Ninth-order,explicit, two-step methods for second-order inhomogeneous linear IVPs

In the present paper, the second-order linear inhomogeneous initial value problems (LI-IVP) with constant coefficients is of our interest. Two-step hybrid methods (ie, of Numerov-type) are considered for addressing this problem. Thus, a special set of order conditions is given and solved for derivation a low cost new method. Actually, we manage to save two stages per step. This is crucial as shown in various numerical tests where our new proposal outperforms standard methods in the relevant literature.     

On the Largest Lyapunov Exponent for Products of Gaussian Matrices

The paper provides a new integral formula for the largest Lyapunov exponent of Gaussian matrices, which is valid in the real, complex and quaternion-valued cases. This formula is applied to derive asymptotic expressions for the largest Lyapunov exponent when the size of the matrix is large and compare the Lyapunov exponents in models with a spike and no spikes.     

Olefin polymerization behavior of titanium(IV) alkoxo complexes with fluorinated diolate ligands: The impact of the chelate ring size and the nature of organoaluminum compounds

Titanium(IV) coordination compounds are effectively used as precatalysts for ethylene polymerization and copolymerization with other olefins. New titanium(IV) complexes 3b – d with ligands containing two diphenylcarbinol fragments linked by the perfluorinated hydrocarbon units –CF₂– or –C₂F₄– were synthesized. The structures of complexes 3b and 3d were determined by X-ray diffraction. Titanium atoms in 3b have a distorted trigonal-bipyramidal coordination environment while spiro-complex 3d is characterized by tetrahedral molecular geometry. The catalytic behavior of complexes activated by mixtures of Bu₂Mg and alkylaluminium chlorides from among Me₂AlCl, Et₂AlCl, EtAlCl₂, and Et₃Al₂Cl₃ were studied. The resulting catalytic systems catalyze ethylene polymerization to afford ultra-high molecular weight polyethylene, suitable for modern processing methods, and the solvent-free solid state formation of super high-strength (1.37–2.75 GPa) and high-modulus (up to 138 GPa) oriented film tapes. The same catalytic systems catalyze ethylene copolymerization with 1-hexene to afford high molecular weight semicrystalline elastomeric polymers containing up to 20% of comonomer units.     

Density functional theory study of the water adsorption at Bi(111) electrode surface

The adsorption of a water molecule on a basal Bi(111) electrode surface, crystallising in the rhombohedral system, has been studied in the framework of cluster model. The quantum chemical calculations were performed at the Density Functional Theory (DFT) level and the electrical double layer effects were analysed by using an external electric field. In contrast to computational predictions reported previously for other metal surfaces, crystallising in the face-centred cubic or hexagonal close-packed systems, a hollow site for Bi(111) was found to be energetically the most preferable; the water adsorption energy amounts to ? 28 kJ mol^? 1. In a wide range of surface charge densities the water molecule is bound preferentially through the O atom in orientation perpendicular to the surface plane. The Bi(111) hydrophilic properties are compared with those for other metals. Some adsorption characteristics of a hydrogen atom and a hydroxyl group at Bi(111) are reported as well, which give evidence in favour of the non-dissociative adsorption of water molecules.     

Highly stereoselective [3+2]-cycloaddition reaction of stabilised N,N′-cyclic azomethine imines with 3-nitro-2-phenyl-2H-chromenes: Synthesis of tetrahydrochromeno[4,3-c]pyrazolo[1,2-a]pyrazol-11-ones

The reactions of 3-nitro-2-phenyl-2H-chromenes with 2-arylmethylidene-5-oxopyrazolidin-2-ium-1-ides proceeded diastereoselectively to afford the corresponding tetrahydrochromeno[4,3-c]pyrazolo[1,2-a]pyrazol-11-ones in good yields as a result of the 1,3-dipolar cycloaddition reaction of stabilised N,N′-cyclic azomethine imines at the Δ³-bond of the chromene system.