Ethylene polymerization over supported catalysts [2,6‐bis(imino)pyridyl iron dichloride/magnesium dichloride] with AlR3 as an activator

Data on ethylene polymerization over supported LFeCl₂/MgCl₂ catalysts {L = 2,6‐bis[1‐(2,6‐dimethylphenylimino)ethyl]pyridyl} containing AlR₃ (R = Me, Et, i‐Bu, or n‐Oct) as an activator are presented. These catalysts are highly active (100–300 kg of polyethylene/g of Fe h bar of C₂H₄) and stable in ethylene polymerization at 70–80 °C. Data on the effects of the iron content, AlR₃ type, Al(i‐Bu)₃ concentration, and hydrogen presence on the catalyst activity are presented. The molecular structure of polyethylene produced with these catalysts (including the molecular masses, molecular mass distribution, branching, and number of C?C bonds) has been studied; data on the effects of AlR₃ and hydrogen on the molecular structure are presented. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2128–2133, 2005     

Ferrocene polymers. Synthesis and thermal polymerization of α-chloro-β-formyl-p-ferrocenylstyrene

The synthesis and thermal polymerization of a new chloroformylated vinyl derivative containing a ferrocenyl residue are reported.The reactivity of α-chloro-β-formyl-p-ferrocenylstyrene in the polymerization reaction is discussed in the light of the experiment results and data obtained from molecular orbital calculations using the Hückel approximation.     

A convenient preparation of mixed allylic and allenic thiosulfinates

The first successful preparation of propargylic and allylic chloroalkoxy disulfides in high yields is reported. Facile 1,4-electrophilic addition of these to 2,3-dimethyl-1,3-butadiene, followed by [2,3]-sigmatropic rearrangements affords mixed allyl allenic and bis-allylic thiosulfinates, respectively. Due to their similarity to allicin, the latter are of potential biological interest.     

Synthesis and properties of new polyazines—I

New polyazines were synthesized by the polycondensation of hydrazine with acenaphthenequinone, 5-chloroacenaphthenequinone, 5-nitroacenaphthenequinone and 5,6-dinitroacenaphthenequinone. The influences of the catalyst and quinone/hydrazine mole ratio on the yield of soluble and insoluble compounds, as well as on the viscosity of a solution of the polymer in DMF, were studied. Some electrophysical properties as well as the polyazine behaviour under heating were also studied by thermogravimetrical analysis.     

Multilayer adsorption of amino acids on oxidized cellulose

The adsorption of amino acids (AA) (glycine, L-alanine, L-proline) on oxidized cellulose (OC) with various carboxyl contents and degrees of crystallinity from aqueous and water/ethanol solutions was studied. It was found that multilayer adsorption occurs in concentrated solutions of AA. It proceeds according to successive mechanisms via adsorption of AA zwitterions onto carboxyls of already adsorbed AA. This leads to formation of chain AA associates in the OC phase. A sharp increase in swelling accompanies multilayer adsorption. It was established that structural characteristics and degree of polymerization of OC are the main factors that affect multilayer adsorption. The distribution of carboxyls in the OC phase also plays an important role. Multilayer adsorption does not proceed in water/ethanol solutions and in the case of the cationic form of AA.     

Discretization of Compact Riemannian Manifolds Applied to the Spectrum of Laplacian

For κ ⩾ 0 and r₀ > 0 let ℳ(n, κ, r₀) be the set of all connected, compact n-dimensional Riemannian manifolds (Mⁿ, g) with Ricci (M, g) ⩾ −(n−1) κ g and Inj (M) ⩾ r₀. We study the relation between the kth eigenvalue λ_k(M) of the Laplacian associated to (Mⁿ,g), Δ = −div(grad), and the kth eigenvalue λ_k(X) of a combinatorial Laplacian associated to a discretization X of M. We show that there exist constants c, C > 0 (depending only on n, κ and r₀) such that for all M ∈ ℳ(n, κ, r₀) and X a discretization of for all k < |X|. Then, we obtain the same kind of result for two compact manifolds M and N ∈ ℳ(n, κ, r₀) such that the Gromov–Hausdorff distance between M and N is smaller than some η > 0. We show that there exist constants c, C > 0 depending on η, n, κ and r₀ such that for all . Mathematics Subject Classification (2000): 58J50, 53C20 Supported by Swiss National Science Foundation, grant No. 20-101 469     

On the dependence of the reflection operator on boundary conditions for biharmonic functions

The biharmonic equation arises in areas of continuum mechanics including linear elasticity theory and the Stokes flows, as well as in a radar imaging problem. We discuss the reflection formulas for the biharmonic functions u(x,y)∈R² subject to different boundary conditions on a real-analytic curve in the plane. The obtained formulas, generalizing the celebrated Schwarz symmetry principle for harmonic functions, have different structures. In particular, in the special case of the boundary, Γ₀:={y=0}, reflections are point-to-point when the given on Γ₀ conditions are u=n_∂u=0, u=Δu=0 or n_∂u=n_∂Δu=0, and point to a continuous set when u=n_∂Δu=0 or n_∂u=Δu=0 on Γ₀.