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Articoli di riviste sul tema "Mathematical Modelling"

Autore: Grafiati

Pubblicato: 4 giugno 2021

Ultima modifica: 9 giugno 2025

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1

Ketova, K. V., I. G. Rusyak, and D. D. Vavilova. "MATHEMATICAL MODELLING OF WORKFORCE POTENTIAL." European Journal of Natural History, no. 3 2020 (2020): 65–69. http://dx.doi.org/10.17513/ejnh.34088.

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2

Smith, D. "Mathematical modelling." Teaching Mathematics and its Applications 15, no. 1 (March 1, 1996): 37–41. http://dx.doi.org/10.1093/teamat/15.1.37.

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3

Campbell, P. "Mathematical modelling." Manufacturing Engineer 77, no. 4 (August 1, 1998): 187–89. http://dx.doi.org/10.1049/me:19980407.

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4

Ziegel, Eric R. "Mathematical Modelling." Technometrics 32, no. 2 (May 1990): 240. http://dx.doi.org/10.1080/00401706.1990.10484666.

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5

Ramos, J. I. "Mathematical Modelling." Applied Mathematical Modelling 14, no. 8 (August 1990): 444. http://dx.doi.org/10.1016/0307-904x(90)90102-b.

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6

Rawson, H. "Mathematical modelling." Journal of Non-Crystalline Solids 73, no. 1-3 (August 1985): 551–63. http://dx.doi.org/10.1016/0022-3093(85)90374-6.

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7

Rawson, H. "Mathematical modelling." Journal of Non-Crystalline Solids 80, no. 1-3 (March 1986): 92. http://dx.doi.org/10.1016/0022-3093(86)90381-9.

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8

Cundy, H. Martyn, J. S. Berry, D. N. Burghes, I. D. Huntley, D. J. G. James, and A. O. Moscardini. "Mathematical Modelling Courses." Mathematical Gazette 72, no. 460 (June 1988): 152. http://dx.doi.org/10.2307/3618954.

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9

Reyniers, Diane, J. S. Berry, D. N. Hughes, I. D. Huntley, D. J. G. James, and A. O. Moscardini. "Mathematical Modelling Courses." Journal of the Operational Research Society 39, no. 12 (December 1988): 1181. http://dx.doi.org/10.2307/2583605.

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10

SMITH, D. N. "Independent Mathematical Modelling." Teaching Mathematics and its Applications 16, no. 3 (September 1, 1997): 101–6. http://dx.doi.org/10.1093/teamat/16.3.101.

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Jones, Mark S. "Teaching mathematical modelling." International Journal of Mathematical Education in Science and Technology 28, no. 4 (July 1997): 553–60. http://dx.doi.org/10.1080/0020739970280409.

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12

Reyniers, Diane. "Mathematical Modelling Courses." Journal of the Operational Research Society 39, no. 12 (December 1988): 1181. http://dx.doi.org/10.1057/jors.1988.197.

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13

Lingefjärd, Thomas. "LEARNING MATHEMATICAL MODELLING." Far East Journal of Mathematical Education 16, no. 2 (April 26, 2016): 149–67. http://dx.doi.org/10.17654/me016020149.

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14

Sodré, Gleison De Jesus Marinho, Raquel Soares do Rêgo Ferreira, and Renato Borges Guerra. "Reverse Mathematical Modelling." Acta Scientiae 24, no. 6 (December 19, 2022): 552–83. http://dx.doi.org/10.17648/acta.scientiae.7372.

