FIXED POINTS AND COUPLED FIXED POINTS FOR INCREASING OPERATORS WITH APPLICMIONS TO DIFFERENTIAL INCLUSIONS IN BANACH SPACES

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Some results from 50 years' research on surface forces

A review is presented about research on surface forces and surface interactions conducted over the past half-century, with some emphasis on the pioneering contributions of the Department of Surface Phenomena at the Institute of Physical Chemistry of the USSR Academy of Sciences.     

Hamiltonian circle actions on symplectic manifolds and the signature

Let M be a symplectic manifold with a Hamiltonian circle action with isolated fixed points. We prove that σ (M) = b₀(M) − b₂(M) + b₄(M) − b₆(M) + … where σ (M) is the signature of M and b_i(M) is the ith Betti number of M.     

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

The effects of polymerization temperature, polymerization time, ethylene and hydrogen concentration, and effect of comonomers (hexene‐1, propylene) on the activity of supported catalyst of composition LFeCl₂/MgCl₂‐Al(i‐Bu)₃ (L = 2,6‐bis[1‐(2,6‐dimethylphenylimino)ethyl] pyridyl) and polymer characteristics (molecular weight (MW), molecular‐weight distribution (MWD), molecular structure) have been studied. Effective activation energy of ethylene polymerization over LFeCl₂/MgCl₂‐Al(i‐Bu)₃ has a value typical of supported Ziegler–Natta catalysts (11.9 kcal/mol). The polymerization reaction is of the first order with respect to monomer at the ethylene concentration >0.2 mol/L. Addition of small amounts of hydrogen (9–17%) significantly increases the activity; however, further increase in hydrogen concentration decreases the activity. The IRS and DSC analysis of PE indicates that catalyst LFeCl₂/MgCl₂‐Al(i‐Bu)₃ has a very low copolymerizing ability toward propylene and hexene‐1. MW and MWD of PE produced over these catalysts depend on the polymerization time, ethylene and hexene‐1 concentration. The activation effect of hydrogen and other kinetic features of ethylene polymerization over supported catalysts based on the Fe (II) complexes are discussed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5057–5066, 2007     

Two differential equation systems for equality-constrained optimization

This paper presents two differential systems, involving first and second order derivatives of problem functions, respectively, for solving equality-constrained optimization problems. Local minimizers to the optimization problems are proved to be asymptotically stable equilibrium points of the two differential systems. First, the Euler discrete schemes with constant stepsizes for the two differential systems are presented and their convergence theorems are demonstrated. Second, we construct algorithms in which directions are computed by these two systems and the stepsizes are generated by Armijo line search to solve the original equality-constrained optimization problem. The constructed algorithms and the Runge–Kutta method are employed to solve the Euler discrete schemes and the differential equation systems, respectively. We prove that the discrete scheme based on the differential equation system with the second order information has the locally quadratic convergence rate under the local Lipschitz condition. The numerical results given here show that Runge–Kutta method has better stability and higher precision and the numerical method based on the differential equation system with the second information is faster than the other one.     

Differential Conditions for Constrained Nonlinear Programming via Pareto Optimization

We deal with the differential conditions for local optimality. The conditions that we derive for inequality constrained problems do not require constraint qualifications and are the broadest conditions based on only first-order and second-order derivatives. A similar result is proved for equality constrained problems, although the necessary conditions require the regularity of the equality constraints.     

Perturbed recurrence relations II the general case

In this paper, we give some new explicit relations between two families of polynomials defined by recurrence relations of all order. These relations allow us to analyze, even in the Sobolev case, how some properties of a family of orthogonal polynomials are affected when the coefficients of the recurrence relation and the order are perturbed. In a paper we have already given a method which allows us to study the polynomials defined by a three-term recurrence relation. Also here some generalizations are given.     

Heat of adsorption and density distribution in slit pores with defective walls: GCMC simulation studies and comparison with experimental data

The adsorption behavior (capacity, density distribution and packing density) and the isosteric heat versus loading in a slit pore whose walls contain defective graphene layers are investigated in this paper. The defective wall is characterized by the extent and size of the defect. Simulation results obtained with the Grand Canonical Monte Carlo method reveal complex patterns of isosteric heat, and this complex behavior is a result of the interplay between three factors: (i) the surface heterogeneity (solid-fluid interaction, sites with varying degree of affinity), (ii) fluid-fluid interaction and (iii) the overlapping of potentials exerted by the two defective walls. We illustrate this with argon adsorption in pores of various sizes, and results obtained from the simulation agree qualitatively with the experimental data at 77 K on Saran microporous S600H and micro-mesoporous S84 charcoals of Beebe et al. [R.A. Beebe, B. Millard, J. Cynarski, J. Am. Chem. Soc. 75 (1953) 839]. The S600H was found to contain pores predominantly in the neighborhood of 7 Å with 30% of defect and a defective size of 2.84 Å. This is consistent with the argument made by Beebe et al. that this sample is a microporous solid and most pores can accommodate only one layer. The other sample, S84, has larger pores than S600H, and it is found that it has a wider pore size distribution and the pore width is centered at about 12 Å.     

Excess enthalpy of ternary mixture for diamine+heptane+cyclohexan

The excess molar enthalpy of ternary mixture for 3-diethylaminopropylamine+heptane+cyclohexane were measured using a Calvet microcalorimeter at 303.15 K. Empirical equations, Redlich-Kister, Tsao-Smith, and Kohler and group contribution models, UNIFAC (modified version) and DISQUAC have been applied. A reasonable representation of ternary data is obtained. This revised version was published online in August 2006 with corrections to the Cover Date.