Synthesis and X-ray diffraction studies of chiral nickel(II), zinc(II), manganese(II), and cobalt(II) complexes with C 2-symmetric 2,6-bis[4′-(R)-ethoxyoxazolin-2′-yl]pyridine

Chiral nickel(II), zinc(II), manganese(II), and cobalt(II) complexes with C ₂-symmetric 2,6-bis[4′-(R)-ethoxyoxazolin-2′-yl]pyridine were prepared, the single crystal of nickel(II) complex, [Ni((R,R)-Et-Py-box)(H₂O)₂Cl]Cl ((R,R)-Et-Pybox is 2,6-bis[4′-(R)-ethoxyoxazolin-2′-yl]pyridine), was obtained and indicated by X-ray diffraction analysis. The nickel(II) complex crystallizes in the orthorhombic system, space group P2₁2₁2₁ with a = 7.7346(4) Å, b = 19.7133(13) Å, c = 25.8014(14) Å, V = 3934.1(4) ų, Z = 8, and R = 0.0526 against 7010 reflections with I > 2σ (I). A feature of interest was noted in the unit cell of the compound, where two types of molecules exist, which similarly have a distorted octahedral geometry but only slightly differ in the orientation of the coordinated atoms to the central Ni atom. These two types of molecules interact with each other by O-H…Cl hydrogen bonds, giving rise to one dimensional ribbon structure.     

Influence of demulsifiers of different structures on interfacial dilational properties of an oil-water interface containing surface-active fractions from crude oil

The influences of two commercial demulsifiers that have a straight chain and branch chain, respectively, on the dilational viscoelasticity of an oil-water interfacial film containing surface-active fractions from crude oil were investigated. The branch-chain demulsifier AE-121 could efficiently substitute surface-active fractions of different average molecular weights from the oil-water interface, while straight-chain SP-169 could only efficiently substitute those of large average molecular weight. It was apt to form a mix-adsorption layer with surface-active fractions of small average molecular weight. The results showed that the molecular size (or represented by average molecular weights) of the surface-active fractions was an important factor influencing the reciprocity of demulsifiers and surface-active fractions at the oil-water interface. This effect could be well explained by the difference between sizes of surface-active fraction molecules and vacancies between demulsifier molecules at the interface. The results of SDBS also proved this explanation.     

Transition metal complexes bearing 2,6-bis(imino)pyridyl: Synthesis,structure, ethylene polymerization/ oligomerization studies

A series of new complexes {2,6-bis[1-((2-methyl-4-methoxyphenyl)imino)ethyl]pyridine}Cl₂ [M=Fe(II) (2), Co(II) (3), Ni(II) (4), Cu(II) (5), Zn(II) (6)] have been synthesized. At 25°C, using 500 equiv of methylaluminoxane (MAO), the activities of Fe(II), Co(II) catalysts can reach 4.02 ×10⁶ g/mol-Fehatm for ethylene polymerization and 3.98×10⁵ g/mol-Cohatm for ethylene oligomerization. The effects of polymerization conditions such as reaction temperature, Al/M molar ratio and time on the activity of catalyst have been explored.     

Theoretical studies on vibrational spectra of some halides of Group IIB elements

The vibrational spectra of Group IIB elements halides MX2 and their dimers M2X4 (M=Zn(II), Cd(II) and Hg(II); X=F, Cl, Br and I) have been systematically investigated by ab initio RHF and B3LYP methods with LanL2MB, LanL2DZ and SDD basis sets. The optimized geometries, calculated vibrational frequencies are evaluated via comparison with the experimental data. The vibrational frequencies, calculated by these methods with different basis sets, are compared to each other too. The best results can be obtained by RHF/SDD method, with this method, the deviations for MX2 and Hg2X4 are <7%. Some vibrational frequencies of M2X4 that have not been experimentally reported are also predicted.     

On the complexity of following the central path of linear programs by linear extrapolation II

A class of algorithms is proposed for solving linear programming problems (withm inequality constraints) by following the central path using linear extrapolation with a special adaptive choice of steplengths. The latter is based on explicit results concerning the convergence behaviour of Newton's method to compute points on the central pathx(r), r>0, and this allows to estimate the complexity, i.e. the total numberN = N(R, ) of steps needed to go from an initial pointx(R) to a final pointx(), R>>0, by an integral of the local weighted curvature of the (primal—dual) path. Here, the central curve is parametrized with the logarithmic penalty parameterr0. It is shown that for large classes of problems the complexity integral, i.e. the number of stepsN, is not greater than constm log(R/), where < 1/2 e.g. = 1/4 or = 3/8 (note that = 1/2 gives the complexity of zero order methods). We also provide a lower bound for the complexity showing that for some problems the above estimation can hold only for 1/3.As a byproduct, many analytical and structural properties of the primal—dual central path are obtained: there are, for instance, close relations between the weighted curvature and the logarithmic derivatives of the slack variables; the dependence of these quantities on the parameterr is described. Also, related results hold for a family of weighted trajectories, into which the central path can be embedded.On leave from the Institute of Mathematics, Eötvös University Budapest, H-1080 Budapest, Hungary.