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Background: Research in mathematics education shows that mathematical modelling is a practice that seeks to “translate” problem situations into possible mathematical models without, however, explaining the complexity involved in the reverse formulation, starting from the mathematical model to delimit the type of situation. Objective: To highlight the problem of reverse mathematical modelling, in the sense of a reverse formulation that goes from the mathematical model to the situation. Design: For this, a course of study and research was carried out guided by the investigative cycle of mathematical modelling that is based on theoretical-methodological resources of the anthropological theory of the didactic. Setting and Participants: Pre-service teachers of a teaching degree at a public institution were faced with a problem in an unusual context about the decimal number system and, more broadly, the positional number system. Data collection and analysis: We present an empirical approach based on research carried out by Ferreira (2020) with teachers in initial training. Results: The empirical results observed confirm the hypothesis of the existence of the problem of reverse mathematical modelling, even in the face of normative models, in the sense that they can faithfully describe a real situation. Conclusions: Ultimately, the study of a type of problem in an unusual context, in addition to highlighting the encounter of teachers with different objects of knowledge, revealed the remarkable difficulty in delimiting the type of quantification situation that can be associated with the mathematical model of the number and as stimulate future research on the teaching of reverse mathematical modelling.

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15

Park, Eun young, and Oh Nam Kwon. "Comparison and Analysis of Middle School Trigonometry Textbook Tasks and Teacher Design Tasks: From the Perspective of Mathematical Modelling." Korean Association For Learner-Centered Curriculum And Instruction 23, no. 7 (April 15, 2023): 817–38. http://dx.doi.org/10.22251/jlcci.2023.23.7.817.

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Objectives In this study, the triangulation task actually used in the middle school class is analyzed from the perspective of the mathematical modelling tasks. Methods Various triangulation tasks were collected from middle school trigonometry textbooks and activity sheets produced and used by teachers, and classified based on whether connectivity and openness, which are the core characteristics of mathematical modelling tasks, were met, and cognitive activities required. Then, mathematical modelling tasks is selected from among the teacher-designed tasks, and the activities of the tasks and the interviews of the teachers in each mathematical modelling tasks are interpreted according to the mathematical modelling cycle. Results Teacher-designed tasks were found to have higher connectivity and openness than textbook tasks, including familiar material, offering practical and specific data, or insufficient data to solve the task. On the other hand, all tasks selected as mathematical modelling tasks among teacher-designed tasks emphasized simplifying, mathematising, and working mathematically, but relatively put less emphasis on understanding, interpretation, and validation. In particular, the process after working mathematically turned out to be limited to the extent of attaching units to the mathematical results, rounding it, or reviewing whether the calculation of the result were correct. In addition, all tasks used only the concept of tangent and did not require other concepts of trigonometric ratio. Conclusions Several examples of triangulation tasks can be found in Korean and foreign mathematical modelling studies. As such, mathematical modelling teaching/learning method is useful to teach trigonometry due to its usefulness in real life. According to the results of this paper, teachers want to design assignments rich in connectivity and openness so that students can recognize the usefulness of the concept of trigonometric ratio. Furthermore, if the various cognitive activities in the mathematical modelling cycle are evenly included, and various trigonometry tasks including various models are designed, it would lead more meaningful teaching and learning of mathematical modelling as well as trigonometry and ultimately it would help students improve problem-solving skills.

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16

Corrêa, Priscila Dias. "The Mathematical Proficiency Promoted by Mathematical Modelling." Journal of Research in Science Mathematics and Technology Education 4, no. 2 (May 15, 2021): 107–31. http://dx.doi.org/10.31756/jrsmte.424.

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This study aims to investigate the mathematical proficiency promoted by mathematical modelling tasks that require students to get involved in the processes of developing mathematical models, instead of just using known or given models. The research methodology is grounded on design-based research, and the classroom design framework is supported by complexity science underpinnings. The research intervention consists of high-school students, from a grade 11 mathematics course, aiming to solve four different modelling tasks in four distinct moments. Data was collected during the intervention from students’ written mathematical work and audio and video recordings, and from recall interviews after the intervention. Data analysis was conducted based on a model of mathematical proficiency and assisted by interpretive diagrams created for this research purpose. This research study offers insight into mathematics teaching by portraying how mathematical modelling tasks can be integrated into mathematics classes to promote students’ mathematical proficiency. The study discusses observed expressions and behaviours in students’ development of mathematical proficiency and suggests a relationship between mathematical modelling processes and the promotion of mathematical proficiency. The study also reveals that students develop mathematical proficiency, even when they do not come to full resolutions of modelling tasks, which emphasizes the relevance of learning processes, and not only of the products of these processes.

