure CD derivatives synthesized in our laboratory were used as chiral selectors in the presence of copper(II) ion. Three enantiomeric pairs of amino acids were submitted to separation experiments in CE, by exploiting the ligand exchange mechanism. The results obtained in the investigated systems, together with those of the analogous systems previously studied, clearly show the usefulness of this technique in chiral separations. By comparing the ligand exchange CE results with potentiometric results, either reported elsewhere or studied here for the first time (system Cu/CDampy/tyrosine), it has been possible to rationalise the separation results. The importance of the availability of pure selectors, and to characterise them both spectroscopically and thermodynamically is discussed.     

Density Deconvolution of Different Conditional Distributions

Recently, a new technique to circumvent the ill-posedness of the deconvolution problem has been suggested. This technique is based on what is known as multi-channel convolution system. In this paper, we modify and develop this technique in order to adapt it for statistical use. We then apply it to the problem of estimation of deconvolution density in the case of different conditional densities. This method enables us to combine equations efficiently for any set of conditional densities and to construct estimators in cases where the characteristic functions of the conditional distributions vanish at some points, as it happens in the case of uniform and triangular distributions.     

Self‐Assembled Regenerated Cellulose Spacer Film in Thin Film and Generator‐Collector Electrodes

Reconstituted cellulose spontaneously self‐assembles at surfaces from an alkaline cellulose solution (ca. 1 wt%, pH 14, prepared with an enzymatic method from wood pulp) into porous films with approximately 300 nm thickness per layer, for example onto immersed tin‐doped indium oxide (ITO) electrodes. Sequential multi‐layer deposition allows control over the thickness of the assembled films. The hydrophilic properties of the cellulose film electrodes are utilised here (i) as dip‐probe with capillary force picking up sample solution and (ii) as flow‐through generator‐collector probe, for example for future application in in situ chromatographic separation in end‐column detection with nano‐molar sensitivity.     

A new maximum likelihood approach with asymmetric residual distribution for multicomponent mass spectra analysis

This paper proposes a new maximum likelihood approach for the deconvolution of identity and quantity of individual compounds based on the multicomponent mass spectra measured by mass spectrometry (MS). Mixture analysis of multicomponent mass spectra is, typically, based on a linear multicomponent mass spectrum model, where the compounds of the measured spectra to be solved are explicitly stated and assumed to be known. In many cases, however, the measured spectrum may contain unknown compounds that are not explicitly stated in the model and a commonly used least square (LS) solution fails. Moreover, a standard improvement over the LS method in these cases, namely the M-estimation (ME) approach, also suffers from this same problem. Our method overcomes the limitations of the LS and ME methods by modeling the effect of the unknown compound(s) to the residual of the linear model. The experimental results presented show that this new approach can separate more robustly the complex multicomponent mass spectra into their individual constituents compared to the LS and ME methods.     

Determination of the enantiomeric composition of some molecules of pharmaceutical interest by chemometric analysis of the UV spectra of guest-host complexes formed with modified cyclodextrins

Multivariate regression modeling techniques (PLS-1 regression modeling) were applied to ordinary UV spectral absorption data obtained on solutions containing inclusion complexes formed between homochiral modified cyclodextrins (methyl-β-cyclodextrin, α-, β-, and γ-carboxymethyl cyclodextrins and α-, β-, and γ-hydroxypropyl cyclodextrins) and four guest molecules of pharmaceutical interest (ephedrine, norephedrine, norepinephrine-l-bitartrate, and tryptophan methyl ester). The PLS-1 regression models were developed by correlating the known enantiomeric composition of laboratory prepared samples with ordinary UV absorption spectral data. The regression models were subsequently validated with laboratory-prepared test sets. The rms percent relative error in the predicted mol fraction of (1S, 2R)-(+)-ephedrine, (1S, 2R)-(+)-norephedrine, (R)-(−)-norepinephrine-l-bitartrate, and d-tryptophan methyl ester obtained with the independently prepared test sets was heavily dependent on the host molecule used.     

Sonochemical asymmetric hydrogenation of isophorone on proline modified Pd/Al2O3 catalysts

The sonochemical asymmetric hydrogenation of isophorone (3,3,5-trimethyl-2-cyclohexenone) by proline-modified Pd/Al2O3 catalysts is described; presonication of a commercial Pd/Al2O3-proline catalytic system resulted in highly enhanced enantioselectivities (up to 85% ee).     

Asymmetric indolylmaleimide derivatives and their complexation with zinc(II)-cyclen

The spectroscopic properties of two asymmetric indolylmaleimide derivatives, 4-bromo-3-(1'H-indol-3'-yl)maleimide and 4-methyl-3-(1'H-indol-3'-yl)maleimide, are investigated. The bromo derivative was crystallized and its X-ray structure was determined. Both compounds are strongly colored while their separate components (indole and maleimide) absorb in the UV region only. To understand the ground- and excited-state behavior, the photophysical properties of the two compounds were studied in detail by steady state and time-resolved absorption and emission spectroscopy. Their solvatochromic behavior was investigated by using the Kamlet-Taft approach, which indicates some charge transfer (CT) character in the excited state. Nano- and femtosecond transient absorption spectroscopy was used for the identification and investigation of the CT state. Furthermore, the effect of the complexation with zinc(II) 1,4,7,11-tetraazacyclododecane (Zn-cyclen) on the photophysical properties of these two compounds was studied. An enhancement of the fluorescence intensity upon self-assembly (up to 90 times) and high association constants were observed, which illustrate the potential use of these compounds as luminescent sensors. DFT calculations indicate that HOMO-1 to LUMO excitation is mainly responsible for the charge transfer character and that this transition changes its character drastically when Zn-cyclen complexation occurs, thus giving it sensor properties.