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Creating an algorithm of a real-life situation as a form of mathematical modelling

100%
Pyzara A.
Didactics of Mathematics
|
2014
|
issue 11(15)
25-42
EN
Algorithmisation is one of the forms of mathematical modelling. The necessity to create an algorithm imposes specific forms of work that brings numerous didactical benefits. The research presented here concerns math students' (future teachers) abilities which relate to mathematical modelling (i.e. creating algorithms) of an everyday situation. The analysis of their work demonstrated their lack of appropriate knowledge in the field of mathematical modelling – more than the half of the models did not work properly. The application of the form of the algorithm did not improve the quality of the models as well. However, it created an impulse to apply different tools (conditional instructions) and to apply the block diagram. The research shown points at weak sides of the students' skills, but on the other hand, it emphasizes the sense of joining modelling with creating algorithms.
2
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Modelling the steady state of sewage networks as a support tool for their planning and analysis

100%
PETRICZEK G., STUDZIŃSKI J., BOGDAN L.
Operations Research and Decisions
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2015
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vol. 25
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issue 3
39-57
EN
Fundamental questions connected with the modelling of communal sewage networks have been considered and formulas used to model the functioning of the basic network have been analyzed. The problem described concerns gravitational sewage networks divided by nodes into branches and sectors. Simulation of the steady state functioning of sewage networks is commonly carried out on the basis of nomograms in the form of charts, in which the relations between network parameters like channel diameters, flow rates, hydraulic slopes and flow velocities are described. In traditional design, the values of such parameters are simply read from such nomogram chart tables. Another way of simulating the functioning of a network is the use of professional software, like SWMM, that models sewage flows along the channels by means of differential equations de-scribing the movement of fluids. In both approaches, the user is a mechanical operator of a “black box” procedure. In this paper, another way of simulating the functioning of sewage net-works has been presented. Numerical solutions of nonlinear equations describing the physical phenomena of sewage flows are applied and explained. The presented algorithms were developed to model the steady state of a sewage network enabling a quick analysis of the network parameters and the possibility of fast, simple and comprehensible network modeling and design.
3

МЕТОДИЧНІ РЕКОМЕНДАЦІЇ ДО НАВЧАННЯ МАТЕМАТИЧНОМУ МОДЕЛЮВАННЮ МАЙБУТНІХ ІНЖЕНЕРІВ ПІД ЧАС АУДИТОРНИХ ЗАНЯТЬ З ТЕОРІЇ ВИПАДКОВИХ ПРОЦЕСІВ

88%
Чумак О.
Педагогічні науки: теорія, історія, інноваційні технології
|
2014
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issue 5(39)
408-417
EN
The importance of formation of the mathematical modeling ability during the study of the theory of probability and stochastic processes by future engineers is substantiated. The notion of mathematical modeling when teaching the students of technical universities to the mathematical disciplines is examined. The paper reveals the difficulties met by students during the construction of models to the problems. The author notes that the universal formalization algorithm of real problems does not exist; therefore the most difficult for students are the first and the second stages of simulation when solving professionally oriented tasks. In order to solve a problem the techniques of heuristic activity are proposed to take advantage in the first stage of modeling. The study displays one of the ways of teaching students to the «art of modeling», namely the implementation of its development as the ability of students to «see different in the same and the same in differences». This article contains an example of building a model to a professionally oriented task during a lecture. It is shown how a teacher in the course of constructing a model can engage students into interactive debate. For this purpose the teacher’s notation on the blackboard should be accompanied by an appropriate dialogue with students. Methodological recommendations for the direction of educational and cognitive activities of students during the construction of models reflecting Markov random process of discrete state and continuous time are suggested. It is shown why such learning activities, which are to build and study models of stochastic process, contribute to the conscious assimilation of the topic by the students, as well as to the building of their understanding of the unity of some sections of higher mathematics, stochastic processes and connection with real engineering studies. The author emphasizes that the work with a mathematical model of a real engineering process enhances motivation to learn the discipline, so that the students actively master the skills necessary for their future careers. The issue of mathematical modeling training and research of other stochastic processes may become the subject of further survey in this area.
4
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A dynamical-systems approach to the evolution of morphonotactic and lexical consonant clusters in English and Polish

