Transverse instability of the line solitary water-waves

We prove the linear and nonlinear instability of the line solitary water waves with respect to transverse perturbations.     

On some ranks of infinite groups

Abstract A group G has finite Hirsch-Zaicev rank r_hz(G) = r if G has an ascending series whose factors are either infinite cyclic or periodic and if the number of infinite cyclic factors is exactly r. The authors discuss groups with finite Hirsch-Zaicev rank and the connection between this and groups having finite section p-rank for some prime p, or p=0. Groups all of whose abelian subgroups are of bounded rank are also discussed. Keywords: p-rank, locally generalized radical group, Hirsch-Zaicev rank, torsion-free rank, rank Mathematics Subject Classification (2000): 20F19, 20E25, 20E15     

Influence of the long-range coulomb interaction upon the energy spectrum of infinite polyenes

It is shown that the energies of AMO's (E _k ) for an arbitrary homonuclear alternating system can be given with the following expression (identical for AMO with α- and β-spin): $$E_{k\sigma } = \alpha + \tfrac{1}{2}\gamma \pm (\delta ^2 \gamma ^2 + [e_k + \Delta _k (\gamma _{\mu v} )]^2 )^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} {\text{ }}\sigma \in \alpha ,\beta $$ where: e _k are the MO energies, obtained by means of the conventional HF method; δ and Δ _k are correlation corrections depending on the one-center (γ), resp. two-center (γ_{μ v} ) coulomb integrals. By means of the above method, where the interactions between non-adjacent AO's are taken into account, it is shown that the energy gap of an infinite polyene, in the π- electron approximation, is different from zero, regardless of the presence or absence of C-C bond alternation. This means that in adiabatic approximation an infinite atomic chain, satisfying the Born-Karman condition, is not a metal model but a dielectric one.     

Scaling of the Distribution of Shortest Paths in Percolation

We present a scaling hypothesis for the distribution function of the shortest paths connecting any two points on a percolating cluster which accounts for (i) the effect of the finite size of the system and (ii) the dependence of this distribution on the site occupancy probability p. We test the hypothesis for the case of two-dimensional percolation.     

Associative block copolymers comprising poly(N‐isopropylacrylamide) and poly(ethylene oxide) end‐functionalized with a fluorophilic or hydrophilic group. Synthesis and aqueous solution properties

A series of block copolymers comprising poly(N‐isopropylacrylamide) (PNIPAM) and poly(ethylene oxide) (PEO) end‐functionalized with a quaternary ammonium group (R_Q) was synthesized by free‐radical polymerization of N‐isopropylacrylamide with well‐defined R_QPEO macroazoinitiators. The radical termination occurred mainly by disproportionation, as confirmed by combining the data from size exclusion chromatography (SEC) and rheology measurements. The copolymers denoted R_QE_xN_y differ in type of the terminal group [F_Q = C₈F₁₇(CH₃)₂N⁺ or M_Q = (CH₃)₃N⁺] and in the length of the PEO (E_x; x = 4, 6, or 10 K) and PNIPAM (N_y; y = 7 or 17–19 K) blocks. The type of the terminal group determined the behavior of the block copolymers in the dilute and semidilute regime. Self‐assembled species formed by both F_Q and M_Q modified block copolymers were detected by static light scattering measurements at 25 °C and above the lower critical solution temperature (LCST). The LCST of the block copolymers depended on the type of the R_Q group and the length of the blocks. F_Q‐modified copolymers form elastic gels below and above the LCST. It was inferred that the F_Q groups and the PNIPAM blocks form segregated microdomains that serve as junctions to maintain a viscoelastic network. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5736–5744, 2004     

