An elementary method of calculating an explicit form of Young measures in some special cases

We present an elementary method of explicit calculation of Young measures for certain class of functions. This class contains in particular functions of a highly oscillatory nature which appear in optimization problems and homogenization theory. In engineering such situation occurs for instance in nonlinear elasticity (solid-solid phase transition in certain elastic crystals). Young measures associated with oscillating minimizing sequences gather information about their oscillatory nature and therefore about underlying microstructure. The method presented in the paper makes no use of functional analytic tools. There is no need to use generalized version of the Riemann {Lebesgue lemma and to calculate weak* limits of functions. The main tool is the change of variable theorem. The method applies both to sequences of periodic and nonperiodic functions.Comment: 11 pages, no figures An article in its new version due to the reviewers' remarks. All the results stated and proved in multidimensional version; corrected innacuracie

Probability density of quantum expectation values

We consider the quantum expectation value \mathcal{A}=\ of an observable A over the state |\psi\> . We derive the exact probability distribution of \mathcal{A} seen as a random variable when |\psi\> varies over the set of all pure states equipped with the Haar-induced measure. The probability density is obtained with elementary means by computing its characteristic function, both for non-degenerate and degenerate observables. To illustrate our results we compare the exact predictions for few concrete examples with the concentration bounds obtained using Levy's lemma. Finally we comment on the relevance of the central limit theorem and draw some results on an alternative statistical mechanics based on the uniform measure on the energy shell.Comment: Substantial revision. References adde

Nonconvex minimization related to quadratic double-well energy - approximation by convex problemsenergy – approximation by convex problems

A double-well energy expressed as a minimum of two quadratic functions, called phase energies, is studied taking into account minimization of the corresponding integral functional. Such integral, as being not sequentially weakly lower semicontinuous, does not admit classical minimizers. To derive the relaxation formula for the infimum, the appropriate minimizing sequence is constructed. It consists of solutions of some approximating convex problems involving characteristic functions related to the phase energies. The weak limit of this sequence and the weak limit of the sequence of solutions of dual problems combined with the weak-star limits of the characteristic functions related to the phase energies allow to establish the final relaxation formula. It is also shown that infimum can be expressed by the Young measure associated with constructed minimizing sequence. An explicit form of Young measure in some regions of the involved domain is calculated

Analysis of optical properties of transparent insulation and impact on thermal performance

W pracy omówiono zagadnienia związane z charakterystykami optycznymi izolacji półprzezroczystej oraz przeprowadzono teoretyczną analizę jej wybranych parametrów. Wykorzystując zaawansowane modele numeryczne przeanali- zowano zestaw teoretycznych charakterystyk optycznych w celu znalezienia najlepszego rozwiązania dla warunków Polskich. Przyjętym kryterium wyboru była charakterystyka energetyczna warstwy izolacji i jej globalny bilans energetyczny, w szczególności zmienne strumienie zysków i strat ciepła przez warstwę materiału transparentnego.The properties of transparent plaster covering transparent insulation materials (TIM) were investigated using a whole building simulation program (ESP-r). The results of the initial analysis showed the desirable optical properties, estimated for sun incident angles on the fasade at a latitude of 52 degrees north. Then, simulations based on real climatic data for Poland were conducted to predict the thermal TIM wall behaviour. The influence of the structure on the diurnal heat storage potential was investigated for summer and winter

Remarks about discrete Young measures and their Monte Carlo simulation

This article is devoted to the problem of simulation of random variables distributed according to Young measures associated with piecewise affine functions determined on bounded intervals. We start with simple functions which can take on a finite number of different values with inverse images being the intervals or their unions. We present some formal results connected with related discrete Young measures and propose an algorithm for generating random variables having such distributions. Next, based on these results we introduce an algorithm designed for approximation of Young measures in various, more general situations. We also present an example where a Young measure associated with a piecewise affine function is approximated with the help of computer simulations. In this benchmarking problem the theoretical results are compared with the ones obtained in the Monte Carlo experiment

Safety of oversize cargo in road transport in Poland

W artykule omówione zostały zagadnienia związane z transportem ładunków ponadgabarytowych dostępnymi środkami transportu drogowego w Polsce, problemy które towarzyszą przewoźnikom podczas transportu i przygotowania takich ładunków, akty prawne regulujące ten rodzaj przewozów oraz sposoby zapewnienia bezpieczeństwa w trakcie przewozu ładunków ponadgabarytowych.The article discusses the issues related to the transport of oversized cargo by road transport in Poland, the problems that accompany during transport and preparation of such cargoes, legal acts regulating this type of transport and ways to ensure safety during transport oversized cargo

Computer simulator of relay interlocking system (type e) at railway station as a tool for teaching and professional training for traffic controllers

Proces przygotowania kadry do obsługi systemów sterowania ruchem kolejowym może być prowadzony przy zastosowaniu komputerowych symulatorów odwzorowujących funkcje rzeczywistych obiektów. Artykuł przedstawia taką możliwość w odniesieniu do przygotowania zawodowego dyżurnych ruchu. Dodatkową zaletą prezentowanego symulatora jest zlokalizowanie go w internecie, co umożliwia korzystającym z niego ćwiczenie funkcji obsługi pulpitu w dowolnym czasie i w dowolnym miejscu. Może to być również elementem e-learningu zawodowego dla dyżurnych ruchu.The process of staff training to handle the rail traffic control systems can be carried out using computer simulators imitating features of real objects. Such opportunity in regards to professional training for traffic controller has been presented in the article. An additional advantage of the presented simulator is its location in the internet. This location gives the users a chance to examine any function of desktop operation in any time and any place. It could also be an element of e-learning training for traffic controllers

Application of computer simulator for relay interlocking tools of train control system type E for teaching and professional training train dispatchers and some possibilities of its development

Artykuł przedstawia możliwe zastosowania prezentowanego symulatora prowadzenia ruchu kolejowego i obsługi przekaźnikowych urządzeń stacyjnych typu E. Największy nacisk położono na zastosowanie programu do szkolenia i doskonalenia zawodowego dyżurnych ruchu, którzy muszą nabywać umiejętności obsługi urządzeń tego typu. Zaproponowano również możliwości rozbudowy programu w celu lepszego jego dopasowania do warunków szkolenia, a także wskazano inne obszary, w których wykorzystać można symulator lub jego elementy.There are shown in the paper some possibilities of application of presented computer simulator for relay interlocking tools of train control system type E. The advantages in teaching and professional training of train dispatchers, who have to improve themselves skills at serving tools of such type have been emphasised. The possibilities of program development in order to its better adaptation to training conditions have been presented. In addition, the other areas, where the simulator could be applied, have been mentioned