On one generalization of a DiPerna and Majda theorem

The weak limits of sequences {f(u^ν)}_ν∈? where u^ν's are vector‐valued µ‐measurable functions defined on a compact set Ω and f is (possibly) discontinuous are investigated. As shown by the author (J. Conv. Anal. (to appear)), they are described in terms of integral formulae involving parametrized measures independent of f, similarly as in the classical theorem by Young and its generalization due to DiPerna and Majda. In the present paper we describe the supports of the involved parametrized measures. Copyright © 2006 John Wiley & Sons, Ltd.     

EPR and XPS measurements of polymeric catalysts doped with hereopolyacids in oxygen adsorption studies

The goal of our studies was to determine the nature of interactions between catalytic active samples, such as polypyrrole (PPy) doped with: chloride anions, heteropolyacids such as H₅PMo₁₀V₂O₄₀, or H₄SiW₁₂O₄₀, and oxygen particles. In order to reveal the mechanism of the linkage between the catalysts and oxygen we provided the electron paramagnetic resonance (EPR) measurements of synthesized samples in O₂ and N₂ flow. Moreover, the X-ray photoelectron spectroscopy (XPS) measurements were performed to show the properties of doped heteropolyacids and the state of nitrogen in polypyrrole matrix. The results of EPR studies of PPy(Cl), PPy(H₄SiW₁₂O₄₀), PPy(H₅PMo₁₀V₂O₄₀) samples, show that the polypyrrole doped with chloride anions interacts much easier with oxygen than polypyrrole doped with heteropolyacids (in the above given order, of preference with the most active polypyrrole system first). It correlates with XPS results, which show that a molybdenium-vanadium anion is more reduced than a silicon-tungsten one. The redox reactions of heteropolyacids involve the oxidation-reduction of the conjugated polymer chain, leaving no or little place for interactions with oxygen. Polypyrrole doped with H₄SiW₁₂O₄₀ shows some oxygen sensitivity as observed in the EPR studies, as opposed to polypyrrole doped with H₅PMo₁₀V₂O₄₀, which is in line with the XPS results.     

Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian.     

On the environmental decoherence and spin interference in mesoscopic loop structures

Mechanisms of ‘environmental decoherence’ such as surface scattering, Elliot–Yafet process and precession mechanisms, as well as their influence on the spin phase relaxation are considered and compared. It is shown that the ‘spin ballistic’ regime is possible, when the phase relaxation length for the spin part of the wave function (L^(s)) is much greater than the phase relaxation length for the ‘orbital part’ (L^(e)). In the presence of an additional magnetic field, the spin part of the electron's wave function (WF) acquires a phase shift due to additional spin precession about that field. If the structure length L is chosen to be L^(s)>L>L^(e), it is possible to ‘wash out’ the quantum interference related to the phase coherence of the ‘orbital part’ of the WF, retaining at the same time that related to the phase coherence of the spin part and, hence, to reveal corresponding conductance oscillations.     

Nonlinear and chaotic oscillations of a constrained cantilevered pipe conveying fluid: A full nonlinear analysis

In this paper, the planar dynamics of a nonlinearly constrained pipe conveying fluid is examined numerically, by considering the full nonlinear equation of motions and a refined trilinear-spring model for the impact constraints—completing the circle of several studies on the subject. The effect of varying system parameters is investigated for the two-degree-of-freedom (N=2) model of the system, followed by less extensive similar investigations forN=3 and 4. Phase portraits, bifurcation diagrams, power spectra and Lyapunov exponents are presented for a selected set of system parameters, showing some rather interesting, and sometimes unexpected, results. The numerical results are compared with experimental ones obtained previously. It is found that in the parameter space that includesN, there exists a subspace wherein excellent qualitative, and reasonably good (N=2) to excellent (N=4) quantitative agreement with experiment. In the latter case, excellent agreement is not only obtained in the threshold flow velocities (u) for the key bifurcations, but the inclusion of the nonlinear terms improves agreement with experiment in terms of amplitudes of motion and by capturing features of behaviour not hitherto predicted by theory.     

Polysiloxanol condensation and disproportionation in the presence of a superacid

Kinetics studies of the condensation of model hydroxyl-terminated oligosiloxanes, pentamethyldisiloxane-1-ol (MDH) and heptamethyltrisiloxane-1-ol (MD₂H), catalysed by protic complex of tetrakis(pentafluorophenyl)borate in the toluene solution were performed. The dominating reaction was condensation, which was accompanied by disproportionation of oligosiloxanols. Water released in the condensation forms separate dispersed phase, but the phase separation and the presence of water does not affect the rate of the polycondensation. Both processes, condensation and disproportionation, show analogous kinetic laws being first order in silanol and half order in catalyst. They exhibit also similar values of activation parameters. The kinetics are explained by the formation of a reactive protic complex of silanol with borate being in fast preequilibrium with an unreactive complex including two borate molecules and the silanol molecules. The equilibrium lies to the side of the unreactive borate complex.     

Mesoporous micelle templated silica with incorporated C<Subscript>8</Subscript> and C<Subscript>18</Subscript> phase

Mesoporous silica material of MCM-41 type was synthesized by co-condensation of highly concentrated octyltriethoxysilane (OTEOS), octadecyltriethoxysilane (ODTEOS) and tetraethoxysilane (TEOS). The obtained hybrid materials were characterized using XRD, TG-DSC and low temperature adsorption/desorption of nitrogen. It was shown that the applied method of synthesis allows to obtain silica of MCM-41 type with a high degree of hydrocarbon saturation.     

Synthesis of macrocyclic tetraamides derived from α-amino acids and their investigations using ESI-MS technique

Chiral α,ω-diesters react under high-pressure conditions (10 kbar) with α,ω-diamines to give chiral cyclic tetraamides of C₂-symmetry. The complexation properties of tetraamides towards alkali metal cations (Li⁺, Na⁺, K⁺, Rb⁺ and Cs⁺) were estimated on the basis of ESI-MS spectra.     

Thiol-ene chemistry as an effective tool for hydrophobization of cotton fabrics

In this paper, several methods of hydrophobization of cotton fabrics using the thio-ene click reaction were compared. Durable, superhydrophobic textiles were obtained in an easy way. Various variants of functionalized silsesquioxanes were used for the hydrophobization of fabrics. The synthesis of bifunctional silsesquioxanes (RSiMe₂O)₄(ViSiMe₂O)₄Si₈O₁₂ and (RSiMe₂O)₄(R’SiMe₂O)₄Si₈O₁₂ were performed via hydrothiolation of silsesquioxane derivative (ViSiMe₂O)₈Si₈O₁₂. Alkoxysilyl, alkyl and fluoroalkyl moieties were introduced as functional groups. Samples were prepared using four methods, differing in the modification method and the number of stages. During the research, fabrics were modified via (a) the dip-coating process, (b) carrying out thiol-ene click reactions directly on the surface of the fabric and (c) using both of these methods. The hydrophobicity of the fabric was evaluated by measuring the Water contact angle (WCA). The obtained samples were also examined using infrared analysis (FT-IR), Scanning electron microscope (SEM), and Elemental analysis (SEM–EDS). All analyses were performed before and after the washing process in order to verify the stability of the performed modifications.

Graphical abstract

     

Path integrals on half-line

In the framework of path integrals we present a solution to the Schrödinger equation for a free particle confined to the half-linex > 0. A solution in question corresponds to the boundary condition (/x) (0,t)= (0,t) where is a real constant.