Properties of the H-bond network for two-dimensional lattice water model

A microscopic Hamiltonian of the hydrogen-bond network in two-dimensional lattice water is proposed, which describes the formation and disruption of the H bonds, their bending, and which satisfies the Bernal-Fowler rules [J. D. Bernal and R. H. Fowler, J. Chem. Phys. 1, 515 (1933)]. The thermodynamic properties of the H-bond network are studied using the method of many-particle irreducible distribution functions, which is a generalization of the Kikuchi cluster approach [R. Kikuchi, Phys. Rev. 81, 988 (1951)] and the Bethe-Peierls quasiactivities method [H. A. Bethe, Prog. R. Soc. A 150, 552 (1935)]. The temperature dependencies of the average number of H bonds per molecules, the contribution of the H bonds into the heat capacity of the system, and the parameters describing the correlations between the states of molecules on the neighboring sites are investigated. It is shown that depending on the magnitude of the interaction between the H bonds in the H-bond subsystem either smooth or sharp first-order phase transition can occur. The role of different factors in the formation of the properties of the H-bond network is discussed.     

One-Atmosphere Argon Dielectric-Barrier Corona Discharge as an Effective Source of Cold Plasma for the Treatment of Polymer Films and Fabrics

The properties of an ac dielectric-barrier corona discharge in argon under atmospheric pressure were studied and the results of testing of this type of gas discharge in the low-temperature treatment of polymer films and fabrics for the purpose of enhancement of their wettability were reported.     

Counterion-induced transformations of cationic surfactant micelles studied by using the displacing effect of solvatochromic pyridinium N-phenolate betaine dyes

In this paper, we demonstrate that the behavior of a set of eight large-sized negatively solvatochromic pyridinium N-phenolate betaine dyes reflects the principle transformations, occurring in aqueous micellar solutions of three cationic surfactants. As surfactants, cetyltrimethylammonium bromide (CTAB), n-octadecyltrimethylammonium chloride (OTAC), and N-cetylpyridinium bromide (CPB) were used. Normally, for such probes coupled with micelles, a red shift of the vis absorption band is expected as a result of a hydrophobization ("drying") of the micellar interface. However, under addition of electrolytes with anions such as tosylate, salicylate, and some n-alkanesulfonates or n-alkanecarboxylates to the micellar solutions, an unexpected effect was observed. Instead of a red shift, a blue shift of the vis absorption band of some of the dissolved betaine dyes was registered, as compared with the spectrum measured in pure aqueous micellar solutions of CTAB, OTAC, or CPB (Deltalambda(max) up to ca. 80 nm). This blue shift, indicating an increase in the polarity of the dye microenvironment, is explained by displacing the large dye dipoles from the thinned micelles toward the aqueous phase. The effect is well expressed at concentrations of C(betaine dye) approximately 10(-5) M, C(cationic surfactant) approximately 0.001 M, and C(organic anion) approximately 0.01 M. Transmission electron microscopy of dried samples confirms the distinct changes occurring in the studied micellar systems upon the addition of organic anions. The excess of inorganic salts [C(NaBr, KBr, or KCl) = 0.5-4.0 M] restored the position of the vis absorption band or even shifted it toward the red. Moreover, some of the betaine dyes studied (i.e., the more hydrophobic ones) stay in the micellar pseudophase or precipitate under the aforementioned concentration conditions. The peculiarities of the behavior of these betaine dyes are in agreement with their molecular structure.     

Structural and catalytic properties of ultra-dispersed silver powders prepared by metal evaporation with high-power electron beam. 1. Structural properties

Summary Structural properties of ultra-dispersed silver powders synthesized via high-temperature electron-beam evaporation of silver in different gases (Ar, N₂, He) were studied with XRD, TEM, EDX and XRF. The formation of specific oxide-like species on the particle surface of an Ag(Ar) powder was found. It was shown that these particles can contain argon atoms.     

The crystal and molecular structures of three germatrane derivatives

The molecular and crystal structure of three germatrane compounds: 1-(1-bromobicyclo[4.1.0]hept-7-yl)germatrane, l-(1-trimethylsilanyl-cyclopropyl)-germatrane and 1-(1-Methyl-1,2-dicarba-closo-dodecaboranyl)germatrane has been determined by X-ray diffraction method in order to investigate main geometrical regularities of the germatrane molecules. There were established all values of the main structural parameters above-mentioned molecules.