Kalman Duality Principle for a Class of Ill-Posed Minimax Control Problems with Linear Differential-Algebraic Constraints

In this paper we present Kalman duality principle for a class of linear Differential-Algebraic Equations (DAE) with arbitrary index and time-varying coefficients. We apply it to an ill-posed minimax control problem with DAE constraint and derive a corresponding dual control problem. It turns out that the dual problem is ill-posed as well and so classical optimality conditions are not applicable in the general case. We construct a minimizing sequence $\hat{u}_{\varepsilon}$ for the dual problem applying Tikhonov method. Finally we represent $\hat{u}_{\varepsilon}$ in the feedback form using Riccati equation on a subspace which corresponds to the differential part of the DAE.     

Structure of salted and discharged globules of hydrophobic polyelectrolytes adsorbed from aqueous solutions

In this article, we compare structures of protonated poly(2-vinylpyridine) globules (2D compact coils on the surface) adsorbed on the mica surface from aqueous solution when the shrinking is brought about either by discharging the molecules at an elevated pH or by adding monovalent and polyvalent salts. We study the structure of the PE coils using in situ atomic force microscopy experiments in aqueous solutions in a liquid cell. The abrupt coil-to-globule transition caused by pH changes and the discharge of polymer chains resulted in compact globules. If the pH corresponding to extended coil conformation remains unchanged, the coil shrinks due to the added salt. The size of the globule in the latter case corresponds to the unperturbed dimension of the polymer coil. There is no essential difference in the dimensions of the globules as obtained in the presence of monovalent and multivalent counterions for the studied ionic strength. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1623–1627, 2010     

Novel 3d-metal complexes with 1,2-diamino-3-(2-benzothiazolyl)-4(5H)-ketopyrrole: Synthesis,spectroscopic and structural investigations

A series of new 3d-metal complexes have been prepared by the reaction of M(CH₃COO)₂ (M = Zn(II), Co(II), Ni(II)) and 1,2-diamino-3-(2-benzothiazolyl)-4(5H)-ketopyrrole (HL) in a methanol (3) or a methanol/dmf (1, 2) medium. All the complexes have been studied by elemental analyses, electronic and IR spectroscopies. The zinc(II) complex 1 and the ligand HL have been investigated using the method of ¹H NMR-spectroscopy at various temperatures. The disappearance of the signal from one proton of the amino group H(5) in the spectrum of complex 1 confirmed the existence of the ligand in the deprotonated form. According to the data of the ¹H NMR-spectroscopy, the ligand HL is coordinated to zinc(II) through the nitrogen atom of the deprotonated amino group and the nitrogen atom of the benzothiazole substituent. These data are in agreement with X-ray structural studies for the ligand HL and the zinc(II) complex 1.     

Modified Electrodes with Switchable Selectivity for Cationic and Anionic Redox Species

The modified electrode functionalized with a mixed‐polymer brush composed of poly(2‐vinylpyridine) and polyacrylic acid tethered to the surface demonstrated switchable interfacial properties discriminating negatively and positively charged redox species. The switchable electrochemical process was characterized by differential pulse voltammetry and Faradaic impedance spectroscopy. The electrochemical system was discussed as a model of an electrochemical multiplexer with two chemical redox inputs, the pH input operating as the selecting signal and one electronic output signal readable by the impedance spectroscopy in the form of the interfacial resistance. The modified electrode represents a novel component for integration with biocatalytic and biocomputing systems aiming at biochemically and electronically controlled actuators.     

Surface morphologies of Langmuir-Blodgett monolayers of PEOnPSn multiarm star copolymers

Star polymers composed of equal numbers of poly(ethylene oxide) (PEO) and polystyrene (PS) arms with variable lengths and a large (up to 38 total) number of arms, PEO(n)PS(n), have been examined for their ability to form domain nanostructures at the air-water and air-solid interfaces. All PEO(n)PS(n) star polymers formed stable Langmuir-Blodgett (LB) monolayers transferable to a solid substrate. A range of nanoscale surface morphologies have been observed, ranging from cylindrical to circular domains to bicontinuous structures as the weight fraction of the PEO block varied from 19% to 88% and n from 8 to 19. For the PS-rich stars and at elevated surface pressure, a two-dimensional supramolecular netlike nanostructure was formed. In contrast, in the PEO-rich star polymer with the highest PEO content, we observed peculiar dendritic superstructures caused by intramolecular segregation of nonspherical core-shell micellar structures. On the basis of Langmuir isotherms and observed monolayer morphologies, three different models of possible surface behavior of the star polymers at the interfaces were proposed.     

Darwin and mass-velocity relativistic corrections in the non-Born-Oppenheimer calculations of pure vibrational states of H2

The Darwin and mass-velocity relativistic corrections have been calculated for all pure vibrational states of the H2 using the perturbation theory and very accurate variational wave functions obtained without assuming the Born-Oppenheimer (BO) approximation. Expansions in terms of explicitly correlated Gaussians with premultipliers in the form of even powers of the internuclear distance were used for the wave functions. With the inclusion of the two relativistic corrections to the non-BO energies the transition energies for the highest states agree more with the experimental results.     

6,6'-Disubstituted benzothiazole trimethine cyanines--new fluorescent dyes for DNA detection

The influence of methyl-, 2-hydroxyethyl-, dimethyl-, diethyl- and benzoyl-amino substituents in the 6,6'-positions of benzothiazole heterocycle of trimethine cyanines on their spectral-luminescent properties and behavior in presence of DNA, RNA and BSA was studied. It was shown that incorporation of 6,6'-substituents generally leads to the increase in dyes tendency to aggregation, resulting in the considerable decrease in the emission intensity of the disubstituted dyes as compared to the unsubstituted ones. Emission of the studied 6,6'-disubstited dyes in DNA presence is considerably more intensive than in presence of RNA, that points on the existing of DNA binding preference for the mentioned dyes. Insertion of benzoyl-amino groups into the 6,6'-positions permitted us to design the DNA-sensitive dyes on the basis of symmetric trimethine cyanines with unsubstituted polymethine chain, while typically such dyes slightly respond on the presence of biopolymers. 6,6'-Benzoyl-amino-disubstituted trimethine cyanines are proposed as efficient dyes for DNA detection.     

Non-Born-Oppenheimer variational calculation of the ground-state vibrational spectrum of LiH+

Very accurate, rigorous, variational, non-Born-Oppenheimer (non-BO) calculations have been performed for the fully symmetric, bound states of the LiH(+) ion. These states correspond to the ground and excited vibrational states of LiH(+) in the ground (2)Sigma(+) electronic state. The non-BO wave functions of the states have been expanded in terms of spherical N-particle explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance and 5600 Gaussians were used for each state. The calculations that, to our knowledge, are the most accurate ever performed for a diatomic system with three electrons have yielded six bound states. Average interparticle distances and nucleus-nucleus correlation function plots are presented.     

Calix[4]arene alpha-aminophosphonic acids: asymmetric synthesis and enantioselective inhibition of an alkaline phosphatase

[structure: see text] Chiral calix[4]arene alpha-aminophosphonic acids were obtained through diastereoselective Pudovik-type addition of sodium ethyl phosphites to the chiral calixarene imines, removal of chiral auxiliary groups, and mild dealkylation of phosphonate fragments. The diacids obtained show inhibitory activity toward porcine kidney alkaline phosphatase that depends considerably on the absolute configuration of the alpha-carbon atoms.