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17

Schleicher, Jörg, Lei Wang, and Jin Yun Yuan. "Mathematical Modelling and Mathematical Methods in Energy." Numerical Linear Algebra with Applications 14, no. 4 (2007): 255. http://dx.doi.org/10.1002/nla.521.

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18

ARALOVA, N. I. "MATHEMATICAL MODELLING OF IMMUNE PROCESSES AND ITS APPLICATION." Biotechnologia Acta 13, no. 5 (October 2020): 5–18. http://dx.doi.org/10.15407/biotech13.05.005.

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The aim of the study was to develop a mathematical model to research hypoxic states in case of simulation of an organism infectious lesions. The model is based on the methods of mathematical modeling and the theory of optimal control of moving objects. The processes of organism damage are simulated with the mathematical model of immune response developed by G.I. Marchuk and the members of his scientific school, adapted to current conditions. This model is based on Burnet’s clone selection theory of the determining role of antigen. Simulation results using the model are presented. The dependencies of infectious courses on the volumetric velocity of systemic blood flow is analyzed on the complex mathematical model of immune response, respiratory and blood circulation systems. The immune system is shown to be rather sensitive to the changes in blood flow via capillaries. Thus, the organ blood flows can be used as parameters for the model by which the respiratory, immune response, and blood circulation systems interact and interplay.

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19

Wilson, D. P. "Mathematical modelling of Chlamydia." ANZIAM Journal 45 (April 13, 2004): 201. http://dx.doi.org/10.21914/anziamj.v45i0.883.

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20

Bunday, Brian D. "Mathematical Modelling of Queues." Mathematical Gazette 79, no. 486 (November 1995): 499. http://dx.doi.org/10.2307/3618077.

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21

Abram, J., Dilwyn Edwards, and Mike Hamson. "Guide to Mathematical Modelling." Mathematical Gazette 75, no. 472 (June 1991): 243. http://dx.doi.org/10.2307/3620299.

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22

Kasprowicz, Magdalena, Agnieszka Kazimierska, Arkadiusz Ziółkowski, Afroditi Lalou, Zofia Czosnyka, and Marek Czosnyka. "Mathematical Modelling in Hydrocephalus." Neurology India 69, no. 8 (2021): 275. http://dx.doi.org/10.4103/0028-3886.332259.

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23

Ferrucci, Beverly J., and Jack A. Carter. "Technology-active mathematical modelling." International Journal of Mathematical Education in Science and Technology 34, no. 5 (January 2003): 663–70. http://dx.doi.org/10.1080/0020739031000148921.

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24

Gammon, Katharine. "Mathematical modelling: Forecasting cancer." Nature 491, no. 7425 (November 2012): S66—S67. http://dx.doi.org/10.1038/491s66a.

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25

Nuttall, Ben. "Mathematical modelling study group." MSOR Connections 11, no. 3 (September 2011): 10. http://dx.doi.org/10.11120/msor.2011.11030010.

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26

BAOWAN, DUANGKAMON. "MATHEMATICAL MODELLING OF NANOSTRUCTURES." Bulletin of the Australian Mathematical Society 78, no. 2 (October 2008): 351–52. http://dx.doi.org/10.1017/s0004972708000786.

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27

Gombert, Andreas Karoly, and Jens Nielsen. "Mathematical modelling of metabolism." Current Opinion in Biotechnology 11, no. 2 (April 2000): 180–86. http://dx.doi.org/10.1016/s0958-1669(00)00079-3.

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28

Alonso, E. E., N. M. Pinyol, and A. Yerro. "Mathematical Modelling of Slopes." Procedia Earth and Planetary Science 9 (2014): 64–73. http://dx.doi.org/10.1016/j.proeps.2014.06.002.

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29

Giersch, C. "Mathematical modelling of metabolism." Current Opinion in Plant Biology 3, no. 3 (June 1, 2000): 249–53. http://dx.doi.org/10.1016/s1369-5266(00)00072-8.

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30

Brushlinsky, K. V. "Mathematical modelling in plasmastatics." Computer Physics Communications 126, no. 1-2 (April 2000): 37–40. http://dx.doi.org/10.1016/s0010-4655(99)00244-1.

