Two soliton collision for nonlinear Schrödinger equations in dimension 1

We study the collision of two solitons for the nonlinear Schrödinger equation iψt=−ψxx+F(²|ψ|)ψ, F(ξ)=−2ξ+O(ξ²) as ξ→0, in the case where one soliton is small with respect to the other. We show that in general, the two soliton structure is not preserved after the collision: while the large soliton survives, the small one splits into two outgoing waves that for sufficiently long times can be controlled by the cubic NLS: iψt=−ψxx−2²|ψ|ψ.     

Growth and fire resistance of colloidal silica-polyelectrolyte thin film assemblies

Thin films of colloidal silica were deposited on cotton fibers via layer-by-layer (LbL) assembly in an effort to reduce the flammability of cotton fabric. Negatively charged silica nanoparticles of two different sizes (8 and 27 nm) were paired with either positively charged silica (12 nm) or cationic polyethylenimine (PEI). PEI/silica films were thicker due to better (more uniform) deposition of silica particles that contributed to more than 90% of the film weight. Each coating was evaluated at 10 and 20 bilayers (BL). All coated fabrics retained their weave structure after being exposed to a vertical flame test, while uncoated cotton was completely destroyed. Micro combustion calorimetry confirmed that coated fabrics exhibited a reduced peak heat release rate, by as much as 20% relative to the uncoated control. The 10 BL PEI-8 nm silica recipe was the most effective because the coating is relatively thick and uniform relative to the other systems. Soaking cotton in basic water (pH 10) prior to deposition resulted in better assembly adhesion and flame-retardant behavior. These results demonstrate that LbL assembly is a useful technique for imparting flame retardant properties through conformal coating of complex substrates like cotton fabric.     

Redox strategy for reversible attachment of biomolecules using bifunctional linkers

Soft attachment of streptavidin to β-cyclodextrin-modified pegylated SAMs was efficiently performed in a reversible and repetitive way via orthogonal bifunctional linkers involving streptavidin-biotin recognition and redox-driven multivalent host-guest (β-cyclodextrin-ferrocene) interactions.     

Fluorolactonization of norbornenecarboxylic acids and their methyl esters with F-TEDA-BF4 and XeF2

The selective fluorolactonization was achieved by treatment of cis-5-norbornene-2,3-endo-dicarboxylic acid or its monomethyl and dimethyl esters with F-TEDA-BF₄ or XeF₂. The reactions of 5-norbornene-endo-2-carboxylic acid and its monomethyl ester with F-TEDA-BF₄ or XeF₂ proceed in a non-selective manner to give fluorolactonization, addition and rearrangement products. The basic factor responsible for selectivity of the fluorolactonization is the presence of two endo-oriented carboxyl groups in the substrate molecule. The electrophilicity and type of the fluorinating agent is of secondary importance in this regard. It is postulated that the fluorolactonization of norbornenecarboxylic acids and their methyl esters with F-TEDA-BF₄ or XeF₂ is realized mainly via “open” fluoronorbornyl carbocation intermediates which in the reaction with XeF₂ are postulated as the tight ion pairs.     

Specific Features of the Reaction of 2-Nitro- and 2-Bromo-2-Nitroethenylphosphonates with Furan

Investigation of the reactions of phosphorylated 2-nitro- and 2-bromo-2-nitroethenes with furan showed that bis(2-chloroethyl) 2-nitroethenylphosphonate reacts with this heterocycle according to the pathway of diene condensation, while in the case of 2-bromo-2-nitroethenylphosphonate by two pathways, the complete diene synthesis accompanied by aromatization, and the electrophilic substitution at C²-atom of the furan with the subsequent partial dehydrohalogenation.     

Modelling of electrolyte mixtures with application to chemical equilibria in mixtures—prototypes of blood''s plasma and calcification of soft tissues

Modelling of the biologic solutions has a great importance for basic physicochemical backgrounds of the living processes, mechanism of the diseases and drugs action, etc. The modelling of the chemical equilibria in solution that served as a prototype of the blood plasma with application to calcification of the tissues is performed. The concentrations of molecular–ionic forms containing calcium and hydrogen cations and phosphate anions in the range of ionized-calcium and total phosphorus concentrations from 0.5 to 3.0 mM and at the solution pH of 7.1–7.8 were calculated. The activities of the ionized species were described in approach to Debye–Hückel's theory. The full set of the equilibria taking into consideration dissociation of the water, phosphoric acid, formation of both inert and ionic calcium phosphates was considered. The states of calcium hydrophosphate dihydrate CaHPO₄·2H₂O (CHPD), calcium phosphate Ca₃(PO₄)₂ (CP), calcium hydrophosphate-phosphate dihydrate Ca₄H(PO₄)₃·2H₂O (CHPPD) and hydroxyapatite Ca₃OH(PO₄)₃ (HA) with respect to the boundary of the region in which they crystallise were determined. A criterion has been introduced to characterize the degree of salt supersaturation with respect to crystallisation, which is based on the concentration distance between the states of a salt in solution and at the boundary of its crystallisation. This criterion is used to provide a quantitative characteristic of the supersaturation of the phosphates and their tendency to crystallise in blood's plasma. It was established that the most soluble of the phosphates, CaHPO₄·2H₂O, is undersaturated and the other phosphates are supersaturated with respect to crystallisation. Thus, this phosphate does not take part in the calcification, and this is the source for ionized calcium in a blood plasma from the soft tissues. The role of the other phosphates in calcification of the soft tissues is decreased in the series HA>CP>CHPPD. The dependencies of the supersaturation of the solution on the pH and on the concentrations of calcium and phosphorus in a mixture are discussed.     

Solutions of some singular integral equation

A singular integral equation with a Holderian second member function on [a,b] is considered and solved for four different type of kernels in the class of functions that are unbounded at the end points of the interval.     

Novel α-fluorinated cyclic phosphite and phosphinite ligands and their Rh-complexes as suitable catalysts in hydroformylation

Asymmetrical cyclic phosphite and phosphinite ligands of a novel type bearing either trifluoromethyl or pentafluorophenyl group were synthesized using >PCl or >PN< species and racemic fluorinated alcohols. The P-ligands were converted to complexes of Rh^III(L)(Cp^∗)Cl₂ type (where L = phosphite or phosphinite) and, in two instances, their stereostructures were evaluated by X-ray analysis. These complexes along with in situ systems, formed from Rh(CO)₂(acac) precursor and the corresponding ligand, were tested in the hydroformylation of styrene. Both systems provided excellent hydroformylation activities at 100 °C. Using the Rh^I in situ systems, moderate and high regioselectivities towards the branched aldehyde (2-phenyl-propanal) were obtained at 100 and 40 °C, respectively.