Wybrane aspekty funkcjonowania Sejmu w latach 1997–2007

Praca recenzowana / peer-reviewed paperPraca naukowa finansowana ze środków na naukę w latach 2006–2008 jako projekt badawczy własny Nr 1 H02E 052 3

Purification of large volume of liquid argon for LEGEND-200

The design, construction and performance of the system capable of purifying 65m$^{3}$ of liquid argon to sub-ppm level designed for LEGEND–200 experiment is presented. The quality of the purified liquid argon is monitored in real-time during the purification process, by measuring the argon triplet state lifetime and simultaneous direct measurements of the concentrations of impurities such as water, oxygen, and nitrogen with a sensitivity of 0.1 ppm. The achieved argon triplet lifetime value measured inside the LEGEND cryostat, when filled in 70% of its capacity, was at the level of $\tau_{3}$ = 1.3 μs. If needed, the system may also be used later to purify liquid argon already filled into the LEGEND cryostat in the loop mode

Relative and discrete utility maximising entropy

The notion of utility maximising entropy (u-entropy) of a probability density, which was introduced and studied by Slomczynski and Zastawniak (Ann. Prob 32 (2004) 2261-2285, arXiv:math.PR/0410115 v1), is extended in two directions. First, the relative u-entropy of two probability measures in arbitrary probability spaces is defined. Then, specialising to discrete probability spaces, we also introduce the absolute u-entropy of a probability measure. Both notions are based on the idea, borrowed from mathematical finance, of maximising the expected utility of the terminal wealth of an investor. Moreover, u-entropy is also relevant in thermodynamics, as it can replace the standard Boltzmann-Shannon entropy in the Second Law. If the utility function is logarithmic or isoelastic (a power function), then the well-known notions of the Boltzmann-Shannon and Renyi relative entropy are recovered. We establish the principal properties of relative and discrete u-entropy and discuss the links with several related approaches in the literature.Comment: 19 page