Stability criteria for positive linear discrete-time systems

Positivity - We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have...     

Synthesis and cytotoxicity of new 2-oxo-7-phenyl-2,3-dihydrothiazolo[4,5-b]pyridine-5-carboxylic acid amides

Abstract

The synthesis and anticancer activity evaluation of new thiazolo[4,5-b]pyridine-5-carboxylic acid amides is described. The structures of the synthesized compounds were confirmed by spectroscopic data and a single crystal X-ray diffraction analysis for 2.4. The synthesized compounds were screened for their in vitro anticancer activity according to US NCI protocols. The most active 7-(4-fluorophenyl)-2-oxo-2,3-dihydrothiazolo[4,5-b]pyridine-5-carboxylic acid (4-chlorophenyl)amide 2.2 and 7-(4-chlorophenyl)-2-oxo-2,3-dihydrothiazolo[4,5-b]pyridine-5-carboxylic acid (4-chlorophenyl)amide 2.5 were screened for their cytotoxicity effects on C6 Rat glioma cells and U373 Human glioblastoma astrocytoma cells which revealed promising results comparable to temozolamide as reference control according MTT assay data.     

Structure and intermolecular interactions of the fully negative solvatochromic merocyanine in the crystal phase

Structural Chemistry - Herein we report an X-ray crystallographic characterization of tetramethine merocyanine based on benzimidazole and thiobarbituric acid, which shows negative solvatochromism...     

Positivity and time behavior of a linear reaction–diffusion system,non-local in space and time

We consider a general linear reaction–diffusion system in three dimensions and time, containing diffusion (local interaction), jumps (nonlocal interaction) and memory effects. We prove a maximum principle and positivity of the solution and investigate its asymptotic behavior. Moreover, we give an explicit expression of the limit of the solution for large times. In order to obtain these results, we use the following method: We construct a Riemannian manifold with complicated microstructure depending on a small parameter. We study the asymptotic behavior of the solution to a simple diffusion equation on this manifold as the small parameter tends to zero. It turns out that the homogenized system coincides with the original reaction–diffusion system. Using this and the facts that the diffusion equation on manifolds satisfies the maximum principle and its solution converges to a easily calculated constant, we can obtain analogous properties for the original system. Copyright © 2008 John Wiley & Sons, Ltd.     

Fractal approach to the CO oxidation on silica porous materials

We present an approach establishing a relation between the activation energy of heterogeneous catalytic processes and the fractal dimension of a catalyst. The approach is verified by experimental study of the CO oxidation on various porous silica and zeolite NaX. The fractal dimension of a catalyst (D_F) was calculated from the nitrogen adsorption isotherms. Our results indicate that the activation energy increases with increasing the fractal dimension of a catalyst. We show a good correspondence between theoretical and experimental results.     

A result in asymmetric Euclidean Ramsey theory

It is proved that if the points of the three-dimensional Euclidean space are coloured with red and blue, then there exist either two red points at unit distance, or six collinear blue points with distance one between any two consecutive points.     

Controlled-advancement rigid-body optimization of nanosystems

In this study, we propose a novel optimization algorithm, with application to the refinement of molecular complexes. Particularly, we consider optimization problem as the calculation of quasi-static trajectories of rigid bodies influenced by the inverse-inertia-weighted energy gradient and introduce the concept of advancement region that guarantees displacement of a molecule strictly within a relevant region of conformational space. The advancement region helps to avoid typical energy minimization pitfalls, thus, the algorithm is suitable to work with arbitrary energy functions and arbitrary types of molecular complexes without necessary tuning of its hyper-parameters. Our method, called controlled-advancement rigid-body optimization of nanosystems (Carbon), is particularly useful for the large-scale molecular refinement, as for example, the putative binding candidates obtained with protein–protein docking pipelines. Implementation of Carbon with user-friendly interface is available in the SAMSON platform for molecular modeling at https://www.samson-connect.net . © 2019 Wiley Periodicals, Inc.     

Photodynamics of polyene-polymethine transformations and spectral fluorescent properties of merocyanine dyes

Absorption and fluorescence spectrum band moments (center of gravity, width, asymmetry, excess, and fine structure) have been determined in a wide range of solvents with different polarities for inverse solvatochromic di-, tetra-, and hexamethinemerocyanines derived from 1,3-diphenyl-2,3-dihydro-1H-benzimidazole. Juxtaposition of the quantum-chemically calculated (by the semiempirical AM1 method) charges, bond orders, and dipole moments of the merocyanine molecules in the ground and excited singlet states with the experimentally observed spectral fluorescent characteristics suggests that the molecular electronic structure in the two states can vary from a nonpolar polyene via a polymethine to a charge-separated polyene, depending on the length of the polymethine chain and the medium polarity. As shown, solvatofluorochromism gives rise to smaller spectral band shifts than those of solvatochromism. This effect is attributable to weaker intermolecular solute-solvent interactions in the fluorescent excited state due to the more equalized charges as compared to those of the ground state. A lack of mirror symmetry of the absorption and fluorescence spectra has been revealed for di- and tetramethinemerocyanines (broadened fluorescence bands) as well as for hexamethinemerocyanines (narrowed fluorescence bands); the two cases are accounted for by the different behavior of vibronic and intermolecular interactions in the course of absorption and emission. As found for merocyanines, the electronic structure of their fluorescent state approaches the cyanine limit and the ground state becomes increasingly polyene-like with lengthening of the polymethine chain. A close vicinity of the excited state to the cyanine limit causes a dramatic increase in fluorescence quantum yields and a decrease in Stokes shifts observed for higher merocyanine vinylogues.