Density functional study for the polymerization of ethylene monomer using a new nickel catalyst

The present computational study was designed to study the polymerization of ethylene catalyzed by a new Ni‐based PymNox organometallic compound. Recently, we have synthesized and tested the behavior of this type of catalyst in olefin polymerization. It has been experimentally observed that the unsubstituted catalyst Ni2 (aldimino PymNox catalyst ) is less active than the methyl substituted Ni1 (acetaldimino PymNox catalyst ) analogue. The reactivity of both catalysts was examined using density functional theory (DFT) models. Our results indicate that the methyl substituted Ni1 introduces some additional steric hindrance that probably renders a more suitable catalyst conformation for the monomer incorporation. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1160–1165, 2010     

Gamma coloration of mixed crystals of KCl–KBr doped with Pb

The amount of the first stage coloration in KCl_1−xBr_x doped with Pb²⁺ has been investigated as a function of the dose rate and impurity concentration. For a dose rate of 12.88 kGy/h, the F color center production was independent of the quantity of Pb²⁺, and varied according to the ratio KCl/KBr. At a proportion of 50% of each halogen the typical stages were observed. However, if the dose rate is less than 3.22 kGy/h, the coloration production depends on the quantity of Pb²⁺.     

Inclusion-exclusion complexes for pseudodisk collections

Let B be a finite pseudodisk collection in the plane. By the principle of inclusion—exclusion, the area or any other measure of the union is We show the existence of a two-dimensional abstract simplicial complex, , so the above relation holds even if is substituted for 2 ^B . In addition, can be embedded in R ² so its underlying space is homotopy equivalent to , and the frontier of is isomorphic to the nerve of the set of boundary contributions. Received March 6, 1995, and in revised form December 16, 1995.     

Asymptotic stability analysis in uncertain multi-delayed state neural networks via Lyapunov–Krasovskii theory

This paper presents a new approach to the analysis of asymptotic stability of artificial neural networks (ANN) with multiple time-varying delays subject to polytope-bounded uncertainties. This approach is based on the Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique with the use of a recent Leibniz–Newton model based transformation without including any additional dynamics.Three examples with numerical simulations are used to illustrate the effectiveness of the proposed method. The first example considers the neural network with multiple time-varying delays, which may be seen as a particular case of the second example where it is subject to uncertainties and multiple time-varying delays. Finally, the third example analyzes the stability of the neural network with higher numbers of neurons subject to a single time-delay. The Hopf bifurcation theory is used to verify the stability of the system when the origin falls into instability in the bifurcation point.     

Solitary waves of the EW and RLW equations

Eight finite difference methods are employed to study the solitary waves of the equal-width (EW) and regularized long–wave (RLW) equations. The methods include second-order accurate (in space) implicit and linearly implicit techniques, a three-point, fourth-order accurate, compact operator algorithm, an exponential method based on the local integration of linear, second-order ordinary differential equations, and first- and second-order accurate temporal discretizations. It is shown that the compact operator method with a Crank–Nicolson discretization is more accurate than the other seven techniques as assessed for the three invariants of the EW and RLW equations and the L₂-norm errors when the exact solution is available. It is also shown that the use of Gaussian initial conditions may result in the formation of either positive or negative secondary solitary waves for the EW equation and the formation of positive solitary waves with or without oscillating tails for the RLW equation depending on the amplitude and width of the Gaussian initial conditions. In either case, it is shown that the creation of the secondary wave may be preceded by a steepening and an narrowing of the initial condition. The creation of a secondary wave is reported to also occur in the dissipative RLW equation, whereas the effects of dissipation in the EW equation are characterized by a decrease in amplitude, an increase of the width and a curving of the trajectory of the solitary wave. The collision and divergence of solitary waves of the EW and RLW equations are also considered in terms of the wave amplitude and the invariants of these equations.     

Thermal Stability of Sol-Gel Hydrotalcites

Sol-Gel Hydrotalcites were synthesized using magnesium ethoxide and variable aluminum sources: aluminum acetilacetonate, aluminum chloride, aluminum nitrate and aluminum sulfate; in all cases, the gelation was done at pH 10. X-ray diffraction studies show that the crystallinity depends on the aluminum precursor used. The crystallinity was found in the order aluminum acetylcetonate>aluminum chloride>aluminum nitrate>aluminum sulfate. The precursor determines the sintering behavior as well.     

The effects of fluctuating body forces on annular liquid jets

Summary The nonlinear dynamics of axisymmetric, inviscid, incompressible, thin, annular liquid jets subjected to fluctuating body forces is studied numerically by means of an adaptive finite difference method which maps the time-dependent, curvilinear geometry of the jet into a unit square. The fluctuating body forces may arise from fluctuations in the gravitational acceleration in inertial frames or from the acceleration of a non-inertial frame of reference which translates parallelly to an inertial one. It is shown that both the pressure coefficient and the axial location at which the annular jet becomes a solid one are periodic functions of time with a period equal to that of the imposed body force fluctuations, and that their magnitude increases as the amplitude of the body force fluctuations is increased. It has also been shown that, for both intermittent, sinusoidal or rectangular excitations, increases in the frequency of the excitation result in the creation of superharmonics, broad, albeit peaked, spectra, and closed phase planes with many loops.The research reported in this paper was supported by Project PB91-0767 from the D.G.I.C.Y.T. of Spain.     

Homotopical linking and Morse index estimates in min-max theorems

The authors extend some well-known Morse estimates for critical points of saddle point type to some linking conditions recently considered in the literature. Applications are given for multiplicity results in PDE and existence of subharmonic solutions for a class of conservative ODE. Research supported by Program STRIDE (contract STRDA/C/CEN/531/92) and EC (contract ERBCHRXCT940555).