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1

Wątpliwości dotyczące modelowania matematycznego filtracji pospiesznej wody

Dąbrowski Wojciech

Instal

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2023

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nr 12

113--116

PL

Opisano metody matematycznego modelowania filtracji pospiesznej wody zwracając szczególną uwagę na rozbieżności w poglądach dotyczących zjawisk towarzyszących filtracji wgłębnej zawiesin wodnych. Opisano te wątpliwości, które zostały wyjaśnione i w jaki sposób je rozstrzygnięto. Chociaż żadna z metod nie okazała się efektywna w modelowaniu filtracji zawiesiny poddanej koagulacji, a więc nie znalazła bezpośredniego zastosowania w technologii wody, to jednak każda z nich, w różnym stopniu, pozwoliła lepiej zrozumieć ten proces.

EN

Methods of mathematical modelling of rapid water filtration are described, paying particular attention to the divergences in views on the phenomena accompanying the depth filtration of water suspensions. These doubts were described and clarified. It was also described how they were resolved. Although none of the methods proved to be effective in modelling the filtration of coagulated suspensions, and thus did not find direct application to water technology, each of them provided a better understanding of the process to varying degrees.

2

Persistent Stochastic Non-Interference

Hillston Jane, Marin Andrea, Piazza Carla, Rossi Sabina

Fundamenta Informaticae

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2021

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Vol. 181, nr 1

1--35

EN

In this paper, we study an information flow security property for systems specified as terms of a quantitative Markovian process algebra, namely the Performance Evaluation Process Algebra (PEPA). We propose a quantitative extension of the Non-Interference property used to secure systems from the functional point view by assuming that the observers are able to measure also the timing properties of the system, e.g., the response time of certain actions or its throughput. We introduce the notion of Persistent Stochastic Non-Interference (PSNI) based on the idea that every state reachable by a process satisfies a basic Stochastic Non-Interference (SNI) property. The structural operational semantics of PEPA allows us to give two characterizations of PSNI : one based on a bisimulation-like equivalence relation inducing a lumping on the underlying Markov chain, and another one based on unwinding conditions which demand properties of individual actions. These two different characterizations naturally lead to efficient methods for the verification and construction of secure systems. A decision algorithm for PSNI is presented and an application of PSNI to a queueing system is discussed.

3

Prediction of the road pavement condition index using stochastic models

Batrakova Angelika G., Troyanovsky Vladimir V., Batrakov Dmitry O., Pilicheva Maryna O., Skrypnyk Nataliia S.

Roads and Bridges - Drogi i Mosty

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2020

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Vol. 19, no. 3

225--242

EN

Mathematical models for prediction of road network condition based on the so-called Markov chains are presented in this article. The data for calculation of elements of the transition matrix from one condition to another are taken from visual evaluation as well as from instrumental reading. It is recommended to prepare data sets in the form of pavement management system data tables based on a representative sample of measuring sections. Discrete time intervals – of one year – are used when constructing the model of transition matrices. The procedure of forming Markov transition matrix with partially complete data sets is proposed also in paper. The basis of this procedure is information on the previous condition of the structure and the results of the instrumental evaluation, which enables correction of the predicted values. The final matrix takes into account not only the probability, but also the speed of transition from one condition to another. It is also possible to work with the initial data using appropriate databases or other software.

PL

W artykule omówiono modele matematyczne prognozowania stanu sieci drogowej z zastosowaniem tzw. łańcuchów Markowa. Dane do obliczeń elementów macierzy przejścia pomiędzy stanami są uzyskiwane na podstawie oceny wizualnej oraz w wyniku pomiarów instrumentalnych. Zalecane jest przygotowanie zestawów danych w postaci tablic systemu zarządzania stanem nawierzchni drogowej sporządzanych na podstawie reprezentatywnej próby odcinków pomiarowych. Macierze przejścia pomiędzy stanami są tworzone w przedziałach czasu o długości jednego roku. W artykule przedstawiono także procedurę tworzenia macierzy przejścia na podstawie częściowo niepełnych zestawów danych, w których wykorzystano informacje o wcześniejszym stanie nawierzchni oraz wyniki pomiarów instrumentalnych, pozwalających na skorygowanie prognozowanych wartości. Uzyskana ostatecznie macierz uwzględnia nie tylko prawdopodobieństwo, lecz również prędkość przejścia pomiędzy stanami. Ponadto możliwe jest także przetwarzanie danych wejściowych z odpowiednich baz lub ich wykorzystanie przy zastosowaniu innego oprogramowania.

