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- Neuner, Christoph
(författare)
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Generalized Titchmarsh-Weyl functions and super singular perturbations
- 2015
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we study certain singular Sturm-Liouville differential expressions from an operator theoretic point of view.In particular we are interested in expressions that involve strongly singular potentials as introduced by Gesztesy and Zinchenko.On the ODE side, analyzing these expressions involves the so-called $m$-functions, often generalized Nevanlinna functions, who encapsulate spectral information of the underlying problem.The aim of the two papers in this thesis is to further understanding on the operator theory side.In the first paper, we use a model for super singular perturbations to describe a family of induced self-adjoint realizations of a perturbed Schr\"o\-din\-ger operator, i.e., with a potential of the form $c/x^2 + q$ where $q$ is a perturbation.Following the unperturbed example of Kurasov and Luger, we find that the so-called $Q$-function appearing in this approach is in good agreement with the above named $m$-function.Furthermore, we show that the operator model can be chosen such that $Q \equiv m$.In the second paper, we present a negative result in this area, namely that the supersingular perturbations model cannot be used for all strongly singular potentials.For a potential with a stronger singularity at the origin, namely $1/x^4$, we discuss the asymptotic behaviour of the Weyl solution at zero.It turns out that this function cannot be regularized appropriately and the operator model breaks down.
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- Rich, Rebecca L., et al.
(författare)
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A global benchmark study using affinity-based biosensors
- 2009
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Ingår i: Analytical Biochemistry. - : Elsevier BV. - 0003-2697 .- 1096-0309. ; 386:2, s. 194-216
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Tidskriftsartikel (refereegranskat)abstract
- To explore the variability in biosensor studies, 150 participants from 20 countries were given the same protein samples and asked to determine kinetic rate constants for the interaction. We chose a protein system that was amenable to analysis using different biosensor platforms as well as by users of different expertise levels. The two proteins (a 50-kDa Fab and a 60-kDa glutathione S-transferase [GST] antigen) form a relatively high-affinity complex, so participants needed to optimize several experimental parameters, including ligand immobilization and regeneration conditions as well as analyte concentrations and injection/dissociation times. Although most participants collected binding responses that could be fit to yield kinetic parameters, the quality of a few data sets could have been improved by optimizing the assay design. Once these outliers were removed, the average reported affinity across the remaining panel of participants was 620 pM with a standard deviation of 980 pM. These results demonstrate that when this biosensor assay was designed and executed appropriately, the reported rate constants were consistent, and independent of which protein was immobilized and which biosensor was used.
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