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31

Ramos, J. I. "Mathematical modelling of fires." Applied Mathematical Modelling 14, no. 1 (January 1990): 52. http://dx.doi.org/10.1016/0307-904x(90)90164-z.

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32

Rodin, ErvinY. "Educational mathematical modelling modules." Mathematical and Computer Modelling 10, no. 1 (1988): 65. http://dx.doi.org/10.1016/0895-7177(88)90122-7.

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33

Rachev, S. "Mathematical and Computer Modelling." Mathematical and Computer Modelling 36, no. 7-8 (November 2002): 949. http://dx.doi.org/10.1016/s0895-7177(02)00239-x.

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34

El Khatib, N., O. Kafi, A. Sequeira, S. Simakov, Yu Vassilevski, and V. Volpert. "Mathematical modelling of atherosclerosis." Mathematical Modelling of Natural Phenomena 14, no. 6 (2019): 603. http://dx.doi.org/10.1051/mmnp/2019050.

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The review presents the state of the art in the atherosclerosis modelling. It begins with the biological introduction describing the mechanisms of chronic inflammation of artery walls characterizing the development of atherosclerosis. In particular, we present in more detail models describing this chronic inflammation as a reaction-diffusion wave with regimes of propagation depending on the level of cholesterol (LDL) and models of rolling monocytes initializing the inflammation. Further development of this disease results in the formation of atherosclerotic plaque, vessel remodelling and possible plaque rupture due its interaction with blood flow. We review plaque-flow interaction models as well as reduced models (0D and 1D) of blood flow in atherosclerotic vasculature.

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Rodin, ErvinY. "Mathematical and computer modelling." Mathematical and Computer Modelling 12, no. 12 (1989): I—II. http://dx.doi.org/10.1016/0895-7177(89)90345-2.

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36

Middleton, A., M. Owen, M. Bennett, and J. King. "Mathematical modelling of gibberellinsignalling." Comparative Biochemistry and Physiology Part A: Molecular & Integrative Physiology 150, no. 3 (July 2008): S46. http://dx.doi.org/10.1016/j.cbpa.2008.04.023.

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37

Leng, G., and D. J. MacGregor. "Mathematical Modelling in Neuroendocrinology." Journal of Neuroendocrinology 20, no. 6 (June 2008): 713–18. http://dx.doi.org/10.1111/j.1365-2826.2008.01722.x.

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38

Hickman, F. R. "Mathematical modelling in physics." Physics Education 21, no. 3 (May 1, 1986): 173–80. http://dx.doi.org/10.1088/0031-9120/21/3/311.

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Pescetti, D. "Mathematical modelling of hysteresis." Il Nuovo Cimento D 11, no. 8 (August 1989): 1191–216. http://dx.doi.org/10.1007/bf02459024.

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M, Chamuchi Nyaboe, Johana Sigey K, and Kangethe Giterere. "Mathematical Modelling of HIV/AIDS and Transmission Dynamics." SIJ Transactions on Computer Science Engineering & its Applications (CSEA) 06, no. 06 (December 7, 2018): 01–08. http://dx.doi.org/10.9756/sijcsea/v6i6/06050090101.

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41

Ural, Alattin. "A Classification of Mathematical Modeling Problems of Prospective Mathematics Teachers." Journal of Educational Issues 6, no. 1 (April 9, 2020): 98. http://dx.doi.org/10.5296/jei.v6i1.16566.

