Kriterien erster und zweiter Ordnung für lokal beste Approximationen bei Problemen mit Nebenbedingungen

In a previous paper [6] we considered the problem of approximating (in the Chebyshev-norm) a real-valued functionf(x) on a compact subsetX<ℝm,m≥1, by an element of a set of functionsa(p, x),p∈P,P<ℝn an open set. Both necessary and sufficient conditions of the second order for ana(p0,x) to be a locally best approximation were derived. In this paper we generalize these results to problems where the setP of admitted parameters is constrained by some inequality. Included are subjects as monotone, one-sided or restricted range approximation

Kriterien zweiter Ordnung für lokal beste Approximationen

Consider the problem of approximating (in the Chebyshev-norm) a real-valued functionf(x) on a compact subsetX of ℝm,m≧1, by an element of a set of functionsa(p, x), p∈P,P⊆ ℝn an open set. Both necessary and sufficient conditions of the second order for ana(p0,x) to be a locally best approximation are derived. Apart from conditions on the differentiability off anda, onX, and on the error functionf(x)−a(p0,x) we impose no restrictions on the problem. This makes the results applicable to a broad class of problems

Measuring the quantum efficiency of single radiating dipoles using a scanning mirror

Using scanning probe techniques, we show the controlled manipulation of the radiation from single dipoles. In one experiment we study the modification of the fluorescence lifetime of a single molecular dipole in front of a movable silver mirror. A second experiment demonstrates the changing plasmon spectrum of a gold nanoparticle in front of a dielectric mirror. Comparison of our data with theoretical models allows determination of the quantum efficiency of each radiating dipole.Comment: 4 pages, 4 figure

Primary stability of a press-fit cup in combination with impaction grafting in an acetabular defect model

The objectives of this study were to (a) assess primary stability of a press-fit cup in a simplified acetabular defect model, filled with compacted cancellous bone chips, and (b) to compare the results with primary stability of a press-fit cup combined with two different types of bone graft substitute in the same defect model. A previously developed acetabular test model made of polyurethane foam was used, in which a mainly medial contained defect was implemented. Three test groups (N = 6 each) were prepared: Cancellous bone chips (bone chips), tricalciumphosphate tetrapods + collagen matrix (tetrapods + coll), bioactive glass S53P4 + polyethylene glycol-glycerol matrix (b.a.glass + PEG). Each material was compacted into the acetabulum and a press-fit cup was implanted. The specimens were loaded dynamically in the direction of the maximum resultant force during level walking. Relative motion between cup and test model was assessed with an optical measurement system. At the last load step (3000 N), inducible displacement was highest for bone chips with median [25th percentile; 75th percentile] value of 113 [110; 114] µm and lowest for b.a.glass + PEG with 91 [89; 93] µm. Migration at this load step was highest for b.a.glass + PEG with 868 [845; 936] µm and lowest for tetrapods + coll with 491 [487; 497] µm. The results show a comparable behavior under load of tetrapods + coll and bone chips and suggest that tetrapods + coll could be an attractive alternative to bone chips. However, so far, this was found for one specific defect type and primary stability should be further investigated in additional/more severe defects

Transcriptomic and proteomic insights into innate immunity and adaptations to a symbiotic lifestyle in the gutless marine worm Olavius algarvensis

Background: The gutless marine worm Olavius algarvensis has a completely reduced digestive and excretory system, and lives in an obligate nutritional symbiosis with bacterial symbionts. While considerable knowledge has been gained of the symbionts, the host has remained largely unstudied. Here, we generated transcriptomes and proteomes of O. algarvensis to better understand how this annelid worm gains nutrition from its symbionts, how it adapted physiologically to a symbiotic lifestyle, and how its innate immune system recognizes and responds to its symbiotic microbiota. Results: Key adaptations to the symbiosis include (i) the expression of gut-specific digestive enzymes despite the absence of a gut, most likely for the digestion of symbionts in the host's epidermal cells; (ii) a modified hemoglobin that may bind hydrogen sulfide produced by two of the worm's symbionts; and (iii) the expression of a very abundant protein for oxygen storage, hemerythrin, that could provide oxygen to the symbionts and the host under anoxic conditions. Additionally, we identified a large repertoire of proteins involved in interactions between the worm's innate immune system and its symbiotic microbiota, such as peptidoglycan recognition proteins, lectins, fibrinogen-related proteins, Toll and scavenger receptors, and antimicrobial proteins. Conclusions: We show how this worm, over the course of evolutionary time, has modified widely-used proteins and changed their expression patterns in adaptation to its symbiotic lifestyle and describe expressed components of the innate immune system in a marine oligochaete. Our results provide further support for the recent realization that animals have evolved within the context of their associations with microbes and that their adaptive responses to symbiotic microbiota have led to biological innovations

Coculture with hemicellulose-fermenting microbes reverses inhibition of corn fiber solubilization by Clostridium thermocellum at elevated solids loadings

Background: The cellulolytic thermophile Clostridium thermocellum is an important biocatalyst due to its ability to solubilize lignocellulosic feedstocks without the need for pretreatment or exogenous enzyme addition. At low concentrations of substrate, C. thermocellum can solubilize corn fiber \u3e 95% in 5 days, but solubilization declines markedly at substrate concentrations higher than 20 g/L. This differs for model cellulose like Avicel, on which the maximum solubilization rate increases in proportion to substrate concentration. The goal of this study was to examine fermentation at increasing corn fiber concentrations and investigate possible reasons for declining performance. Results: The rate of growth of C. thermocellum on corn fiber, inferred from CipA scaffoldin levels measured by LC–MS/MS, showed very little increase with increasing solids loading. To test for inhibition, we evaluated the effects of spent broth on growth and cellulase activity. The liquids remaining after corn fiber fermentation were found to be strongly inhibitory to growth on cellobiose, a substrate that does not require cellulose hydrolysis. Additionally, the hydrolytic activity of C. thermocellum cellulase was also reduced to less-than half by adding spent broth. Noting that \u3e 15 g/L hemicellulose oligosaccharides accumulated in the spent broth of a 40 g/L corn fiber fermentation, we tested the effect of various model carbohydrates on growth on cellobiose and Avicel. Some compounds like xylooligosaccharides caused a decline in cellulolytic activity and a reduction in the maximum solubilization rate on Avicel. However, there were no relevant model compounds that could replicate the strong inhibition by spent broth on C. thermocellum growth on cellobiose. Cocultures of C. thermocellum with hemicellulose-consuming partners—Herbinix spp. strain LL1355 and Thermoanaerobacterium thermosaccharolyticum—exhibited lower levels of unfermented hemicellulose hydrolysis products, a doubling of the maximum solubilization rate, and final solubilization increased from 67 to 93%. Conclusions: This study documents inhibition of C. thermocellum with increasing corn fiber concentration and demonstrates inhibition of cellulase activity by xylooligosaccharides, but further work is needed to understand why growth on cellobiose was inhibited by corn fiber fermentation broth. Our results support the importance of hemicellulose-utilizing coculture partners to augment C. thermocellum in the fermentation of lignocellulosic feedstocks at high solids loading