4

Elaboration of occupational risks evaluation models considering the dynamics of impact of harmful factors

Bochkovskyi A. P.

Journal of Achievements in Materials and Manufacturing Engineering

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2020

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Vol. 102, nr 2

76--85

EN

Purpose: Elaborate and substantiate stochastic models of occupational risk evaluation for application in the occupation health and safety. Design/methodology/approach: Analysis of scientific and technical literature and regulatory framework for risk evaluation in the occupation health and safety; methods of probability theory, theory of Markov processes; methods of restoration theory. Findings: A system of differential equations and limit conditions for finding the limit distribution of probabilities of a random process of occupational dangers is derived. Based on the results of solving the limit value task, expressions to determine a number of key indicators by which the level of occupational risk can be evaluated are obtained. Research limitations/implications: The proposed approach aims to evaluation the risk associated with the impact on the employee of harmful factors, but can also be used to evaluate the injury risk. But in this case the received limit value task will be much more difficult. Practical implications: The application of the proposed approach allows to increase the level of occupational safety by taking into account the stochastic characteristics of the negative factors impact on the employee during occupational risks evaluating, as well as the possibility of setting such values of controllable parameters that will allow with a certain probability to ensure not to exceed the level of impact accumulation in the employee of the consequences of these factors. Originality/value: Stochastic models of occupational risk evaluation based on the application of Markov drift processes for the modeling the hybrid nature of the negative factors impact on the employee, which occurs within the real systems "man - technical system - production environment" were elaborated and substantiated for the first time.

5

Elements of Method Improvement of Flood Zones Determination

Kryzhovets Tetiana

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

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2020

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Vol. 9, No 1

25--29

EN

The article suggests a possible application of mathematical modeling zones and flooding characteristics that will improve the methodological basis in hydrological calculations and forecasting will provide opportunities for a better understanding of the complex mechanisms of formation flow. The computational scheme is applicable for vertically homogeneous flow conditions extending from steep river flows to tidal influenced estuaries. The system has been used in numerous engineering studies.

6

Review of stochastic differential equations in statistical arbitrage pairs trading

Endres Sylvia

Managerial Economics

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2019

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Vol. 20, no. 2

71--118

EN

The use of stochastic differential equations offers great advantages for statistical arbitrage pairs trading. In particular, it allows the selection of pairs with desirable properties, e.g., strong mean-reversion, and it renders traditional rules of thumb for trading unnecessary. This study provides an exhaustive survey dedicated to this field by systematically classifying the large body of literature and revealing potential gaps in research. From a total of more than 80 relevant references, five main strands of stochastic spread models are identified, covering the ‘Ornstein–Uhlenbeck model’, ‘extended Ornstein–Uhlenbeck models’, ‘advanced mean-reverting diffusion models’, ‘diffusion models with a non-stationary component’, and ‘other models’. Along these five main categories of stochastic models, we shed light on the underlying mathematics, hereby revealing advantages and limitations for pairs trading. Based on this, the works of each category are further surveyed along the employed statistical arbitrage frameworks, i.e., analytic and dynamic programming approaches. Finally, the main findings are summarized and promising directions for future research are indicated.

7

Stochastic Models of Electromagnetic Vacuum in Resonance Phenomena

Cong N. H., Thanh T. D., Hoang T. N.

Computational Methods in Science and Technology

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2010

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Vol. spec. iss. (2)

53-60

EN

In this article, we both presented the concept of coherent and squeezed stochastic vacuum and simultaneously specified the way to calculate resonant fluorescent spectrum in two- or three-level system with configuration Ë in the presence of squeezed stochastic vacuum. The effects that occurred in the presence of squeezed stochastic vacuum were the change of both the width and the height of central spectrum and of additional narrow peaks. The impacts of squeezed vacuum on fluorescence spectrum represent the dependence on the squeezed parameter of both amplitude and phase. In the absence of unsqueezed vacuum, fluorescent spectrum returns to normal Mollow spectral type.

