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José A. Iglesias Martin Rumpf Otmar Scherzer 《Foundations of Computational Mathematics》2018,18(4):891-927
A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane energy measuring the rate of tangential distortion when deforming the reference shell into the template shell, and a bending energy measuring the bending under the deformation in terms of the change of the shape operators from the undeformed into the deformed configuration. The variational method applies to surfaces described as level sets. It is mathematically well-posed, and an existence proof of an optimal matching deformation is given. The variational model is implemented using a finite element discretization combined with a narrow band approach on an efficient hierarchical grid structure. For the optimization, a regularized nonlinear conjugate gradient scheme and a cascadic multilevel strategy are used. The features of the proposed approach are studied for synthetic test cases and a collection of geometry processing examples. 相似文献
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Wolfgang G. Kreyling Pratim Biswas Maria E. Messing Neil Gibson Marianne Geiser Alexander Wenk Manoranjan Sahu Knut Deppert Izabela Cydzik Christoph Wigge Otmar Schmid Manuela Semmler-Behnke 《Journal of nanoparticle research》2011,13(2):511-524
The intensive use of nano-sized titanium dioxide (TiO2) particles in many different applications necessitates studies on their risk assessment as there are still open questions on their safe handling and utilization. For reliable risk assessment, the interaction of TiO2 nanoparticles (NP) with biological systems ideally needs to be investigated using physico-chemically uniform and well-characterized NP. In this article, we describe the reproducible production of TiO2 NP aerosols using spark ignition technology. Because currently no data are available on inhaled NP in the 10?C50 nm diameter range, the emphasis was to generate NP as small as 20 nm for inhalation studies in rodents. For anticipated in vivo dosimetry analyses, TiO2 NP were radiolabeled with 48V by proton irradiation of the titanium electrodes of the spark generator. The dissolution rate of the 48V label was about 1% within the first day. The highly concentrated, polydisperse TiO2 NP aerosol (3?C6 × 106 cm?3) proved to be constant over several hours in terms of its count median mobility diameter, its geometric standard deviation, and number concentration. Extensive characterization of NP chemical composition, physical structure, morphology, and specific surface area was performed. The originally generated amorphous TiO2 NP were converted into crystalline anatase TiO2 NP by thermal annealing at 950 °C. Both crystalline and amorphous 20-nm TiO2 NP were chain agglomerated/aggregated, consisting of primary particles in the range of 5 nm. Disintegration of the deposited TiO2 NP in lung tissue was not detectable within 24 h. 相似文献
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Pure anomers of either α or β 3-(2-deoxyribofuranosyl)propynoates reacted with the tetramethylcyclobutadiene–aluminum trichloride complex to yield the corresponding diastereoisomeric Dewar benzenes. Thermal- or ultraviolet light–initiated rearrangement gave rise to highly substituted C-aryldeoxyribosides as single anomers. The same compounds as well as other substituted deoxyribosides were obtained also by transition metal–mediated cycloaddition reactions. 相似文献
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Christoph Seger Thomas Pacher Harald Greger Ekarin Saifah Otmar Hofer 《Monatshefte für Chemie / Chemical Monthly》2002,191(4):97-100
The bisamide aglairubine was isolated from different Aglaia species. The original structure was revised on the basis of FDMS and 2D-NMR data. Since all isolates were obtained from species belonging to the section Amoora of the genus Aglaia, aglairubine might serve as a taxonomic marker. 相似文献
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We investigate several versions of a cardinal characteristic defined by Frankiewicz. Vojtáš showed , and Blass showed . We show that all the versions coincide and that is greater than or equal to the splitting number. We prove the consistency of and of .
Received: 2 October 1996 / Revised version: 22 May 1997 相似文献
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We continue [21] and study partition numbers of partial orderings which are related to (ω)/fin. In particular, we investigate Pf, be the suborder of ((ω)/fin)ω containing only filtered elements, the Mathias partial order M, and (ω), (ω)ω the lattice of (infinite) partitions of ω, respectively. We show that Solomon's inequality holds for M and that it consistently fails for Pf. We show that the partition number of (ω) is C. We also show that consistently the distributivity number of (ω)ω is smaller than the distributivity number of (ω)/fin. We also investigate partitions of a Polish space into closed sets. We show that such a partition either is countable or has size at least D, where D is the dominating number. We also show that the existence of a dominating family of size 1 does not imply that a Polish space can be partitioned into 1 many closed sets. 相似文献