Living copolymerization of ethylene with norbornene by fluorinated enolato‐imine titanium catalyst

Complex [Ti(κ²‐N,O‐{2,6‐F₂C₆H₃N?C(Me)C(H) ?C(CF₃) O})₂Cl₂] ( 1 ) was evaluated as catalyst for living copolymerization of ethylene (E) with norbornene (N) upon activation with dried methylaluminoxane (d‐MAO) at temperatures between 25 and 90 °C. Copolymerization performed at different [N]/[E] feed ratios afforded stereoirregular alternating high molar mass P(E‐co‐N) with narrow molar mass distribution. The living nature of E‐co‐N copolymerization by 1 /d‐MAO was demonstrated by kinetics at 50 °C. This catalyst system was used for the synthesis of block copolymers such as polyethylene (PE)‐block‐P(E‐co‐N) with a crystalline PE block and an amorphous P(E‐co‐N) block as well as P(E‐co‐N)₁‐block‐P(E‐co‐N)₂, having different norbornene contents in the segments and thus having different T_g values. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Polynomial Inequalities with an Exponential Weight on (0,+∞)

We consider the weight ${{u(x) = x^{\gamma} e^{-x^{-\alpha}-x^{\beta}}}}$ , with ${{x \in(0,+\infty)}}$ , α >  0, β >  1 and γ ≥  0 and prove Remez-, Bernstein–Markoff-, Schurand Nikolskii-type inequalities for algebraic polynomials with the weight u on (0, + ∞).     

Some new results on orthogonal polynomials for Laguerre type exponential weights

We prove some results on the root-distances and the weighted Lebesgue function corresponding to orthogonal polynomials for Laguerre type exponential weights.     

Evidence of the Quasi‐Living Character of the ansa‐Zirconocene/MAO‐Catalyzed Copolymerization of Ethylene and Norbornene

The kinetics of the ethylene‐norbornene copolymerization, catalyzed by rac‐Et(Ind)₂ZrCl₂/MAO, 90%rac/10%meso‐Et(4,7‐Me₂Ind)₂ZrCl₂/MAO and rac‐H₂C(3‐tert‐BuInd)₂ZrCl₂/MAO was followed by sampling from the reaction mixture at fixed time intervals. Catalyst activity, copolymer composition and molar mass were studied as a function of time. The polymers showed an unusually low polydispersity and a significant increase in their molar mass with time, suggesting a quasi‐living polymerization.     

Gaussian quadrature rules with exponential weights on (−1, 1)

We study the behavior of some “truncated” Gaussian rules based on the zeros of Pollaczek-type polynomials. These formulas are stable and converge with the order of the best polynomial approximation in suitable function spaces. Moreover, we apply these results to the related Lagrange interpolation process and to prove the stability and the convergence of a Nyström method for Fredholm integral equations of the second kind. Finally, some numerical examples are shown.     

Polynomial inequalities and embedding theorems with exponential weights on (−1,1)

Letting 0<p≦∞, we prove Remez-, Bernstein–Markoff-, Schur- and Nikolskii-type inequalities for algebraic polynomials with exponential weights on (−1,1) multiplied by another weight function, which will satisfy the doubling or the A ^∗ condition at different occurrences. Moreover, we state embedding theorems between some function spaces related with exponential weights.