8

Modele stochastyczne zanieczyszczeń powietrza w aglomeracjach przemysłowych

Tumidajski T., Foszcz D., Niedoba T., Siewior J.

Rocznik Ochrona Środowiska

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2009

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Tom 11

543-554

EN

The Upper Silesian Industrial Region (GOP) is one of the most polluted regions in Poland. Because of the location of several important heavy industrial plants it is necessary to permanently monitor the various sort of dust and gas pollutantsconcentrations in this area. The paper presents the possibilities of stochastic air pollution modeling on the basis of data collected by monitoring stations. Several types of models were shown, including models applied in regions of big cities, like Stockholm, Vienna and Madrid, with special impact to so-called adaptive models. It was statistically proved that the formulae of the SO2 propagation model for the GOP S(t)=a+bS(t-1)+c(T-T0)2+d(v-v0)2+eQ1=eQ2. This equation was applied practically on the basis of the empirical data collected by selected monitoring stations.For the chosen monitoring station the directions of pollution flows and winds wereshown graphically (fig. 1). Nest step was derivation of the SO2 propagation model bytraditional regressive techniques (models from equations 6, 7 and 8), taking into considerationdirections of air flows, and adaptive models (fig. 3) basing on the previous model formulae. The obtained models were statistically evaluated. It occurred that the models considering air flows directions show changes of pollution propagation characteristics The advantage of adaptive models, which take into consideration data from previous periods of time, was proved, as they forecast concentration of pollution far better than the traditional regressive models.

9

Optimal resource allocation in stochastic activity networks via the electromagnetism approach: a platform implementation in Java

Tereso A. P., Novais R. A., Araujo M. M., Elmaghraby S. E.

Control and Cybernetics

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2009

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Vol. 38, no 3

745-782

EN

An optimal resource allocation approach to stochastic multimodal projects had been previously developed by applying a Dynamic Programming model which proved to be very demanding computationally. A new approach, the Electromagnetism-like Mechanism, has also been adopted and implemented in Matlab, to solve this problem. This paper presents the implementation of the Electromagnetism approach using an Object Oriented language, Java, and a distributed version to be run in a computer network, in order to take advantage of available computational resources.

10

Transkrypcja genów jako ciągły lub dyskretny proces produkcyjny

Śmieja J.

Przegląd Elektrotechniczny

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2008

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R. 84, nr 9

93-95

PL

W komórkach żywych organizmów zachodzi wiele procesów biochemicznych podlegających skomplikowanym mechanizmom regulacji. Jednym z nich jest proces produkcji cząsteczek mRNA, zachodzący w jądrze komórkowym. Z praktycznego punktu widzenia jest to proces dyskretny. W niektórych przypadkach może być on jednak opisywany modelami ciągłymi. W niniejszej pracy pokazane są warunki, w jakich zarówno opis dyskretny, jak i ciągły prowadzą do takich samych jakościowo wyników.

EN

Biochemical processes in living cells are controlled by complex regulatory systems. One of such processes is production of mRNA molecules during gene transcription, taking place in the nucleus. The nature of this production process is discrete but in some cases it can be described by means of continuous models. This work presents cases in which both discrete and continuous models lead to qualitatively equivalent results.

11

Stohasticeskoe modelirovanie mehanostrukturnyh prevrasenij v polimerah i neoraniceskih vesestvah

Padohin V.

Czasopismo Techniczne. Mechanika

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2008

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R. 105, z. 2-M

269-294

EN

The developed stochastic models are extremely convenient for carrying out of computing experiments, for the decision optimization and engineering settlement tasks. They are a basis for formation of computer bank of typical models mechanical-chemical processes in inorganic substance and the high-molecular connections, the automated calculation necessary for construction systems and designing new aktivacionnogo the equipment, and also resursosberegausih technologies on their basis.

12

Splot funkcji zmiennych losowych w redukcji modelu stochastycznego

Snopkowski R.

