Homology and cohomology theories on manifolds

We study generalized homology and cohomology theories on the category of manifolds. Ordinary (co-)homology including the cup product is characterized axiomatically

Exotic Spaces in Quantum Gravity I: Euclidean Quantum Gravity in Seven Dimensions

It is well known that in four or more dimensions, there exist exotic manifolds; manifolds that are homeomorphic but not diffeomorphic to each other. More precisely, exotic manifolds are the same topological manifold but have inequivalent differentiable structures. This situation is in contrast to the uniqueness of the differentiable structure on topological manifolds in one, two and three dimensions. As exotic manifolds are not diffeomorphic, one can argue that quantum amplitudes for gravity formulated as functional integrals should include a sum over not only physically distinct geometries and topologies but also inequivalent differentiable structures. But can the inclusion of exotic manifolds in such sums make a significant contribution to these quantum amplitudes? This paper will demonstrate that it will. Simply connected exotic Einstein manifolds with positive curvature exist in seven dimensions. Their metrics are found numerically; they are shown to have volumes of the same order of magnitude. Their contribution to the semiclassical evaluation of the partition function for Euclidean quantum gravity in seven dimensions is evaluated and found to be nontrivial. Consequently, inequivalent differentiable structures should be included in the formulation of sums over histories for quantum gravity.Comment: AmsTex, 23 pages 5 eps figures; replaced figures with ones which are hopefully viewable in pdf forma

Monitoring method for carbon nanotubes (CNT): Personal sampler and corresponding reading device

At present, CNT and other nanofiber materials in air can only be detected by deposition on a substrate and the use of off-line imaging analysis such as scanning electron microscopy. The majority of techniques suitable for the quasi- real-time measurement of engineered nanoparticles such as electrical low pressure impactor, condensation particle counter, optionally combined with a scanning mobility particle sizer (SMPS) can not distinguish between nanoparticles in general and airborne nanofibres in particular. In common workplace settings the considerable background of fine and ultrafine particles thus poses a challenge for these instruments. Furthermore, a true portability of the present devices is not given due to their size and power consumption. However, there is an urgent need due to the expected toxicity of nanofibres to control workplace environments with a robust and mobile device to ensure the safety of the working personnel as soon as possible. To meet these challenges, a suitable personal sampler together with a corresponding reading device is under development in the NANODEVICE-project, funded by the European Commission under grant agreement FP7-211464-2. A pre-prototype personal sampler for CNT sampling, the used Raman-spectroscopic inspection of deposited CNTs and a possible approach in determining the qualitative presence of CNTs will be shown. Additionally, it seems even possible to distinguish between carbon nanofibers from different manufacturers based on Raman spectroscopy and data analysis

Identification and quantification of carotenoids in pumpkin cultivars (Cucurbita maxima L.) and their juices by liquid chromatography with ultraviolet-diode array detection

The carotenoid pigments of different cultivars of Cucurbita maxima L. (pumpkin) were investigated in pulp, peel and genuine juice by means of HPLC. In dependence of the variety different concentrations and distributions of α-carotene, β-carotene, violaxanthin, neoxanthin, all-trans-lutein, zeaxanthin, lutheoxanthin and the isomers 9-cis-β-carotene and 13-cis-β-carotene were obtained. The total carotenoid content (expressed as dry weight) of the pumpkin peel depends on the variety with 12 mg/kg for „Butternut“ up to 1751 mg/kg for „Rouge“, whereas total carotenoid contents in the pulp differed from 17 mg/kg for „Baby Bear“ to 683 mg/kg for „Rouge“. The variety „Hokkaido“ showed high total carotenoid contents in pulp (218 mg/kg) and peel (1048 mg/kg), whereas for „Butternut“ minor concentrations in pulp (44 mg/kg) and peel (12 mg/kg) were detected. The red and orange coloured Cucurbita maxima L. varieties are valuable sources of carotenoids among vegetables or vegetable juices

Proposal of a population wide genome-based testing for Covid-19

Our lives (and deaths) have by now been dominated for two years by COVID-19, a pandemic that has caused hundreds of millions of disease cases, millions of deaths, trillions in economic costs, and major restrictions on our freedom. Here we suggest a novel tool for controlling the COVID-19 pandemic. The key element is a method for a population-scale PCR-based testing, applied on a systematic and repeated basis. For this we have developed a low cost, highly sensitive virus-genome-based test. Using Germany as an example, we demonstrate by using a mathematical model, how useful this strategy could have been in controlling the pandemic. We show using real-world examples how this might be implemented on a mass scale and discuss the feasibility of this approach

Contact structures on M × S2 {Mathematical expression}

We show that if a manifold {Mathematical expression} admits a contact structure, then so does {Mathematical expression}. Our proof relies on surgery theory, a theorem of Eliashberg on contact surgery and a theorem of Bourgeois showing that if {Mathematical expression} admits a contact structure then so does {Mathematical expression}. © 2013 Springer-Verlag Berlin Heidelberg

Manifolds with almost nonnegative curvature operator and principal bundles

We study manifolds with almost nonnegative curvature operator (ANCO) and provide first examples of closed simply connected ANCO mannifolds that do not admit nonnegative curvature operator