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The purpose of this research is to classify the mathematical modelling problems produced by pre-service mathematics teachers in terms of the number of variables and to determine the mathematical modelling skills and mathematical skills used in solving the problems in each class. The current study is a qualitative research and the data was analyzed using descriptive analysis. The data of the study was obtained from the mathematical modelling problem written by 59 senior mathematics teachers. They were given a 1-week period to write the problems and solutions. The participants took mathematical modelling course for one semester period prior to the research. The problems are the original problems that the participants themselves produced. The mathematical modelling problems produced are categorically as follows: “Which option is more economical” problems, “Profit-making” problems, “Future prediction” problems and “Relationship between two quantities” problems. The mathematical modelling skills used are as follows: to be able to collect appropriate data, organize the data, write dependent and independent variables, write fixed values, visualize the real situation mathematically or geometrically, use mathematical concepts. The mathematical skills used are generally; to be able to do four operations with rational numbers, draw distribution and column graph, write algebraic expression, do arithmetic operation in algebraic rational expressions, write/solve equation and inequality in 1 or 2 variables, write an appropriate mathematical function explaining the data related to the data, solve 1st degree equations in 1 variable, establish proportion, use trigonometric ratios in right triangle, use basic geometry information, draw and interpret a 1st degree inequality in 2 variables.

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42

Alexander, R. McN. "Modelling approaches in biomechanics." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358, no. 1437 (August 6, 2003): 1429–35. http://dx.doi.org/10.1098/rstb.2003.1336.

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Conceptual, physical and mathematical models have all proved useful in biomechanics. Conceptual models, which have been used only occasionally, clarify a point without having to be constructed physically or analysed mathematically. Some physical models are designed to demonstrate a proposed mechanism, for example the folding mechanisms of insect wings. Others have been used to check the conclusions of mathematical modelling. However, others facilitate observations that would be difficult to make on real organisms, for example on the flow of air around the wings of small insects. Mathematical models have been used more often than physical ones. Some of them are predictive, designed for example to calculate the effects of anatomical changes on jumping performance, or the pattern of flow in a 3D assembly of semicircular canals. Others seek an optimum, for example the best possible technique for a high jump. A few have been used in inverse optimization studies, which search for variables that are optimized by observed patterns of behaviour. Mathematical models range from the extreme simplicity of some models of walking and running, to the complexity of models that represent numerous body segments and muscles, or elaborate bone shapes. The simpler the model, the clearer it is which of its features is essential to the calculated effect.

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43

Lei, Jinzhi. "Viewpoints on modelling: Comments on "Achilles and the tortoise: Some caveats to mathematical modelling in biology"." Mathematics in Applied Sciences and Engineering 1, no. 1 (February 29, 2020): 85–90. http://dx.doi.org/10.5206/mase/10267.

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Mathematical modelling has been proven to be useful in understanding some problems from biological science, provided that it is used properly. However, it has also attracted some criticisms as partially presented in a recent opinion article \cite{Gilbert2018} from biological community. This note intends to clarify some confusion and misunderstanding in regard to mathematically modelling by commenting on those critiques raised in \cite{Gilbert2018}, with a hope of initiating some further discussion so that both applied mathematicians and biologist can better use mathematical modelling and better understand the results from modelling.

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44

Pockett, Susan. "The Unreasonable Political Effectiveness of Mathematical Modelling." Journal of NeuroPhilosophy 2, no. 2 (November 23, 2023): 276–88. https://doi.org/10.5281/zenodo.10200253.

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Ever since Thomas Malthus used simple mathematics to model the evolution of food production vs the increasing human population of planet Earth and declared that we would very soon eat ourselves out of house and home, politicians have been falling hook, line and sinker for mathematical models.  This paper examines how and why the mathematical modelling of complex systems has proved unreasonably effective in convincing mathematically illiterate politicians to take practical measures that have turned out to be disastrous. It then suggests that mathematical modelling of the human brain is not a good strategy to pursue.

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Butler, George, Jonathan Rudge, and Philip R. Dash. "Mathematical modelling of cell migration." Essays in Biochemistry 63, no. 5 (October 2019): 631–37. http://dx.doi.org/10.1042/ebc20190020.

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Abstract The complexity of biological systems creates challenges for fully understanding their behaviour. This is particularly true for cell migration which requires the co-ordinated activity of hundreds of individual components within cells. Mathematical modelling can help understand these complex systems by breaking the system into discrete steps which can then be interrogated in silico. In this review, we highlight scenarios in cell migration where mathematical modelling can be applied and discuss what types of modelling are most suited. Almost any aspect of cell migration is amenable to mathematical modelling from the modelling of intracellular processes such as chemokine receptor signalling and actin filament branching to larger scale processes such as the movement of individual cells or populations of cells through their environment. Two common ways of approaching this modelling are the use of models based on differential equations or agent-based modelling. The application of both these approaches to cell migration are discussed with specific examples along with common software tools to facilitate the process for non-mathematicians. We also highlight the challenges of modelling cell migration and the need for rigorous experimental work to effectively parameterise a model.

