Polymerization of butadiene on nanoparticles’ surfaces and formation of metal/polymer nanocomposites

In this paper, we demonstrate that laser vaporization of metals in the presence of a small concentration of butadiene vapor leads to the polymerization of butadiene and incorporation of the metal nanoparticles within the polymer matrix. The metal nanocomposites are characterized by electron microscopy, X-ray diffraction and EDX. The results from high pressure mass spectrometry indicate that multiple additions of butadiene molecules on the metal cations Fe⁺, Ni⁺ and Pt⁺, generated by laser vaporization, take place at room temperature thus providing an efficient means of initiating further polymerization reactions. The Pt⁺ reactions show extensive fragmentations and elimination steps generating hydrocarbon ions. The laser vaporization/polymerization method provides the ability to encapsulate several different metals or metal oxides which undoubtedly will play a significant role in tuning the various properties of the polymer composites.     

Estimate for the Gradient of the Solution to the Neumann Problem for (p,q)-Nonlinear Equations

We consider the Neumann boundary value problem for the class of (p,q)-nonlinear elliptic equations. The numbers p and q, 2 ⩽ p < q, characterize the power growth with respect to the gradient of eigenvalues of the leading matrix of the equation. An a priori estimate for the maximum of the modulus of the gradient of the solution is obtained in a neighborhood of the boundary of the domain for some interval of p and q. Bibliography: 5 titles. __________ Translated from Problemy Matematicheskogo Analiza, No. 31, 2005, pp. 47–57.     

Bases on multipunctured Riemann surfaces and interacting strings amplitudes

The Krichever-Novikov bases are studied on Riemann surfaces with more-than-two punctures. The bases are presented and the completness theorem is proven for the case of integer (up to a common constant) momenta. Then the interacting strings are considered, the amplitudes and partition functions are obtained, comparable with that of path-integral approach. For the amplitudes the simple geometric implication is proposed.