Sufficient Stochastic Maximum Principle for the Optimal Control of Jump Diffusions and Applications to Finance

We give a verification theorem by employing Arrow's generalization of the Mangasarian sufficient condition to a general jump diffusion setting and show the connections of adjoint processes to dynamic programming. The result is applied to financial optimization problems.     

Synthese und Struktur von γ-Halogenpropyl-octa(silasesquioxanen)

Synthesis and Structures of γ-Halopropyl-octa(silasesquioxanes) As a more rapid and versatile synthetic approach, we have studied the FeCl₃-catalyzed hydrolytic polycondensation of suited trichlorosilanes in a biphasic system which yields e.g. the new octa(silasesquioxane) (BrCH₂CH₂CH₂)₈Si₈O₁₂.     

Dirichlet forms,quasiregular functions and Brownian motion

Summary Given a quasiregular function on an open setU in ⁿ it is shown that there exists a diffusionX _t inU such that mapsX _t inton-dimensional Brownian motion. The process is constructed from a Dirichlet form which can be described explicitly. This enables us to apply stochastic methods in the investigation of quasiregular mappings. Some examples of applications are given, including boundary behaviour and value distribution.     

Optimisation and robustness analysis of a hydrophobic interaction chromatography step

Process development, optimisation and robustness analysis for chromatography separations are often entirely based on experimental work and generic knowledge. The present study proposes a method of gaining process knowledge and assisting in the robustness analysis and optimisation of a hydrophobic interaction chromatography step using a model-based approach. Factorial experimental design is common practice in industry today for robustness analysis. The method presented in this study can be used to find the critical parameter variations and serve as a basis for reducing the experimental work. In addition, the calibrated model obtained with this approach is used to find the optimal operating conditions for the chromatography column. The methodology consists of three consecutive steps. Firstly, screening experiments are performed using a factorial design. Secondly, a kinetic-dispersive model is calibrated using gradient elution and column load experiments. Finally, the model is used to find optimal operating conditions and a robustness analysis is conducted at the optimal point. The process studied in this work is the separation of polyclonal IgG from BSA using hydrophobic interaction chromatography.     

The relationship between the chemical structure of nematic liquid crystals and their pretilt angles

About 50 different additives in one or more of three different nematic mixtures have been investigated to clarify the relationship between the chemical structure of the liquid crystal and the pretilt angle on a polyimide surface. The pretilts found for cells have been explained within our recently proposed population distribution model. For compounds with cyano-groups at one end, we find that the in-plane order is governed both by the surface-mesogen interaction and by the relative strength of the intermolecular interactions in the nematic phase. This strength is nearly linear in alkyl chain length for the compounds investigated. Changes in the strength due to variations in the core of the molecules can be calculated easily by using group contributions from the known Parachors. The in-plane order can be treated as a simple product of the contributions from the liquid crystal and from the polyimide. Different polar end groups will give different angles between the surface and the optical axis of the individual mesogens in the first monolayer. The cyano-group gives the highest angle and alkyl groups the lowest. For nitro-compounds the dimers formed are so strongly bound that they do not break up at the surface. Nitro-compounds will thus act as dialkyl compounds. For dialkyl compounds the pretilt angles are dominated by the difference between the chain lengths at the two ends of the molecule.     

Matrix-assisted laser desorption/ionization mass spectrometry with additives to 2,5-dihydroxybenzoic acid

Selected benzoic acid derivatives and related substances were used as additives to 2,5-dihydroxybenzoic acid (2,5DHB) and the performance of the mixtures in matrix-assisted laser desorption/ionization mass spectrometry was investigated. Using benzoic acid derivatives substituted at position 2 and/or 5 or related substances as a co-matrix in the 1–10% range with 2,5DHB results in improved ion yields and signal-to-noise ratio of analyte molecules, especially for the high-mass range. The enhanced performance is prominent for 2-hydroxy-5-methoxybenzoic acid and exists for both proteins and oligosaccharides. It is suggested that the improvement is caused by a disorder in the 2,5DHB crystal lattice allowing ‘softer’ desorption. Charge transfer from matrix ions to additive molecules at the expense of analyte ionization gives a simple explanation for the deteriorating effects of some tested additives.