Sensitivity of trust-region algorithms to their parameters

In this paper, we examine the sensitivity of trust-region algorithms on the parameters related to the step acceptance and update of the trust region. We show, in the context of unconstrained programming, that the numerical efficiency of these algorithms can easily be improved by choosing appropriate parameters. Recommended ranges of values for these parameters are exhibited on the basis of extensive numerical tests. MSC classification: 65K05, 90C26, 90C30     

Entropy and irreversibility in a dilute gas of hard disks

The partition of the canonical entropy (invariant of motion) into a thermodynamic part 5th and a nonthermodynamic oneS _nonth, respectively increasing and decreasing functions of time for a system approaching equilibrium, was proposed by Prigogine and co-workers. This viewpoint is critically examined in the special case of an initially uncorrelated gas of hard disks. BothSth and the leading term ofS _nonth are evaluated for finite assemblies of 400,1600, and 6400 disks, by the method of molecular dynamics. There is good evidence that, in the limit of an infinite system, the Prigogine scheme is verified.On leave of absence from the University of Brussels, Belgium.     

Asymptotic behaviour of self-avoiding walks in continuous space

The asymptotic behaviour of self-avoiding walks that do not lie on a lattice has been investigated by a Monte-Carlo procedure. Its dependence on the fine structure of the walk is discussed.     

Molar extinction coefficients of some carbohydrates in aqueous solutions

Molar extinction coefficients of some carbohydrates viz. l-arabinose (C₅H₁₀O₅), d-glucose (C₆H₁₂O₆), d-mannose (C₆H₁₂O₆), d-galactose (C₆H₁₂O₆), d(-) fructose (C₆H₁₂O₆) and maltose (C₁₂H₂₄O₁₂) in aqueous solutions have been determined at 81, 356, 511, 662, 1173 and 1332 keV by gamma ray transmission method in a narrow beam good geometry set-up. These coefficients have been found to depend upon the photon energy following a 4-parameter polynomial. These extinction coefficients for different sugars having the same molecular formula have same values varying within experimental uncertainty. Within concentration ranges studied, Beer-Lambert law is obeyed very well.     

Easily grafted polyurethanes with reactive main chain functional groups. Synthesis,characterization, and antithrombogenicity of poly(ethylene glycol)-grafted poly(urethanes)

A novel synthesis of poly(ethylene glycol) (PEG)-grafted poly(urethanes) (PURs) is described based on a precursor PUR containing free amino groups in the main chain. Three different poly(urethane) backbones were prepared: a homopoly(urethane) comprised of N-Bocdiethanolamine (BDA) and 4,4′-methylenebis(phenyl isocyanate) (MDI), a copoly(urethane) (COPUR) consisting of BDA, N-benzyldiethanolamine and MDI, and a poly(urethane urea) (PUU) that was prepared from BDA, MDI, and ethylenediamine as the chain extender. The M_n of these poly(urethanes) ranged from 32,000 to 72,000 g/mol. PEG (750, 1,900, and 5,000 g/mol) was grafted onto the boc-deprotected poly(urethanes) via the chloroformate. Films of the polymers were spin cast from dilute solutions, annealed, and the surfaces analyzed by goniometry. Water contact angle data indicates increasing PEG surface coverage of the poly(urethanes) with increasing PEG molecular weight. Reorientation of the polymer films is evidenced by contact angle hysteresis. Polymer thrombogenicity, which was studied using blood perfusion experiments, shows that COPUR-g-PEG5000 and PUU-g-PEG5000 exhibit very little platelet adhesion. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 3441–3448, 1999     

A primal–dual regularized interior-point method for convex quadratic programs

Interior-point methods in augmented form for linear and convex quadratic programming require the solution of a sequence of symmetric indefinite linear systems which are used to derive search directions. Safeguards are typically required in order to handle free variables or rank-deficient Jacobians. We propose a consistent framework and accompanying theoretical justification for regularizing these linear systems. Our approach can be interpreted as a simultaneous proximal-point regularization of the primal and dual problems. The regularization is termedexact to emphasize that, although the problems are regularized, the algorithm recovers a solution of the original problem, for appropriate values of the regularization parameters.     

Micellar Nanocarriers Assembled from Doxorubicin‐Conjugated Amphiphilic Macromolecules (DOX–AM)

Amphiphilic macromolecules (AMs) have unique branched hydrophobic domains attached to linear PEG chains. AMs self‐assemble in aqueous solution to form micelles that are hydrolytically stable in physiological conditions (37 °C, pH 7.4) over 4 weeks. Evidence of AM biodegradability was demonstrated by complete AM degradation after 6 d in the presence of lipase. Doxorubicin (DOX) was chemically conjugated to AMs via a hydrazone linker to form DOX–AM conjugates that self‐assembled into micelles in aqueous solution. The conjugates were compared with DOX‐loaded AM micelles (i.e., physically loaded DOX) on DOX content, micellar sizes and in vitro cytotoxicity. Physically encapsulated DOX loading was higher (12 wt.‐%) than chemically bound DOX (6 wt.‐%), and micellar sizes of DOX‐loaded AMs (≈16 nm) were smaller than DOX–AMs (≈30 nm). In vitro DOX release from DOX–AM conjugates was faster at pH 5.0 (100%) compared to pH 7.4 (78%) after 48 h, 37 °C. Compared to free DOX and physically encapsulated DOX, chemically bound DOX had significantly higher cytotoxicity at 10^?7 M DOX dose against human hepatocellular carcinoma cells after 72 h. Overall, DOX–AM micelles showed promising characteristics as stable, biodegradable DOX nanocarriers.