Labeling of organic biomolecules with ethynylferrocene

The Sonogashira coupling reaction of ethynylferrocene with adenine, uracil, tyrosine and steroid derivatives was studied; with the exception of tyrosine it was proved to be a good route for the attachment of ferrocene to these representative biomolecules. In addition the transformation of alkynyl uracil to furanopyrimidone derivatives was investigated and the formation of the furanopyrimidone ring was confirmed by an X-ray crystallographic analysis carried out on product 16.     

A variational principle for adaptive approximation of ordinary differential equations

Summary A variational principle, inspired by optimal control, yields a simple derivation of an error representation, global error=local errorweight, for general approximation of functions of solutions to ordinary differential equations. This error representation is then approximated by a sum of computable error indicators, to obtain a useful global error indicator for adaptive mesh refinements. A uniqueness formulation is provided for desirable error representations of adaptive algorithms. Mathematics Subject Classification (2000):65L70, 65G50This work has been supported by the EU–TMR project HCL # ERBFMRXCT960033, the EU–TMR grant # ERBFMRX-CT98-0234 (Viscosity Solutions and their Applications), the Swedish Science Foundation, UdelaR and UdeM in Uruguay, the Swedish Network for Applied Mathematics, the Parallel and Scientific Computing Institute (PSCI) and the Swedish National Board for Industrial and Technical Development (NUTEK).     

On the large time behavior of the heat kernels of quasiperiodic differential operators

We prove an analog of the Berry-Esseen estimate for the heat kernel of second order elliptic differential operators with quasiperiodic coefficients. As an application of this result, we prove the L^p boundedness of the associated Riesz transform operators.     

Extended UNIQUAC model for thermodynamic modeling of CO2 absorption in aqueous alkanolamine solutions

The extended UNIQUAC model [K. Thomsen, P. Rasmussen, Chem. Eng. Sci. 54 (1999) 1787–1802] was applied to the thermodynamic representation of carbon dioxide absorption in aqueous monoethanolamine (MEA), methyldiethanolamine (MDEA) and varied strength mixtures of the two alkanolamines (MEA–MDEA). For these systems, altogether 13 interaction model parameters are adjusted. Out of these parameters, 11 are temperature dependent.     

On a posterior evaluation of a simple greedy method for set packing

We consider an approach for ex post evaluation of approximate solutions obtained by a well known simple greedy method for set packing. A performance bound is derived that is a function of the highest average reward per item over subsets as well as the number of allocated subsets and ground items. This a posterior bound can enable much revelation of optimality when the solution is near optimal. One of the advantages of the ex post analysis is that it does not require computing the optimal solution to the LP relaxation. The ex post bound will not be guaranteed to reveal substantial levels of optimality for all problem instances but can be a useful tool that is complementary to other traditional methods for ex post evaluation for the set packing problem.     

Incompressible surfaces in handlebodies and isotopies

It is shown that every properly embedded incompressible surface in a handlebody can be constructed by a canonical gluing process. A simple condition is given which asserts that the result of the gluing process is an incompressible surface. A new notion of isotopy is introduced in order to distinguish surfaces belonging to distinct isotopy classes. Several examples (known and new) are constructed.     

Application of Complexity Theory to an Information Processing Model in Science Education

The current work examines the role of working-memory capacity in problem solving in science education. It treats an information-processing model with tools of complexity theory. Nonlinear methods are used to correlate the subjects' achievement scores with working-memory capacity. Data have been taken from the achievement scores in simple organic-synthesis chemical problems. The subjects (N = 319) were in grade twelve (age 17–18). Problems of various Z-demands (that is the number of steps needed to solve the problem) from two to eight were used. Rank-order sequences of the subjects, according to their scores, were generated, and each score was then replaced by the value of subject's working memory capacity measured by the digit backward span test. Then the sequences were mapped onto a one-dimensional random walk model and when treated as dynamic flows were found to possess fractal geometry with characteristics depending on the Z-demand of the problem. The findings were interpreted using concepts from complexity theory, such as correlation exponents, fractal dimensions and entropy. The null hypothesis was tested with surrogate data.     

Valuing Asian options using the finite element method and duality techniques

The main objective of this paper is to develop an adaptive finite element method for computation of the values, and different sensitivity measures, of the Asian option with both fixed and floating strike. The pricing is based on Black–Scholes PDE-model and a method developed by Ve?e? where the resulting PDEs are of parabolic type in one spatial dimension and can be applied to both continuous and discrete Asian options. We propose using an adaptive finite element method which is based on a posteriori estimates of the error in desired quantities, which we derive using duality techniques. The a posteriori error estimates are tested and verified, and are used to calculate optimal meshes for each type of option. The use of adapted meshes gives superior accuracy and performance with less degrees of freedom than using uniform meshes. The suggested adaptive finite element method is stable, gives fast and accurate results, and can be applied to other types of options as well.