Lifespan Theorem for simple constrained surface diffusion flows

We consider closed immersed hypersurfaces in R³ and R⁴ evolving by a special class of constrained surface diffusion flows. This class of constrained flows includes the classical surface diffusion flow. In this paper we present a Lifespan Theorem for these flows, which gives a positive lower bound on the time for which a smooth solution exists, and a small upper bound on the total curvature during this time. The hypothesis of the theorem is that the surface is not already singular in terms of concentration of curvature. This turns out to be a deep property of the initial manifold, as the lower bound on maximal time obtained depends precisely upon the concentration of curvature of the initial manifold in L² for M² immersed in R³ and additionally on the concentration in L³ for M³ immersed in R⁴. This is stronger than a previous result on a different class of constrained surface diffusion flows, as here we obtain an improved lower bound on maximal time, a better estimate during this period, and eliminate any assumption on the area of the evolving hypersurface.     

Under-three minute PCR: probing the limits of fast amplification

Nucleic acid amplification is enormously useful to the biotechnology and clinical diagnostic communities; however, to date point-of-use PCR has been hindered by thermal cycling architectures and protocols that do not allow for near-instantaneous results. In this work we demonstrate PCR amplification of synthetic SARS respiratory pathogenic targets and bacterial genomic DNA in less than three minutes in a hardware configuration utilizing convenient sample loading and disposal. Instead of sample miniaturization techniques, near-instantaneous heating and cooling of 5 μL reaction volumes is enabled by convective heat transfer of a thermal fluid through porous media combined with an integrated electrical heater. This method of rapid heat transfer has enabled 30 cycles of PCR amplification to be completed in as little as two minutes and eighteen seconds. Surprisingly, multiple enzymes have been shown to work at these breakthrough speeds on our system. A tool for measuring enzyme kinetics now exists and can allow polymerase optimization through directed evolution studies. Pairing this instrument technology with modified polymerases should result in a new paradigm for high-throughput, ultra-fast PCR and will hopefully improve our ability to quickly respond to the next viral pandemic.     

Photopatterning poly(p-phenylenevinylene) from xanthate precursor polymers

A simple, direct method for photopatterning poly(p-phenylenevinylene) (PPV) from a xanthate precursor polymer is presented. The effect of UV exposure on the resultant PPV is examined by UV-Vis, XPS, FTIR, and DC conductivity measurements. By optimizing the photolithographic conditions, a spatial resolution of one micron is obtained, with minimal impact to the properties of the photopatterned PPV.     

Zur Bestimmung von Zinn in Bronzen

Ohne Zusammenfassung     

Zum Nachweis der Lignozellulosen

Ohne Zusammenfassung     

Quantitative Bestimmung des Stickstoffs

Ohne Zusammenfassung