Moment Operators of Observables in Quantum Mechanics, with Applications to Quantization and Homodyne Detection

The questions studied in this thesis are centered around the moment operators of a quantum observable, the latter being represented by a normalized positive operator measure. The moment operators of an observable are physically relevant, in the sense that these operators give, as averages, the moments of the outcome statistics for the measurement of the observable. The main questions under consideration in this work arise from the fact that, unlike a projection valued observable of the von Neumann formulation, a general positive operator measure cannot be characterized by its first moment operator. The possibility of characterizing certain observables by also involving higher moment operators is investigated and utilized in three different cases: a characterization of projection valued measures among all the observables is given, a quantization scheme for unbounded classical variables using translation covariant phase space operator measures is presented, and, finally, a mathematically rigorous description is obtained for the measurements of rotated quadratures and phase space observables via the high amplitude limit in the balanced homodyne and eight-port homodyne detectors, respectively. In addition, the structure of the covariant phase space operator measures, which is essential for the above quantization, is analyzed in detail in the context of a (not necessarily unimodular) locally compact group as the phase space.

Fasilitoitua kommunikaatiota tutkittiin Jyväskylässä

Artikkelissa kerrotaan Jyväskylän yliopiston erityispedagogiikan laitoksella valmistuneesta Ulla Ojalammin ja Marjatta Leppäsen pro gradu -tutkielmasta "Fasilitointi - faktaa, fiktiota vai filunkia?, joka esittelee huolellisesti valmistellun kokeellisen tutkimuksen fasilitoidun kommunikaation toimivuudesta.

Effects of Dietary Fat Oxidation Products and Flavonols on Lipoprotein Oxidation

Various studies suggest that oxidative modifications of low density lipoprotein (LDL), and also other lipoproteins, have an important role in the development of atherosclerosis. In addition to the oxidation products formed endogenously, oxidised triacylglycerols (TAG) and oxysterols in the diet contribute to the oxidised lipoproteins found in circulation. However, studies on both the effect of oxidised dietary lipids on lipoprotein lipid oxidation and the reactions that modify oxidised fat after ingestion have been scarce. Studies on the effects of dietary antioxidants on the lipid oxidation in vivo and the risk of atherosclerosis have been inconclusive. More clinical trials are needed to test the importance of lipoprotein oxidation as a cardiovascular risk factor in humans. In the recent years, various methods have been optimised and applied to the analysis of lipid oxidation products in vivo, and information on the molecular structures of oxidised lipids in plasma, lipoproteins and atherosclerotic plaques has started to accumulate. However, specific structures of oxidised TAG molecules present in these tissues and lipoprotein fractions have not been investigated earlier. In the orginal research in this thesis, an approach based on highperformance liquid chromatographyelectrospray ionisationmass spectrometry (HPLCESIMS) and baseline diene conjugation (BDC) methods was used in order to investigate lipid oxidation level and oxidised TAG molecular structures in pig and human lipoproteins after dietary interventions. The approach was optimised with human LDL samples, which contained various oxidation products of TAG. LDL particles of hyperlipidaemic subjects contained an elevated amount of conjugated dienes. In the pig studies, several oxidised TAG structures with hydroxy, keto, epoxy or aldehydic groups were found in chylomicrons and VLDL after diets rich in sunflower seed oil. Also, the results showed that oxidised sunflower seed oil increased the oxidation of lipoprotein lipids and their TAG molecules. TAG hydroperoxides could be detected neither in the small intestinal mucosa of the pigs fed on the oxidised oil nor in their chylomicrons or VLDL.6 In the clinical studies, dietary flavonol aglycones extracted from sea buckthorn berries did not have an effect on lipoprotein lipid oxidation and other potential risk factors of atherosclerosis, but their absorption was demonstrated. Oil supplementation seemed to increase the bioavailability of the flavonols. Oxidised TAG molecules were detected in LDL particles of the subjects after both flavonol and control diets.