Numerical solution of multiple nonlinear Volterra integral equations

We analyze a discretization method for solving nonlinear integral equations that contain multiple integrals. These equations include integral equations with a Volterra series, instead of a single integral term, on one side of the equation. We prove existence and uniqueness of solutions, and convergence and estimates of the order of convergence for the numerical methods of solution.     

On Truncated Matricial Stieltjes Type Moment Problems

We study two slightly different versions of truncated generalized matricial moment problems of Stieltjes type. A central topic is the construction and investigation of distinguished solutions of both moment problems under consideration. These solutions turn out to be nonnegative Hermitian Borel measures on the real axis which are concentrated on a finite number of points. Our approach is mainly algebraic. It is based on the use of particular matrix polynomials constructed from a nonnegative Hermitian block Hankel matrix.     

Synthesis of 4-polyfluoroalkyl-1,3-dithiolanes via [3+2] cycloaddition of thiocarbonyl ylide to polyfluoroalkanethioamides

Chemistry of Heterocyclic Compounds - New 4-polyfluoroalkyl-1,3-dithiolanes were synthesized by reaction of polyfluoroalkanethioamides with thiocarbonyl ylide that was generated in situ by...     

Sulfonimidamides and Imidosulfuric Diamides: Compounds from an Underexplored Part of Biologically Relevant Chemical Space

Two novel solid reagents—1-sulfonimidoyl- and 1-sulfamimidoyl-3-methylimidazolium derivatives—for the synthesis of sulfonimidamides and imidosulfuric diamides, respectively, were developed. It is shown that these reagents are very effective in substitution reactions with various N- and O-nucleophiles; therefore, they significantly extend the accessibility to the chemical space covered by organosulfur(VI) compounds with S=N bonds. In addition, previously unknown imidosulfuric diamides with free imino nitrogen groups were prepared, and their physical and chemical properties were characterized (including molecular geometry, pK_a, Log P, microsomal stability, and reactivity towards typical electrophiles). Similar to other organosulfur(VI) derivatives with S=N bonds, these compounds can be considered as promising bioisosteres of amides, ureas, or sulfonamides.     

Phase behaviour,structural properties and intermolecular interactions of systems based on substituted thiacalix[4]arene and nonionic surfactants

Supramolecular organised materials were prepared from nonionic surfactants and the following macrocyclic ionic liquids: n-tert-butylthiacalix[4]arenes containing quaternary ammonium fragments with amino acid substituents. Tetraethylene glycol monododecyl ether and decadiethylene glycol monododecyl ether were used as nonionic surfactants. They form lamellar and hexagonal mesophases in aqueous media, respectively. Liquid crystal and structural properties of these systems were studied. Intermolecular interactions of system components leading to formation of lyomesophases were estimated. Molecular structure of thiacalixarene contributes to the formation of a hydrogen bonding with surfactants. This process, in turn, initiates formation of a denser packed hexagonal structure.     

Koszul duality for extension algebras of standard modules

We define and investigate a class of Koszul quasi-hereditary algebras for which there is a natural equivalence between the bounded derived category of graded modules and the bounded derived category of graded modules over (a proper version of) the extension algebra of standard modules. Examples of such algebras include, in particular, the multiplicity free blocks of the BGG category O, and some quasi-hereditary algebras with Cartan decomposition in the sense of König.     

Analytic description of enhanced backscattering and negative polarization from a cloud of dipoles

We develop a second-order model of the light scattered by a cloud of randomly positioned dipoles and consider the interference of reciprocal rays that lead to enhanced backscatter and negative polarization. For large pathlength separations, we derive analytic expressions for the individual polarization intensities.     

Time-dependent electrical properties of liquid crystal cells: unravelling the origin of ion generation

An understanding of possible sources of ion generation in liquid crystal materials is of utmost importance to ensure uncompromised performance of modern liquid crystal devices. In this paper, time-dependent electrical properties of filled liquid crystal cells are used to reveal important information about often overlooked source of ion generation in liquid crystals. This source of ions originates from the ionic contamination of substrates of the liquid crystal cell. Ionic contaminants can be inherently present in the alignment layers or can be induced by external factors such as mechanical rubbing or irradiation with light. The model of this ion generation process is presented and tested using existing experimental data.