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

Role of the CipA Scaffoldin Protein in Cellulose Solubilization, as Determined by Targeted Gene Deletion and Complementation in Clostridium thermocellum

The CipA scaffoldin protein plays a key role in the Clostridium thermocellum cellulosome. Previous studies have revealed that mutants deficient in binding or solubilizing cellulose also exhibit reduced expression of CipA. To confirm that CipA is, in fact, necessary for rapid solubilization of crystalline cellulose, the gene was deleted from the chromosome using targeted gene deletion technologies. The CipA deletion mutant exhibited a 100-fold reduction in cellulose solubilization rate, although it was eventually able to solubilize 80% of the 5 g/liter cellulose initially present. The deletion mutant was complemented by a copy of cipA expressed from a replicating plasmid. In this strain, Avicelase activity was restored, although the rate was 2-fold lower than that in the wild type and the duration of the lag phase was increased. The cipA coding sequence is located at the beginning of a gene cluster containing several other genes thought to be responsible for the structural organization of the cellulosome, including olpB, orf2p, and olpA. Tandem mass spectrometry revealed a 10-fold reduction in the expression of olpB, which may explain the lower growth rate. This deletion experiment adds further evidence that CipA plays a key role in cellulose solubilization by C. thermocellum, and it raises interesting questions about the differential roles of the anchor scaffoldin proteins OlpB, Orf2p, and SdbA

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

Electronic interactions in fullerene spheres

The electron-phonon and Coulomb interactions inC$_{60}$, and larger fullerene spheres are analyzed. The coupling between electrons and intramolecular vibrations give corrections $\sim 1 - 10$ meV to the electronic energies for C$_{60}$, and scales as $R^{-4}$ in larger molecules. The energies associated with electrostatic interactions are of order $\sim 1 - 4$ eV, in C$_{60}$ and scale as $R^{-1}$. Charged fullerenes show enhanced electron-phonon coupling, $\sim 10$ meV, which scales as $R^{-2}$. Finally, it is argued that non only C$_{60}^{-}$, but also C$_{60}^{--}$ are highly polarizable molecules. The polarizabilities scale as $R^3$ and $R^4$, respectively. The role of this large polarizability in mediating intermolecular interactions is also discussed.Comment: 12 pages. No figure