88%
Baumann A., Kaźmierski K.
Yearbook of the Poznań Linguistic Meeting
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2016
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vol. 2
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issue 1
EN
Consonant clusters appear either lexically within morphemes or morphonotactically across morpheme boundaries. According to extant theories, their diachronic dynamics are suggested to be determined by analogical effects on the one hand as well as by their morphological signaling function on the other hand. This paper presents a mathematical model which allows for an investigation of the interaction of these two forces and the resulting diachronic dynamics. The model is tested against synchronic and diachronic language data. It is shown that the evolutionary dynamics of the cluster inventory crucially depend on how the signaling function of morphonotactic clusters is compromised by the presence of lexical items containing their morpheme internal counterparts.
5
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Nash – Disequilibrium, Random Decisions and Imbalance of Society: Is it Relevant to Ukraine?

88%
Hurnyak I., Struk O., Hrytsyshyn A.
Political Preferences
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2023
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vol. 31
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issue 1
5-30
EN
Ukrainian society is undergoing rapid transformational changes. The authors attempted to identify the main behavioral strategies before the war as well as possible changes in the following years. Attempting to recognize the most prevalent behavior in society, the interaction and attitude of students during the exam were taken into consideration. The student group includes representatives of various regions in proportionate numbers. The research is based on the simulation of the interaction of different groups in society by means of game theory and programming. The study proposes using Schumpeter market disturbances and ‘Nash disequilibrium’ to invigorate the current ineffective system. It has been shown that pre-war Ukrainian society exhibited a very high level of collusion. The interim conclusions were tested using Axelrod’s tournament algorithms and strategies. A simulation of the cooperative equilibrium in Ukrainian society during the pre-war period was demonstrated. The study also contains important predictions about the changes in the institutional environment in the aftermath of the war in Ukraine.
6
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Simultaneous pickup and delivery model suggestion for personnel transportation in COVID-19 pandemic conditions

88%
KÖSE E., KORKMAZER A., VURAL D., GÖKCEOĞLU G. G., ŞAVLI P.
Operations Research and Decisions
|
2023
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vol. 33
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issue 4
119-131
EN
The impact of COVID-19 on the transportation costs of a large-scale company has been examined. Before the pandemic, shift personnel were transported to the factory by shuttles, and after a quick shift change, other shift personnel were transported back to their homes. However, with the implementation of laws mandating the reduction of shuttle seat capacities, transportation costs have risen significantly. To address this issue, a new simultaneous Pickup and Delivery Model is proposed as an alternative to the separate transportation of shift workers. The results of this study indicate that the proposed model provides a substantial advantage in terms of both the number of vehicles used and the total distance travelled, leading to a significant reduction in costs. This research underscores the importance of effective operations research practices for the profitability of companies, particularly in extraordinary circumstances such as the COVID-19 pandemic.
7
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Simultaneous pickup and delivery model suggestion for personnel transportation in COVID-19 pandemic conditions

88%
Köse E., Kokmazer A., Vural D., Gökceoğlu G. G., Şavlı P.
Operations Research and Decisions
|
2023
|
vol. 33
|
issue 4
EN
The impact of COVID-19 on the transportation costs of a large-scale company has been examined. Before the pandemic, shift personnel were transported to the factory by shuttles, and after a quick shift change, other shift personnel were transported back to their homes. However, with the implementation of laws mandating the reduction of shuttle seat capacities, transportation costs have risen significantly. To address this issue, a new simultaneous pickup and delivery model is proposed as an alternative to the separate transportation of shift workers. The results of this study indicate that the proposed model provides a substantial advantage in terms of both the number of vehicles used and the total distance traveled, leading to a significant reduction in costs. This research underscores the importance of effective operations research practices for the profitability of companies, particularly in extraordinary circumstances such as the COVID-19 pandemic.
8
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Формування споживних властивостей цукрового печива за рахунок використанням шроту з насіння гарбуза

