Extreme Observables and Optimal Measurements in Quantum Theory

Optimization of quantum measurement processes has a pivotal role in carrying out better, more accurate or less disrupting, measurements and experiments on a quantum system. Especially, convex optimization, i.e., identifying the extreme points of the convex sets and subsets of quantum measuring devices plays an important part in quantum optimization since the typical figures of merit for measuring processes are affine functionals. In this thesis, we discuss results determining the extreme quantum devices and their relevance, e.g., in quantum-compatibility-related questions. Especially, we see that a compatible device pair where one device is extreme can be joined into a single apparatus essentially in a unique way. Moreover, we show that the question whether a pair of quantum observables can be measured jointly can often be formulated in a weaker form when some of the observables involved are extreme. Another major line of research treated in this thesis deals with convex analysis of special restricted quantum device sets, covariance structures or, in particular, generalized imprimitivity systems. Some results on the structure ofcovariant observables and instruments are listed as well as results identifying the extreme points of covariance structures in quantum theory. As a special case study, not published anywhere before, we study the structure of Euclidean-covariant localization observables for spin-0-particles. We also discuss the general form of Weyl-covariant phase-space instruments. Finally, certain optimality measures originating from convex geometry are introduced for quantum devices, namely, boundariness measuring how ‘close’ to the algebraic boundary of the device set a quantum apparatus is and the robustness of incompatibility quantifying the level of incompatibility for a quantum device pair by measuring the highest amount of noise the pair tolerates without becoming compatible. Boundariness is further associated to minimum-error discrimination of quantum devices, and robustness of incompatibility is shown to behave monotonically under certain compatibility-non-decreasing operations. Moreover, the value of robustness of incompatibility is given for a few special device pairs.

Explaining the intention to play and behavior of playing sports betting games of young Finnish adults : an application of the theory of planned behavior

The aim of this Master’s Thesis was to examine the determinants of intention and behavior of playing sports betting games in order to explain the intention to play in a more precise way and to be able to understand the behavior of playing. The theory of planned behavior was applied in explaining the intention of young Finnish adults aged 18 to 34. A quantitative research method was applied and an online survey was sent to the students of Lappeenranta University of Technology and to the subscribers of Urheilulehti in order to reach a sample that present the young population of Finland. The theory of the study focused on the theory of planned behavior and its antecedents, attitude towards behavior, subjective norms, perceived behavioral control as well as motivation. By analyzing the data, causal relationships were found through which the explanation of intention was possible. The results showed that attitude towards playing, subjective norms, perceived behavioral control and motivation impact the formation of intention significantly. The results also indicated that intention impacts significantly to the playing frequency.

[Förteckning öfver böcker, som komma att å auction försäljas]

Nimeke luetteloijan sepittämä.

Förteckning öfver aflidne professoren Gabr. Palanders boksamling, som genom öppen auction försäljes i Åbo d. 16 martii 1822, uti gården n:o 44 i Klösterqvarteret

Julkaisuvuosi nimekkeestä.

Förteckning öfver framledne mathematum professoren Joh. Fredr. Ahlstedts boksamling, som kommer att genom offentlig auction försäljas i Åbo den [ ] mars 1825

Sivu 33 on virheellisesti sivu 29.

Förteckning öfver framlidne rådmannen M. Renbergs efterlemnade boksamling, samt åtskilliga andra böcker, som komma att, genom offentelig auction försäljas uti gården n:o 9 i Klöster qvarteret af Åbo stad 4 junii 1825 kl. 3 efter middagen

Julkaisuvuosi nimekkeestä.

Förteckning öfver framlidne studeranden Axel Gabriel Gestrins boksamling, som genom auction kommer att försäljas i Helsingfors, den [ ] april 1832

S. [3]: Ofvannämnde böcker måga å auction försäljas. Helsingfors 9.5.1831. A. F. Wasenius.

Förteckn[ing] öfver rectoren mag. Nils Kynzells boksamling, som genom offentlig auction kommer att försäljas i Åbo den 7 maji 1831

S. 8: Ofvanstående böcker få försäljas [ ]. Helsingfors, 29.3.1831. J. M. af Tengström.

Förteckning öfver framlidne kapellanen David Johan Wegelii efterlemnade boksamling, som, efter skeende kungörelse, kommer att försäljas å offentlig auction i Åbo

S. 7: Ofvanförtecknade böcker, skrifter och tidningar måga å offentlig auktion försäljas. Helsingfors 14.9.1831. A. J. Wasenius.