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Limitierungsverfahren von Reihen mehrdimensionaler Kugelfunktionen und deren Saturationsverhalten
(1968)
Die vorliegende Arbeit untersucht das approximationstheoretische Verhalten von Summationsprozessen von Reihen von Kugelfunktionen, sogenannten Laplace-Reihen. Zunächst wird die Theorie der besten Approximation auf der Kugel, also die Erweiterung der Sätze von D. Jackson und S. Bernstein, skizziert. Nimmt man nun spezielle Verfahren zur Summation von Laplace-Reihen, dann lassen sich auch hier Sätze vom Jacksonschen und Bernsteinschen Typ beweisen. Darüber hinaus zeigen viele Verfahren ein Saturationsverhalten, d.h. es gibt eine nur vom Verfahren abhängige optimale Approximationsordnung. Das Saturationsproblem besteht nun darin, diejenige Klasse von Funktionen (Saturationsklasse) zu bestimmen, welche genau von der optimalen Ordnung approximiert werden.
This paper develops a new finite element method (FEM)-based upper bound algorithm for limit and shakedown analysis of hardening structures by a direct plasticity method. The hardening model is a simple two-surface model of plasticity with a fixed bounding surface. The initial yield surface can translate inside the bounding surface, and it is bounded by one of the two equivalent conditions: (1) it always stays inside the bounding surface or (2) its centre cannot move outside the back-stress surface. The algorithm gives an effective tool to analyze the problems with a very high number of degree of freedom. Our numerical results are very close to the analytical solutions and numerical solutions in literature.
Image reconstruction analysis for positron emission tomography with heterostructured scintillators
(2022)
The concept of structure engineering has been proposed for exploring the next generation of radiation detectors with improved performance. A TOF-PET geometry with heterostructured scintillators with a pixel size of 3.0×3.1×15 mm3 was simulated using Monte Carlo. The heterostructures consisted of alternating layers of BGO as a dense material with high stopping power and plastic (EJ232) as a fast light emitter. The detector time resolution was calculated as a function of the deposited and shared energy in both materials on an event-by-event basis. While sensitivity was reduced to 32% for 100 μm thick plastic layers and 52% for 50 μm, the CTR distribution improved to 204±49 ps and 220±41 ps respectively, compared to 276 ps that we considered for bulk BGO. The complex distribution of timing resolutions was accounted for in the reconstruction. We divided the events into three groups based on their CTR and modeled them with different Gaussian TOF kernels. On a NEMA IQ phantom, the heterostructures had better contrast recovery in early iterations. On the other hand, BGO achieved a better contrast to noise ratio (CNR) after the 15th iteration due to the higher sensitivity. The developed simulation and reconstruction methods constitute new tools for evaluating different detector designs with complex time responses.
This paper investigates the interior transmission problem for homogeneous media via eigenvalue trajectories parameterized by the magnitude of the refractive index. In the case that the scatterer is the unit disk, we prove that there is a one-to-one correspondence between complex-valued interior transmission eigenvalue trajectories and Dirichlet eigenvalues of the Laplacian which turn out to be exactly the trajectorial limit points as the refractive index tends to infinity. For general simply-connected scatterers in two or three dimensions, a corresponding relation is still open, but further theoretical results and numerical studies indicate a similar connection.
In this paper, methods of sample preparation for potentiometric measurement of phenylalanine are presented. Basing on the spectrophotometric measurements of phenylalanine, the concentrations of reagents of the enzymatic reaction (10 mM L-Phe, 0,4 mM NAD+, 2U L-PheDH) were determined. Then, the absorption spectrum of the reaction product, NADH, was monitored (maximum peak at 340 nm). The results obtained by the spectrophotometric method were compared with the results obtained by the colourimetry, using pH indicators. The above-mentioned two methods will be used as references for potentiometric measurements of phenylalanine concentration.
In this paper, methods of surface modification of different supports, i.e. glass and polymeric beads for enzyme immobilisation are described. The developed method of enzyme immobilisation is based on Schiff’s base formation between the amino groups on the enzyme surface and the aldehyde groups on the chemically modified surface of the supports. The surface of silicon modified by APTS and GOPS with immobilised enzyme was characterised by atomic force microscopy (AFM), time-of-flight secondary ion mass spectroscopy (ToF-SIMS) and infrared spectroscopy (FTIR). The supports with immobilised enzyme (urease) were also tested in combination with microreactors fabricated in silicon and Perspex, operating in a flow-through system. For microreactors filled with urease immobilised on glass beads (Sigma) and on polymeric beads (PAN), a very high and stable signal (pH change) was obtained. The developed method of urease immobilisation can be stated to be very effective.
An enzyme-based multi-parameter biosensor is developed for monitoring the concentration of formate, d-lactate, and l-lactate in biological samples. The sensor is based on the specific dehydrogenation by an oxidized β-nicotinamide adenine dinucleotide (NAD+)-dependent dehydrogenase (formate dehydrogenase, d-lactic dehydrogenase, and l-lactic dehydrogenase, respectively) in combination with a diaphorase from Clostridium kluyveri (EC 1.8.1.4). The enzymes are immobilized on a platinum working electrode by cross-linking with glutaraldehyde (GA). The principle of the determination scheme in case of l-lactate is as follows: l-lactic dehydrogenase (l-LDH) converts l-lactate into pyruvate by reaction with NAD+. In the presence of hexacyanoferrate(III), the resulting reduced β-nicotinamide adenine dinucleotide (NADH) is then regenerated enzymatically by diaphorase. The electrochemical detection is based on the current generated by oxidation of hexacyanoferrate(II) at an applied potential of +0.3 V vs. an Ag/AgCl reference electrode. The biosensor will be electrochemically characterized in terms of linear working range and sensitivity. Additionally, the successful practical application of the sensor is demonstrated in an extract from maize silage.