63%
Bachynska Y.
Path of Science
|
2018
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vol. 4
|
issue 6
1001-1008
UK
Цукрове печиво найбільш поширене серед борошняних кондитерських виробів, воно має високу енергетичну цінність і недостатній вміст основних нутрієнтів. Надмірне вживання печива може привести до виникнення низки захворювань. Це зумовлює необхідність розробки нових харчових продуктів повсякденного попиту, у тому числі борошняних кондитерських виробів високої біологічної цінності. В роботі досліджується вплив шроту з насіння гарбуза при виробництві цукрового печива з підвищеною біологічною цінністю. Наводяться результати товарознавчої експертизи розробленого зразка печива та проводиться порівняння з традиційними зразками печива цукрового інших виробників. Доведена доцільність використання шроту з насіння гарбуза в технології виробництва цукрового печива для розширення асортименту кондитерських виробів підвищеної біологічної цінності та виробів зі зниженим рівнем калорійності. Шляхом моделювання встановлено, що оптимальна кількість шроту з насіння гарбуза – 2,76 % (18 г) від маси борошна. При збільшенні кількості шроту зменшується здатність до намокання, тому саме це співвідношення сприятиме збагаченню печива цукрового корисними речовинами та збереженню якості фізико-хімічних показників. Додавання до складу печива шроту з насіння гарбуза, позитивно вплинуло на хімічний склад готового виробу, наситивши його білками, харчовими волокнами, поліненасиченими жирними кислотами, вітамінами та мінеральними елементами. Адже при споживанні 100 г продукту спостерігаються тенденції в компенсації більше 10 % добової норми в білках, жирах, вуглеводах; мінеральних речовинах – від 2,33 % до 25,78 %; вітамінах від 3,35 % до 9,44 %, що пояснюється позитивним впливом на організм та задоволенням в основних нутрієнтах різних категорій населення. Було досліджено динаміку змін якості розробленого зразка на момент виготовлення та після його зберігання. Доведено, що в основному змінюються органолептичні показники – з’являється присмак та запах згіркнення, що пояснюється окисненням жирів.
XX
Sugar cookies are the most common among flour confectionery, they have high energy value and insufficient content of basic nutrients. Excessive consumption of cookies can lead to a number of diseases. This necessitates the development of new food products of everyday demand, including flour confectionery products of high biological value. The paper studies the effect of pumpkin seed pomace on the production of sugar biscuits with the increased biological value. The results of the commodity examination of the developed cookie sample are presented and the comparison with traditional samples of sugar cookies of other producers is carried out. The expediency of using pumpkin seed pomace in the technology of sugar biscuit production has been proved to expand the range of high biological value confectionery products and products with the reduced level of caloric content. Through simulation it has been found that the optimum amount of pumpkin seed pomace is 2.76 % (18 g) of the weight of the flour. With an increase in the amount of pomace the ability to soak decreases, which is why this ratio will contribute to the enrichment of sugar cookies and the preservation of the quality of physics-chemical indicators. The addition of pumpkin seed pomace to cookies composition positively influenced the chemical composition of the ready product, saturating it with proteins, food fibers, polyunsaturated fatty acids, vitamins and minerals. After all, when consuming 100 g of the product there are tendencies in compensation of more than 10 % of daily norm in proteins, fats, carbohydrates; mineral substances - from 2.33 % to 25.78 %; vitamins from 3,35 % to 9,44 %, which is explained by the positive effect on the body and satisfying basic nutrients to different categories of the population. The dynamics of changes in the quality of the developed sample at the time of fabrication and after its storage was investigated. It is proved that organoleptic parameters change basically - there appears a taste and a smell of rancidity, which is explained by the oxidation of fats.
9
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Estymacja stanu z nieciągłymi pomiarami dla modelu matematycznego opisanego równaniami różniczkowymi typu hiperbolicznego