Przegląd Górniczy

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2006

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T. 62, nr 2

30-35

PL

Modele stochastyczne oraz wykorzystanie symulacji stochastycznej do ich analizy, stanowią metodę badawczą, stosowaną w przypadku analizy procesów niezdeterminowanych. W przypadku procesów górniczych, realizowanych np. w kopalniach węgla kamiennego, można zauważyć, że wpływ czynników określanych ogólnie jako geologiczno-górnicze oraz techniczno-organizacyjne może powodować, że dany proces można traktować jako nie do końca zdetern1inowany (niekoniecznie w zakresie technologii procesu, lecz np. biorąc pod uwagę czas jego realizacji). W pracy zwrócono uwagę na możliwości redukcji modelu stochastycznego z wykorzystaniem właściwości splotu funkcji, zarówno dla funkcji o charakterze dyskretnym, jak i ciągłym. W ten sposób przeprowadzona redukcja eliminuje potrzebę analizy tych fragmentów modelu metodą symulacji stochastycznej.

EN

The stochastic models as well as Rusing stochastic simulation for analysis of them are research metod used in case of the undetermined processes analysis. In case of mining processes, realized e.g. in hard coal mines, one can notice that influence of factors generally determined as geological as well as technical and economical can cause, that given process can be treated as not finally determined (not necessarily in the range of the process technology, but e.g. taking into consideration time of its realization). Possibilities of stochastic model reduction basing on the use of convolution properties as well for the discrete as continuous character functions is pointed out in the paper. The carried out reduction eliminates in this way the necessity of analysis of these model fragments by means of the stochastic simulation method.

13

Application of the Moving Average Method of Simplifying Simulation of Random Fields

Maciejewski S., Gorczewska-Langner W.

Archives of Hydro-Engineering and Environmental Mechanics

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2006

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Vol. 53, nr 2

126-136

EN

A method of simulating random fields using a moving average is proposed in this paper. Random fields were simulated for different sizes of sub-field and different numbers of cycles of calculations of the moving average. For the fields obtained the covariance function was analyzed. In order to estimate the efficiency of the proposed simulation method of random field based on the method of diagonal covariance matrix was performed. It is shown that two of the simulation methods presented are able to generate a multidimensional random variable with required correlation function. However, the method of diagonal covariance matrix has some limitations caused by the size of the simulated random field, which result from the necessity of converting a relatively large matrix. Using the proposed simulation method it is possible to simulate, in a comparatively quick and simple manner, a random field with a large number of nodes on PC-s. The presented method can be useful in the stochastic analysis of transport phenomena in soil.

14

Understanding the dynamics of bank vole populations: demographic variability, stochasticity and density dependence

Yoccoz N., Stenseth N.

Polish Journal of Ecology

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2000

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Vol. 48, Suppl.

75-86

EN

The observed variability of population dynamics in influenced by many interacting components, most of them being difficult to estimate. Sampling variance, demographic and environmental stochasticity, together with density dependence and more deterministic changes in the environment such as changes in forestry practice and landscape patterns, simultaneously affect our understanding of bank vole population dynamics patterns. Integrating these difference variability components in a common framework is a considerable challenge. We explore in this paper some of the tools currently available for analysing population dynamics and demographic patterns in the bank vole, Clethrionomys glareolus. The study of an alpine population of bank voles is used to illustrate how demographic studies and time-series analysis may be associated in the future.

15

Stochastic FEM analysis of strip foundation

Przewłócki J., Górski J.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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1999

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Vol. 3, No 2

171-186

EN

The paper affords a stochastic description of a random soil medium subjected to an external loading. The strip foundation on a soil layer in the 3-D and the 2-D strain states is analysed. It is assumed that the soil medium is statistically homogeneous and its mechanical behaviour governed by the linear elasticity theor y. It is also assumed that elastic parameters can be modelled as the multidimens ional random fields. Stochastic 2-D and 3-D finite element methods (SFEM), based on the Monte Carlo technique were used. The influence of elements supports atta ched along vertical planes on standard deviations of displacements and stresses is discussed. Local averages of random field of elastic parameters are introduce d. The convergence of applied in SFEM simulation algorithm was tested. The analy sis performed enables determination of the standard deviations of components of the stress tensor and the displacement vector for the 3-D state, based on the so lution for the 2-D plane strain state.