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Environmental emissions dispersion modelling, principles and algorithms; cross-border CZ-PL course for master’s students

Štěpánek Vladimír, Kříž Jan, Hyšplerová Lidmila, Keder Josef, Ziembik Zbigniew, Lyčka Antonín

Chemistry-Didactics-Ecology-Metrology

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2022

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R. 27, NR 1-2

165--181

EN

Regular mathematical modelling of the dispersion of emissions from large sources is required by law in all EU countries. It is also used in risk analysis to predict releases of toxic substances from various technologies, from volcanic activity and possibly also terrorist acts. However, there is a shortage of experts in this very specific and demanding profession in the labour market in most EU countries. In a collaboration between academicians from neighbouring University of Hradec Králové and University of Opole and experts from important ecological companies of both regions we designed and verified as a part of a four-year pedagogical project supported by the EU a comprehensive education system in mathematical modelling of emission dispersion with exchange field trips and internships of students during cross-border Polish-Czech university education. The paper consists of two separate parts. The first part is focused on implementation of innovative lesson ”Principles, algorithms, and differences of environmental dispersion emissions models”, used on both sides of Polish-Czech border region. An example of the use of the educational package of the Gaussian plume model with PC Templates, who was modified in cooperation between teachers from both cross-border universities and experts from professional companies is presented here too. Our four-year experience with student motivational field trips to professional companies in both border regions and exchange one-month professional internships for interested students to two Czech professional companies, where students learn to work with to the Gaussian plume model and one Polish professional company, where students are introduced to the Gaussian puff model is also discussed. The following separate second part will be focused on the innovative lesson of multivariate statistical methods of environmental data analysis, which are required for processing materials for modern mathematical modelling of the dispersion of emissions in practice. The target users of this two-part innovative courses are students of the MSc degree in Physical Measurement and Modelling at the University of Hradec Králové and students of the MSc degree in environmental studies at the University of Opole. However, it is also open to other Czech and foreign students and professionals.

2

On the Consistency of k-means++ algorithm

Kłopotek Mieczysław A.

Fundamenta Informaticae

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2020

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Vol. 172, nr 4

361--377

EN

We prove in this paper that the expected value of the objective function of the k-means++ algorithm for samples converges to population expected value. As k-means++, for samples, provides with constant factor approximation for k-means objectives, such an approximation can be achieved for the population with increase of the sample size. This result is of potential practical relevance when one is considering using subsampling when clustering large data sets (large data bases).

3

Matematyczne podstawy techniki lotniczej

Krasoń E.

Zeszyty Naukowe / Wyższa Szkoła Oficerska Sił Powietrznych

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2003

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Nr 1

34--53

PL

Treścią artykułu jest analiza wybranych zagadnień z techniki lotniczej, takich jak: dynamika lotu samolotu, systemy sterowania lotem, nawigacja, optymalne projektowanie statków powietrznych, dokonana w celu wyodrębnienia pojęć i metod matematycznych, które służą ich opisowi teoretycznemu. W oparciu o ten materiał przedstawiony został wykaz treści programowych z matematyki, które powinny zostać ujęte w programie kształcenia słuchaczy WSOSP na poziomach: inżynierskim, magisterskim i podyplomowym.

4

Contextual probability

Wang H.

Journal of Telecommunications and Information Technology

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2003

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nr 3

92-97

EN

In this paper we present a new probability function G that generalizes the classical probability function. A mass function is an assignment of basic probability to some context (events, propositions). It represents the strength of support for some contexts in a domain. A context is a subset of the basic elements of interest in a domain - the frame of discernment. It is a medium to carry the "probabilistic" knowledge about a domain. The G function is defined in terms of a mass function under various contexts. G is shown to be a probability function satisfying the axioms of probability. Therefore G has all the properties attributed to a probability function. If the mass function is obtained from probability function by normalization, then G is shown to be a linear function of probability distribution and a linear function of probability. With this relationship we can estimate probability distribution from probabilistic knowledge carried in some contexts without any model assumption.

5

Basic mathematical relations of fluid dynamics for modified panel methods

Goraj Z., Pietrucha J.

Journal of Theoretical and Applied Mechanics

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1998

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nr 1

47-66

EN

Classical panel methods need some modifications in order to account for important features of real flow fields. The list of these features includes a wide spectrum of effects (appearing in many fluid dynamics problems), and their mathematical description is non-standard in some cases. Fundamental relationships and boundary conditions can have different, although equivalent forms. The paper presents foundation of potential flows and is prepared as a common foundation for any next papers devoted to the review of selected modified panel methods and their application to complex flow field calculations.

PL

Klasyczne metody panelowe wymagają pewnych modyfikacji, aby mogły uwzględniać ważne cechy przepływów rzeczywistych. Zbiór tych cech obejmuje szerokie widmo różnych efektów (pojawiających się w różnych zagadnieniach mechaniki płynów), a ich opis matematyczny jest w pewnych sytuacjach niestandardowy. Związki matematyczne i warunki brzegowe, zarówno na powierzchni bryły, jak i na śladzie wirowym i w nieskończoności, mogą mieć bardzo różne, choć równoważne formy. Praca omawia podstawy matemetyczne przepływów potencjalnych, zarówno ustalonych jak i nieustalonych. Oprócz sformułowania klasycznego z wykorzystaniem potencjału prędkości omawia również sformułowania niestandardowe, między innymi zastosowanie potencjału przyspieszeń. Jest napisana przy założeniu, że będzie stanowić podstawę opisu matematycznego dla innych prac z dziedziny metod panelowych, zarówno o charakterze przeglądowym jak i dla prac oryginalnych w zakresie zastosowań do obliczeń przepływów złożonych.