63%
KRUTYS P., KWATER T., ŻESŁAWSKA E., PĘKALA R.
Edukacja-Technika-Informatyka
|
2014
|
vol. 5
|
issue 1
605-610
PL
W artykule przedstawiono model matematyczny zanieczyszczonej rzeki opisanej równaniami różniczkowymi typu hiperbolicznego oraz rozważania estymacji za pomocą filtra Kalmana-Bucy z dyskretnymi pomiarami. W rezultacie otrzymano dwa etapy badań, tj. filtrację i predykcję. W procesie estymacji wykorzystano pomiary jakości rzeki w stałych jej punktach, otrzymując wartości dyskretne, co następnie było kluczowe dla zagadnienia predykcji rozumianej jako równania w postaci ciągłej z warunkami początkowymi uzyskanymi w procesie filtracji generujące wartości przewidywane do następnych pomiarów. W badaniach uwzględniono dobór odpowiednich współczynników wzmocnienia filtru mającego istotne znaczenie na wartości błędu estymacji.
EN
This paper presents a mathematical model of a polluted river described differential equations of hyperbolic type, and consider estimation using the filter Kalman-Bucy with discrete measurements. As a result, it received two steps of etimation i.e. filtration and prediction. In the estimation process of river quality was used measurements of the fixed point, yielding discrete values, which then was crucial to issue a prediction understood as a continuous equation with the initial conditions obtained by a filtration process to generate the predicted values of subsequent measurements. The study included the selection of appropriate filter gain factors having a major influence on the estimation error.
10
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Symulacje komputerowe modelu matematycznego zanieczyszczonej biochemicznie wody z uwzględnieniem zjawiska dyfuzji

63%
KWATER T., KWIATKOWSKI B., KRUTYS P., ŻESŁAWSKA E.
Edukacja-Technika-Informatyka
|
2013
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vol. 4
|
issue 2
345-350
PL
W artykule przedstawiono eksperymenty badań modeli matematycznych zanieczyszczonej biochemicznie wody dla różnych stopni złożoności. Jakość wody reprezentowana jest przez następujące wskaźniki: Biochemiczne Zapotrzebowanie na Tlen oraz Rozpuszczony Tlen. Badania symulacyjne przeprowadzono dla modelu matematycznego w postaci równań różniczkowych cząstkowych II rzędu, w których uwzględniono zjawisko dyfuzji, a także prędkości przepływu
XX
This paper presents experimental study of mathematical models of biochemical polluted water for different degrees of complexity. Water quality is represented by the following indicators: Biochemical Oxygen Demand and Dissolved Oxygen. Simulation studies were performed for a mathematical model of in the form of partial differential equations II-th order, which takes into account the phenomenon of diffusion, and flow velocity.
11
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Jakość estymacji stanu z ciągłymi pomiarami dla modelu zanieczyszczonej rzeki

63%
KWATER T., ŻESŁAWSKA E., KRUTYS P.
Edukacja-Technika-Informatyka
|
2014
|
vol. 5
|
issue 1
611-616
PL
W artykule przedstawiono zagadnienia związane z badaniami symulacyjnymi jakości estymacji stanu filtrem typu Kalman-Bucy. Badany obiekt stanowiła rzeka zanieczyszczona biochemicznie opisana równaniami różniczkowymi cząstkowymi typu hiperbolicznego. Jakość estymacji określano przy pomocy funkcjonału reprezentującego sumę kwadratu błędu w rozważanej przestrzeni rozwiązań. Na symulowany obiekt oddziaływano stochastycznymi zakłóceniami o rozkładzie gaussowskim dla różnych parametrów. Omówiono także problematykę doboru współczynnika wzmocnienia filtru, wartości początkowej estymacji, intensywności zakłóceń pomiarowych i ich wpływu na dokładność odwzorowania. Uzyskano zróżnicowaną jakość estymacji stanu, dobierając różne wartości parametrów podczas symulacji.
EN
The article presents the problems of the simulation study the quality of state estimation by filter Kalman-Bucy type. The test object was a river polluted biochemically described partial differential equations of hyperbolic type. Quality estimation determined using the sum square errors of estimation representing a functional of the solutions under consideration. On the simulated object interaction of stochastic interference of Gaussian distributions for various parameters. Also discussed the issue of selection of the filter gain, the initial estimation, the intensity of interference and measuring their impact on the accuracy of the mapping. Obtained varied quality of state estimation by choosing different values of parameters during the simulation
12
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Використання нетрадиційної сировини при виробництві борошняних кондитерських виробів як прогресивний напрямок створення продуктів підвищеної біологічної цінності

