Exact Scaling Functions for One-Dimensional Stationary KPZ Growth

We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a Riemann–Hilbert problem related to the Painlevé II equation. We solve these equations numerically with very high precision and compare our, up to numerical rounding exact, result with the prediction of Colaiori and Moore⁽¹⁾ obtained from the mode coupling approximation.     

Total synthesis of (±) maculalactone A, maculalactone B and maculalactone C and the determination of the absolute configuration of natural (+) maculalactone A by asymmetric synthesis

Maculalactones A, B and C from the marine cyanobacterium Kyrtuthrix maculans are amongst the only compounds based on the tribenzylbutyrolactone skeleton known in nature and (+) maculalactone A from the natural source possesses significant biological activity against various marine herbivores and marine settlers. We now report a concise synthesis of racemic maculalactone A in five steps from inexpensive starting materials. Maculalactones B and C were synthesized by a minor modification to this procedure, and the synthetic design also permitted an asymmetric synthesis of maculalactone A to be achieved in around 85% ee. The (+) and (−) enantiomers of maculalactone A were assigned, respectively, to the S and R configurations on the basis of the chiral selectivity expected for catecholborane reduction of an unsymmetrical ketone in the presence of Corey's oxazoborolidine catalyst. Surprisingly, it appeared that natural (+) maculalactone A was biosynthesized in K. maculans in a partially racemic form, comprising ca. 90-95% of the (S) enantiomer and 5-10% of its (R) enantiomer. Coincidentally therefore, the percentage enantiomeric excess of the product obtained from asymmetric synthesis almost exactly matched that found in nature.     

A Variable Neighborhood Search for the Multi Depot Vehicle Routing Problem with Time Windows

The aim of this paper is to propose an algorithm based on the philosophy of the Variable Neighborhood Search (VNS) to solve Multi Depot Vehicle Routing Problems with Time Windows. The paper has two main contributions. First, from a technical point of view, it presents the first application of a VNS for this problem and several design issues of VNS algorithms are discussed. Second, from a problem oriented point of view the computational results show that the approach is competitive with an existing Tabu Search algorithm with respect to both solution quality and computation times.     

Applying Cognition-Based Assessment to Elementary School Students' Development of Understanding of Area and Volume Measurement

As part of a discussion of cognition-based assessment (CBA) for elementary school mathematics, I describe assessment tasks for area and volume measurement and a research-based conceptual framework for interpreting students' reasoning on these tasks. At the core of this conceptual framework is the notion of levels of sophistication. I provide details on an integrated set of levels for area and volume measurement that (a) starts with the informal, preinstructional reasoning typically possessed by students, (b) ends with the formal mathematical concepts targeted by instruction, and (c) indicates cognitive plateaus reached by students in moving from (a) to (b).     

Capacity Constrained Transit Assignment with Common Lines

This paper proposes the use of absorbing Markov chains to solve the capacity constrained transit network loading problem taking common lines into account. The approach handles congested transit networks, where some passengers will not be able to board because of the absence of sufficient space. The model also handles the common lines problem, where choice of route depends on frequency of arrivals. The mathematical formulation of the problem is presented together with a numerical example. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of maltodextrins on the surface activity of small-molecule surfactants

We report on the effect of commercially important polysaccharides (maltodextrins with variable dextrose equivalent (Paselli SA-2, MD-6 and MD-10) on the surface activity at the air–water interface of small-molecule surfactants (sms), possessing different hydrophobic–lipophilic balance ((SSL (Na⁺), the main component is a sodium salt of stearol–lactoyl lactic acid, and PGE (080), polyglycerol ester of C18 fatty acid), and widely used in food products. A marked change of the surface activity of sms was found in the presence of maltodextrins by tensiometry. The combined data of laser multiangle light scattering and mixing calorimetry have suggested that this result is governed by specific complex formation between maltodextrins and sms in aqueous medium. Measurements have been made of the molar mass, the second virial coefficient and the enthalpy of intermolecular interactions in aqueous solutions. The implication of a degree of polymerization of maltodextrins in this phenomenon was shown. The interrelation between the molecular parameters of the formed complexes and their surface activity at the air–water interface has been revealed and discussed.