An approximation technique for robust nonlinear optimization

Nonlinear equality and inequality constrained optimization problems with uncertain parameters can be addressed by a robust worst-case formulation that is, however, difficult to treat computationally. In this paper we propose and investigate an approximate robust formulation that employs a linearization of the uncertainty set. In case of any norm bounded parameter uncertainty, this formulation leads to penalty terms employing the respective dual norm of first order derivatives of the constraints. The main advance of the paper is to present two sparsity preserving ways for efficient computation of these derivatives in the case of large scale problems, one similar to the forward mode, the other similar to the reverse mode of automatic differentiation. We show how to generalize the techniques to optimal control problems, and discuss how even infinite dimensional uncertainties can be treated efficiently. Finally, we present optimization results for an example from process engineering, a batch distillation.     

Preparation of Super Soft Granules from Nanosized Ceramic Powders by Spray Freezing

Owing to their extremely high specific surfaces and their high surface-to-volume ratios nanosized ceramic powders show a strong tendency to agglomeration and poor flowability. For improved properties of these powders during storage, transport and shaping a granulation step is necessary. However, the granules must be completely destroyed during dry pressing or redispersion; otherwise, the advantages of nanoparticles in comparison to conventional powders will not be realized. Spray freezing is a new granulation technique which combines the advantages of a conventional granulation by spray drying and a sublimation drying process. Different suspensions of nanosized oxide powders were rapidly frozen by spray freezing and subsequently dried by freeze drying. Thus, capillary forces can be excluded by this process. The achieved granulates show spheric granules with very low strength, improved flowability and increased bulk density. They were redispersible and can be destroyed under very low pressures.     

Electronic and chemical properties of supported Au nanoparticles

Oxidation and reduction behaviors of Au nanoparticles with different sizes on highly ordered pyrolytic graphite (HOPG) and silica were studied using X-ray photoelectron spectroscopy (XPS). For Au nanoparticles smaller than 6 nm in diameter, we found a novel oxygen species formed in Au nanoparticles, which is absent in larger particles and Au bulk crystals. This new oxygen species is attributed to the subsurface oxygen: for a complete understanding of the structures of catalytically active Au, the new oxygen species should be taken into account. In this context, it is worth mentioning that the subsurface oxygen species has been suggested to play an important role in heterogeneous catalysis. With decreasing Au particle size, a positive core level shift can be observed, which can be mostly attributed to the final state effects. Increase of the number of undercoordinated atoms with decreasing particle size is evidenced by a reduced splitting between 5d_3/2 and 5d_5/2 states and a band narrowing. Our results on electronic structures of Au nanoparticles on silica are compared to those on other substrates such as zirconia and titania to shed light onto the metal-support interactions.     

Elucidation of the CO‐Release Kinetics of CORM‐A1 by Means of Vibrational Spectroscopy

CO‐releasing molecules (CORMs) are developed for investigations of the interaction between the signaling molecule carbon monoxide (CO) and cells or tissue. Prior to their application these molecules must be fully characterized with respect to their CO‐release mechanism. One widely used CORM for biological application is sodium boranocarbonate (CORM‐A1), which shows pH‐dependent CO liberation. The complete reaction mechanism of CORM‐A1 is not fully understood yet. Therefore, in this contribution time‐resolved gas‐phase IR spectroscopy is used to monitor the headspace above decaying CORM‐A1 solutions at four different pH values (5.8 to 7.4). Borane carbonyl is found as an intermediate in the gas phase, which is formed during CORM degradation and further decays to CO. Concentration profiles of a pseudoconsecutive first‐order reaction are successfully fitted to specific band areas of the measured gas‐phase spectra, and the rate constants are obtained. The production of borane carbonyl is strongly pH dependent (half‐lives between 5 and 106 min), whereas the decay of borane carbonyl in the gas phase is nearly constant with a half‐life of about 33 min. The ratio of liberated CO molecules per CORM‐A1 is determined to be 0.91±0.09, and boric acid is identified as further end product.     

Polymer Capsules as a Theranostic Tool for a Universal In Vitro Screening Assay—The Case of Lysosomal Storage Diseases

Lysosomal storage disorders are rare genetic diseases characterized by a lysosomal enzyme deficiency. The defect leads to an accumulation of normally degraded substrates within the lysosomes. The accumulation of polymeric capsules inside the lysosomes is exploited to create a universal in vitro theranostic tool for lysosomal storage disorders. The diagnostic ability of this tool based on pH‐sensitive fluorophores is demonstrated by monitoring the lysosomal pH in Krabbe‐disease cell models upon accumulation of the substrate psychosine. Krabbe‐affected cells maintain their normal pH, while the lysosomes of their healthy counterparts undergo alkalinization, which can be correlated to toxicity. The potential of this tool for therapy based on enzymes inside the capsules is evaluated within the context of enzyme replacement therapy. Enzymatic degradation of the capsules inside the lysosome leads to release of the encapsulated active enzyme and the prevention of adverse effects of accumulated psychosine upon capsule‐based delivery of the functional enzyme is confirmed. In Fabry‐affected cells the intracellular enzymatic activity of the drug Replagal released from capsules shows the same kinetics as the free enzyme, which constitutes the current therapy, although the activity is smaller. Encapsulating Replagal nevertheless represents an alternative to receptor‐mediated endocytosis, overcoming limitations such as low or absent receptor expression.     

Diels-Alder reaction of 2-phosphaindolizines catalysed by organoaluminium reagent: theoretical and experimental results

Theoretical calculations at the DFT (B3LYP/6-31+G^**) level of the model Diels-Alder (DA) reactions of 1-methyl-3-(methoxycarbonyl)-2-phosphaindolizine with 1,3-butadiene in the presence of methylaluminium dichloride reveal that the co-ordination of organoaluminium reagent to the carbonyl oxygen increases the activation barrier compared to that for the uncomplexed 2-phosphaindolizine. On the other hand, co-ordination of the organoaluminium reagent to the σ², λ³ P atom lowers the activation barrier by ∼6 kcal mol⁻¹. 1-Methyl-2-phosphaindolizines having an electron-withdrawing group at the 3-position only undergo DA reaction with 2,3-dimethylbutadiene in the presence of the ethylaluminium dichloride catalyst in methylene chloride at a low temperature to afford [2+4] cycloadducts. The formation of an intermediate having the ethylaluminium reagent co-ordinated to σ², λ³ P atom has been detected by ³¹P NMR. The products have been characterized by ³¹P and ¹H NMR studies.