51%
Bachinska J.
Path of Science
|
2017
|
vol. 3
|
issue 2
7.1-7.10
UK
В роботі досліджується вплив використання нетрадиційної рослинної сировини при виробництві борошняних кондитерських виробів з підвищеною біологічною цінністю; наводяться результати товарознавчої оцінки розроблених продуктів та проводиться порівняння їх з основними зразками, що представлені в торговельній мережі м. Харкова. Доведена доцільність використання суміші харчових волокон та шроту з насіння гарбуза в технології виробництва борошняних кондитерських виробів для розширення асортименту кондитерських виробів підвищеної біологічної цінності та виробів зі зниженим рівнем калорійності. Додавання до складу печива суміші харчових волокон та шроту з насіння гарбуза, позитивно вплинуло на хімічний склад готового виробу, наситивши його корисними і необхідними людському організму мінеральними елементами, вітамінами, харчовими волокнами.
EN
This paper examines the impact of the use of alternative vegetable raw materials in the manufacture of pastry products with high biological value; it presents the results of evaluation of commodity of the developed products and compares them with the main samples presented in Kharkiv trade network. The feasibility of using a mixture of fiber and pumpkin seeds in technology of pastry production to extend the range of confectionery products of high biological value and products with reduced calories has been proved. Adding the mixture of fiber and pumpkin seeds to biscuits and cakes positively affected the chemical composition of the ready-made product, saturating it with useful and necessary to human body mineral elements, vitamins, dietary fiber.
13

Modelowanie matematyczne w muzyce na podstawie twórczości Iannisa Xenakisa

51%
Grębski T.
Roczniki Kulturoznawcze
|
2019
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vol. 10
|
issue 1
53-85
PL
Poszukiwanie matematycznych zależności w dziełach muzycznych to bardzo częste zjawisko badawcze. Można napotkać wiele utworów, w których artysta świadomie wykorzystywał wiedzę matematyczną podczas ich komponowania. Poszukiwanie matematycznych zależności w muzyce można by nazwać „matematyzowaniem muzyki”. Ale czy można „umuzycznić matematykę”, a dokładniej – obiekty matematyczne? W artykule analizie poddany jest problem „umuzyczniania matematyki”, zaś celem artykułu jest przedstawienie wybranych struktur matematycznych świadomie użytych przez Iannisa Xenakisa w kompozycjach. Jego twórczość jest doskonałym przykładem połączenia matematyki z muzyką. Mowa tu o procesach stochastycznych i rachunku prawdopodobieństwa, o teorii grup, o ruchach Browna i łańcuchach Markowa oraz o teorii gier. Muzyka Xenakisa przeciwstawiała się jakiejkolwiek tradycji w muzyce dzięki zastosowaniu w niej modelowania matematycznego. Była nieprzewidywalna, ale nie przypadkowa. W artykule mowa również o procesie twórczym przy komponowaniu muzyki oraz o matematycznym porządku w utworach muzycznych i walorach estetycznych i artystycznych. Artykuł ten dodatkowo ułatwi odbiór muzyki Xenakisa i pozwala lepiej zrozumieć jego twórczość.
EN
The search for mathematical relationships in musical compositions are often studied. There are many musical compositions, in which the composer consciously used mathematical knowledge during their composing. The search for mathematical dependence in music could be called “mathematization of music”. Can we use math to music illustration of mathematical objects? The problem of using music to math illustration is analyzed in this article and the aim of the article is to present some mathematical structures consciously used in the compositions by Iannis Xenakis. His work is an excellent example of the connection of mathematics with music. There are described stochastic processes and probability theory, group theory, game theory, and Brownian motion and Markov chains. Music of Xenakis opposed any tradition in music by using mathematical modeling in it. It was unpredictable, but not accidental. There is also about the creative process when composing music and about mathematical order in musical works, as well as aesthetic and artistic values. This article facilitates the perception of Xenakis music and enables to understand his work better.
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