Some aspects of the living isobutylene polymerization

The possibilities of increasing the livingness in cationic isobutylene polymerizations has been investigated. It has been assumed that the living chain-end is polarized but non-dissociated and relatively stable, therefore, i) shifting of the dissociation equilibrium by adding salts with common or non-common anion in excess, and ii) increasing of the stability of the chain-end by complexing it with electrondonors, may increase the livingness of the system. Indeed, the addition of n-Bu₄NCl or n-Bu₄NI to systems with BCl₃ or TiCl₄ coinitiators, as well as the addition of dimethyl sulphoxide as electrondonor in a broad concentration range, improved the living character. The possibility of complexation of the chain-end by the monomer has also been supported     

Modulus of curve families and extremality of spiral-stretch maps

We develop a method using the modulus of curve families to study minimisation problems for the mean distortion functional in the class of finite distortion homeomorphisms. We apply our method to prove extremality of the spiral-stretch mappings defined on annuli in the complex plane. This generalises results of Gutlyanskiĭ and Martio [12] and Strebel [23].     

Operator preconditioning with efficient applications for nonlinear elliptic problems

This paper is devoted to the numerical solution of nonlinear elliptic partial differential equations. Such problems describe various phenomena in science. An approach that exploits Hilbert space theory in the numerical study of elliptic PDEs is the idea of preconditioning operators. In this survey paper we briefly summarize the main lines of this theory with various applications.     

Lengths of radii under conformal maps of the unit disc

If is the set of endpoints of radii which have length greater than or equal to under a conformal map of the unit disc, then as for the logarithmic capacity of . The exponent is sharp.

     

In situ UV-vis absorbance measurements for Langmuir films of poly[4'-[[2-(methacryloyloxy)-ethyl]ethylamino]-2-chloro-4-nitroazobenzene] (HPDR13) azopolymer

In situ UV-vis absorbance measurements are used to investigate aggregation in Langmuir films from the azopolymer poly[4'-[[2-(methacryloyloxy)-ethyl]ethylamino]-2-chloro-4-nitroazobenzene] (HPDR13), a methacrylate derivative of DR13. The level of aggregation in a Langmuir film is intermediate between that of HPDR13 in chloroform solution and in a deposited LB film, as expected. Absorption is negligible at large areas per monomer, and starts to increase at a critical area that is the same as the one obtained in surface potential isotherms, being close to twice the area per monomer for a condensed film. This indicates that the onset for light absorption coincides with a critical packing density where monolayer structuring occurs and there is a sharp change in the effective dielectric constant of the film/water interface. Consistent with a featureless pressure-area isotherm for HPDR13, denoting no significant molecular rearrangement upon film compression, the UV-vis spectra did not vary with the surface pressure. The intensity of absorbed light increased, though, as the film was compressed owing to a higher density of chromophores. At higher subphase temperatures, larger flexibility of HPDR13 chains led to a more compact arrangement, causing the area per monomer to decrease and the absorbed light to increase-with approximately opposite trends.     

The Number of Edge Colorings with no Monochromatic Cliques

Let F(n,r,k) denote the maximum possible number of distinctedge-colorings of a simple graph on n vertices with r colorswhich contain no monochromatic copy of K_k. It is shown thatfor every fixed k and all n>n₀(k), and , where t_k–1(n)is the maximum possible number of edges of a graph on n verticeswith no K_k (determined by Turán's theorem). The caser=2 settles an old conjecture of Erds and Rothschild, whichwas also independently raised later by Yuster. On the otherhand, for every fixed r>3 and k>2, the function F(n,r,k)is exponentially bigger than . The proofs are based on Szemerédi's regularity lemmatogether with some additional tools in extremal graph theory,and provide one of the rare examples of a precise result provedby applying this lemma.     

Separation of strength and selectivity of mobile phase by spectral mapping technique

The retention behaviour of seven monotetrazolium and nine ditetrazolium salts was studied in seven different mobile phases on alumina and impregnated alumina stationary phases. The strength and selectivity of the components of mobile phases were separately calculated by the spectral mapping technique. It was established that tetrahydrofuran (THF) has the highest solvent strength while the differences among ethanol, 1-propanol, 2-propanol and dioxane were relatively low. The selectivity of THF was also considerably different from those of other solvents. Hydrophobicity and electronic parameters were equally involved in the retention strength and selectivity of tetrazolium salts, indicating the mixed character of their interaction with the alumina stationary phase.