Linked crystallites in the conducting topmost layer of polymer bilayer films controlled by temperature: from micro- to nanocrystallites.

Temperature has great impact on the structure and size of the linked crystallites of the conducting topmost layer formed at the surface of a polycarbonate film via the reaction BEDT-TTF+IBr [BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene]. We show that fine temperature control permits formation of a semiconducting topmost layer of alpha'-(BEDT-TTF)(2)(I(x)Br(1-x))(3) crystallites with either micro- or nanometre size, a result that opens a route to miniaturized conducting plastic materials.     

Infrared study of hydration and association of functional groups in a perfluorinated Nafion membrane,Part 1

A perfluorosulfonic acid Nafion membrane has been studied with infrared spectroscopy. Infrared spectra of the membrane in acid form at the different degree of hydration were analysed in details and the conclusions about the state of sulfonic groups within clusters were drawn. The results indicate that in swollen samples in acid form hydrate structures involving dissociated sulfonic groups and water molecules are formed. These structures are analogous to those found in polystyrenesulfonic acid. With progressive drying of the Nafion membrane the network of hydrate structures breaks up and functional groups are transformed into their undissociated forms.     

Quantitative determination of mesomorphic regions in oriented polymers from wide-angle X-ray diffraction

A method for quantitative characterization of the noncrystalline region in poly(ethylene terephthalate) (PET) fibers based on x-ray wide-angle diffraction data is elaborated. The procedure consists in a computational resolution of the diffracted intensity into individual peaks for 010, 11 0, and 100 planes and into isotropic and anisotropic components of diffuse scattering. The results show that the content of mesomorphic regions in the noncrystalline part of PET fibers with draw ratio of λ = 3.0 varies from 12% to 32% depending on the temperature of heat treatment.     

Equivalence of the Local Markov Inequality and a Kolmogorov Type Inequality in the Complex Plane

We prove that a compact subset of the complex plane satisfies a local Markov inequality if and only if it satisfies a Kolmogorov type inequality. This result generalizes a theorem established by Bos and Milman in the real case. We also show that every set satisfying the local Markov inequality is a sum of Cantor type sets which are regular in the sense of the potential theory.     

Pseudo Leja sequences

We study pseudo Leja sequences attached to a compact set in the complex plane. The requirements are weaker than those of ordinary Leja sequences, but these sequences still provide excellent points for interpolation of analytic functions and their computation is much easier. We also apply them to the construction of excellent sets of nodes for multivariate interpolation of analytic functions on product sets.     

L-Regularity of Markov Sets and of m-Perfect Sets in the Complex Plane

Let E be a compact subset of C. We prove that if E satisfies the following local Markov property: for each polynomial P,

On the Best Exponent in Markov Inequality

Let E be a compact set preserving the Markov inequality and m(E) be its best exponent i.e., m(E) is the infimum of all possible exponents in this inequality on E. It is known that $\alpha (E) \le \frac1{m(E)}$ where α(E) is the best exponent in Hölder continuity property of the (pluri)complex Green function (with pole at infinity) of E. We show that if E???? ^N (or ? ^N ) with N?≥?2 then the Markov inequality need not be fulfilled with m(E). We also construct a set E????² such that the Markov inequality holds at the tip of exponential cusps composing E but for the whole set E we have m(E)?=?∞. Moreover, we prove that sup m(E)?=?∞ where the supremum is taken over all compact sets E???? preserving the Markov inequality. Finally, we prove that if E is a Markov set in ? then its image F(E) under a holomorphic mapping F is a Markov set too. More precisely, we prove that $m(F(E))\leq m(E)\cdot \Big(1+ \max\limits_{ \partial E\cap\{F'(t)=0\}}\textrm{ord}_t F'\Big)$ .     

Iterated Function Systems and Łojasiewicz–Siciak Condition of Green’s Function

A compact set K ì \mathbbC^N{K \subset \mathbb{C}}^{N} satisfies (ŁS) if it is polynomially convex and there exist constants B,β > 0 such that

How to construct totally disconnected Markov sets?

We deduce a polynomial estimate on a compact planar set from a polynomial estimate on its circular projection, which enables us to prove Markov and Bernstein-Walsh type inequalities for certain sets. We construct