Counting decomposable multivariate polynomials

A polynomial f (multivariate over a field) is decomposable if f=g °h{f=g circ h} with g univariate of degree at least 2. We determine the dimension (over an algebraically closed field) of the set of decomposables, and an approximation to their number over a finite field. The relative error in our approximations is exponentially decaying in the input size.     

Diamantartige Kohlenstoffschichten steigern die Effizienz

Diamond‐like carbon thin films enhance efficiency — laser arc deposition of ta‐C Rising prices for fossil fuels as well as the increasing effects of the climate change due to the emission of greenhouse gases reveal the necessity of saving energy. Low friction coatings have an enormous potential in saving energy. Carbon based coatings — named as DLC coatings — are especially well suited for low friction coatings. In particular hydrogen‐free tetrahedral amorphous carbon (ta‐C) coatings are of great interest due to their extraordinary low wear properties. In addition they show excellent low friction properties and especially in combination with specific lubricants the so‐called super low friction effect. For the deposition of ta‐C coatings PVD methods have to be applied instead of CVD methods as it is the case for conventional DLC coatings. We have developed a deposition method which is based on a pulsed arc steered by a laser (Laser‐Arc). This allows us to use large cathodes resulting in a high long‐term stability. Furthermore, the carbon plasma source can be combined with a filtering unit removing almost all droplets and particles, which usually are characteristic for an arc process. The resulting Laser‐Arc source allows for the deposition of smooth and virtually defect‐free ta‐C coatings with a competitive deposition rate.     

Covalently Immobilized Regenerable Immunoaffinity Layer with Orientation-Controlled Antibodies Based on Z-Domain Autodisplay

A regenerable immunoaffinity layer comprising covalently immobilized orientation-controlled antibodies was developed for use in a surface plasmon resonance (SPR) biosensor. For antibody orientation control, antibody-binding Z-domain-autodisplaying Escherichia coli (E. coli) cells and their outer membrane (OM) were utilized, and a disuccinimidyl crosslinker was employed for covalent antibody binding. To fabricate the regenerable immunoaffinity layer, capture antibodies were bound to autodisplayed Z-domains, and then treated with the crosslinker for chemical fixation to the Z-domains. Various crosslinkers, namely disuccinimidyl glutarate (DSG), disuccinimidyl suberate (DSS) and poly (ethylene glycol)-ylated bis (sulfosuccinimidyl)suberate (BS(PEG)₅), were evaluated, and DSS at a concentration of 500 μM was confirmed to be optimal. The E. coli-cell-based regenerable HRP immunoassay was evaluated employing three sequential HRP treatment and regeneration steps. Then, the Oms of E. coli cells were isolated and layered on a microplate and regenerable OM-based HRP immunoassaying was evaluated. Five HRP immunoassays with four regeneration steps were found to be feasible. This regenerable, covalently immobilized, orientation-controlled OM-based immunoaffinity layer was applied to an SPR biosensor, which was capable of quantifying C-reactive protein (CRP). Five regeneration cycles were repeated using the demonstrated immunoaffinity layer with a signal difference of <10%.     

Pre-adolescent children exhibit lower aerosol particle volume emissions than adults for breathing,speaking, singing and shouting

Speaking and singing are activities linked to increased aerosol particle emissions from the respiratory system, dependent on the utilized vocal intensity. As a result, these activities have experienced considerable restrictions in enclosed spaces since the onset of the COVID-19 pandemic due to the risk of infection from the SARS-CoV-2 virus, transmitted by virus-carrying aerosols. These constraints have affected public education and extracurricular activities for children as well, from in-person music instruction to children’s choirs. However, existing risk assessments for children have been based on emission measurements of adults. To address this, we measured the particle emission rates of 15 pre-adolescent children, all eight to ten years old, with a laser particle counter for the test conditions: breathing at rest, speaking, singing and shouting. Compared with values taken from 15 adults, emission rates for breathing, speaking and singing were significantly lower for children. Particle emission rates were reduced by a factor of 4.3 across all conditions, whereas emitted particle volume rates were reduced by a factor of 4.8. These data can supplement SARS-CoV-2 risk management scenarios for various school and extracurricular settings.     

Site-Directed Immobilization of an Engineered Bone Morphogenetic Protein 2 (BMP2) Variant to Collagen-Based Microspheres Induces Bone Formation In Vivo

For the treatment of large bone defects, the commonly used technique of autologous bone grafting presents several drawbacks and limitations. With the discovery of the bone-inducing capabilities of bone morphogenetic protein 2 (BMP2), several delivery techniques were developed and translated to clinical applications. Implantation of scaffolds containing adsorbed BMP2 showed promising results. However, off-label use of this protein-scaffold combination caused severe complications due to an uncontrolled release of the growth factor, which has to be applied in supraphysiological doses in order to induce bone formation. Here, we propose an alternative strategy that focuses on the covalent immobilization of an engineered BMP2 variant to biocompatible scaffolds. The new BMP2 variant harbors an artificial amino acid with a specific functional group, allowing a site-directed covalent scaffold functionalization. The introduced artificial amino acid does not alter BMP2′s bioactivity in vitro. When applied in vivo, the covalently coupled BMP2 variant induces the formation of bone tissue characterized by a structurally different morphology compared to that induced by the same scaffold containing ab-/adsorbed wild-type BMP2. Our results clearly show that this innovative technique comprises translational potential for the development of novel osteoinductive materials, improving safety for patients and reducing costs.     

Zur Radikalischen Copolymerisation ungesättigter Isocyanate mit Vinylchlorid

On the Free Radical Copolymerization of Unsaturated Isocyanates with Vinylchloride The free radical copolymerization of vinyl-, isopropenyl- and p-vinyl-phenylisocyanate with vinylchloride in mass and tetrahydrofurane solution at 50°C is investigated. The incorporation of the isocyanate monomers in the copolymers is favoured. These monomers effect a great decrease of the rate of copolymerization and a crosslinking of the formed homo- and copolymers, whose extent depends on the kind and the quantity of the incorporated monomers. The crosslinking is caused by the forming of isocyanurate units.     

Radikalabfang. III [1] ESR-spektroskopische Untersuchung von Radikalreaktionen eines bicyclischen 1-Hydroxy-3-imidazolin-3-oxids [2]

Spin Trapping. III. Studies of Radical Reactions of a Bicyclic 1-Hydroxy-3-imidazoline-3-oxide Radical addition reactions to the nitrono group and the oxidation of the 8-hydroxy-1,4,5,7-tetramethyl-6,8-diazabicyclo[3.2.1]oct-6-en-6-oxide 2b were investigated by e.s.r.-spectroscopy. Oxidation of 2b by Ag₂O, PbO₂, hydrogenperoxide, tert.-butoxy and benzoyloxy radicals, respectively, yields a bicyclic nitroxide with typical a(N)-value (1,9 mT). Testing a wide range of carbon-centered radicals we did not find, however, any spin adducts in contrast to the literature. Only H-atoms are found to add to the nitrone function of 2b giving a bicyclic nitroxide 4b (R′ = H) with a(N)-value of 1,4 mT, a(H_ax) = 2,4 mT. The relationship between a ring-chain tautomerism of 2 as previously described and the formation of radicals has been demonstrated by radical reactions of derivatives of ring opened isomers 5b .