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1
Content available remote Wątpliwości dotyczące modelowania matematycznego filtracji pospiesznej wody
Dąbrowski Wojciech
Instal
|
2023
|
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
Content available Elaboration of stochastic models to comprehensive evaluation of occupational risks in complex dynamic systems
Bochkovskyi A. P.
Journal of Achievements in Materials and Manufacturing Engineering
|
2021
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Vol. 104, nr 1
31--41
EN
Purpose: Elaborate stochastic models to comprehensive evaluation of occupational risks in “man - machine - environment” systems taking into account the random and dynamic nature of the impact on the employee of negative factors over time. Design/methodology/approach: Within study, the methods of probability theory and the theory of Markov processes - to find the limit distribution of the random process of dynamic impact on the employee of negative factors over time and obtain main rates against which the level of occupational risks within the "man - machine - environment" systems can be comprehensively evaluated; Erlang phases method, Laplace transform, difference equations theory, method of mathematical induction - to elaborate a method of analytical solution of the appropriate limit task for a system of differential equations in partial derivatives and appropriate limit conditions were used. Findings: A system of differential equations in partial derivatives and relevant limit conditions is derived, which allowed to identify the following main rates for comprehensive evaluation of occupational risks in systems "man - machine - environment": probability of excess the limit of the employee's accumulation of negative impact of the harmful production factor; probability of the employee’s injury of varying severity in a random time. An method to the solution the limit task for a system of differential equations, which allows to provide a lower bounds of the probability of a certain occupational danger occurrence was elaborated. Research limitations/implications: The elaborated approach to injury risk evaluation is designed to predict cases of non-severe injuries. At the same time, this approach allows to consider more severe cases too, but in this case the task will be more difficult. Practical implications: The use of the elaborated models allows to apply a systematic approach to the evaluation of occupational risks in enterprises and to increase the objectivity of the evaluation results by taking into account the real characteristics of the impact of negative factors on the employee over time. Originality/value: For the first time, a special subclass of Markov processes - Markov drift processes was proposed and substantiated for use to comprehensive evaluation of occupational risks in “man - machine - environment” systems.
3
Content available remote 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
|
2020
|
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
Content available 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
Content available 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.
6
Content available Modele stochastyczne zanieczyszczeń powietrza w aglomeracjach przemysłowych
Tumidajski T., Foszcz D., Niedoba T., Siewior J.
Rocznik Ochrona Środowiska
|
2009
|
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.
7
Content available remote Transkrypcja genów jako ciągły lub dyskretny proces produkcyjny
Śmieja J.
Przegląd Elektrotechniczny
|
2008
|
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.
8
Content available remote Couple-stress and surface roughness effects in curvilinear thrust bearings with a porous pad
Walicka A., Walicki E., Jurczak P., Michalski D.
International Journal of Applied Mechanics and Engineering
|
2008
|
Vol. 13, no 2
563-574
EN
On the basic of Christensen's stochastic model of rough surfaces, different forms of Reynolds equation with rotational inertia effect are obtained for various types of surface roughness pattern and for couple stress lubricant. As results one obtained the formulae expressing the mean film pressure distribution for externally pressurized bearings and for bearings with a squeeze film. An example of step bearing is considered.
9
Content available remote Stochastic model of cavitation erosion of low-plasticity metallic materials
Gireń B. G.
Transactions of the Institute of Fluid-Flow Machinery
|
2006
|
nr 118
101-126
EN
Stochastic model of cavitation erosion of low plasticity solids was presented. It is a kinetic type model based on the energy conservation law. Mathematical formulation comprised equations for the energy accumulation and release rates. Micro-cracks were assumed to be the main negative source of energy. In calculations carried out, the random element was omitted and deterministic dependences of energy absorbed and relaxed in the process were found. Conformability of the theoretical and experimental curves was taken in favour of the model. The material fatique effect was expressed by the delay of micro-cracks appearance with respect to the force action time. The model sets a calculation direction of the temporal development of cavitation erosion. An application to practical cases requires the use of proper loading functions, as well as probabilistic distributions of the absorption and relaxation of energy, being the function of material parameters of the destroyed solid.
10
Content available remote Splot funkcji zmiennych losowych w redukcji modelu stochastycznego
Snopkowski R.
Przegląd Górniczy
|
2006
|
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.
11
Content available remote Quality control in mineral preparation processes - theoretical aspects of accuracy of grained material parameters measurements
Walaszek-Babiszewska A., Kowal A.
Management
|
1998
|
nr 3
95-101
EN
Theoretical aspect of accuracy of measuring of grained material parameters has been presented in the paper. Situations involved in different processes have been taken into consideration and on the basis of the stochastic sampling theory formulae defining errors of measurements of coal parameters have been determined.
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