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Weinhandl, Robert, and Zsolt Lavicza. "Real-World Modelling to Increase Mathematical Creativity." Journal of Humanistic Mathematics 11, no. 1 (January 2021): 265–99. http://dx.doi.org/10.5642/jhummath.202101.13.

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Modelling could be characterised as one of the core activities in mathematics education. However, when learning and teaching mathematics, mathematical modelling is mostly used to apply and deepen mathematical knowledge and competencies. Our educational study aims to explore how mathematical modelling, using real objects and high-quality mathematical technologies, could be utilised to acquire mathematical knowledge and competencies, and how learners could creatively use their existing knowledge. To discover the potential of mathematical modelling using real objects and high-quality mathematical technologies to acquire mathematical knowledge and competencies, and to stimulate learners' creativity, first, we combined cognitive and creative spirals and mathematical modelling cycles. Then, in a case study, we tested this combination of cognitive and creative spirals and mathematical modelling cycles in a secondary school and teacher education. Applying the combination of cognitive and creative spirals and mathematical modelling cycles, we discovered that it could be collaboration among learners and technological knowledge and skills of learners that determine whether knowledge can be acquired in mathematical modelling.

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Wilson, Peter D. G., and Jack R. Dainty. "Modelling in nutrition: An introduction." Proceedings of the Nutrition Society 58, no. 1 (February 1999): 133–38. http://dx.doi.org/10.1079/pns19990018.

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The purpose of the present paper is to provide an introduction to modelling, particularly mathematical modelling, for nutritional researchers with little or no experience of the modelling process. It aims to outline the function of modelling, and to give some guidance on factors to consider when designing protocols to generate data as part of the modelling process. It is not intended in any way to be a comprehensive guide to mathematical modelling. The paper discusses the uses of modelling, and presents a ‘hydrodynamic analogy’ to compartmental modelling, to explain the process to the non-mathematically-minded and to examine some of the pitfalls to be avoided when using stable-isotope tracers. Examples of the use of modelling in nutrition are presented, including methods for determining absorption, as well as a discussion of possible future avenues for nutritional modelling.

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Kumar, Prakash. "Mathematical Modelling and Simulating Applications." International Journal for Research in Applied Science and Engineering Technology 12, no. 1 (January 31, 2024): 1188–93. http://dx.doi.org/10.22214/ijraset.2024.58132.

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Abstract: This paper reveals the importance of mathematical modelling, its growing role and its applications. It is a myth that modelling projects progress easily from working throughto utilizing, this is scarcely ever the situation. In computer science, the use of modelling and simulating a computer is utilized to fabricate a mathematical model which contains key boundaries of the actual model. Thus, the study aims to give a basic idea of mathematical modelling, its uses, and its role in recent scenarios.

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Wei, Yicheng, Qiaoping Zhang, and Jing Guo. "Can Mathematical Modelling Be Taught and Learned in Primary Mathematics Classrooms: A Systematic Review of Empirical Studies." Education Sciences 12, no. 12 (December 14, 2022): 923. http://dx.doi.org/10.3390/educsci12120923.

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STEM education has been promoted in schools worldwide to cultivate students’ 21st-century skills. Mathematical modelling is a valuable method for developing STEM education. However, in this respect, more attention is given to secondary level or above compared with kindergarten or primary level. Teaching mathematics at the primary level is closely related to authentic problems, which is a crucial characteristic of mathematical modelling activities. After screening 239 publications from various databases, we reviewed 10 empirical studies on mathematical modelling at the primary level. In this systematic review, we analysed the following three aspects: (1) the use of professional development intervention methods/strategies to enhance the intervention effects and the competencies of primary teachers to utilize mathematical modelling; (2) the effects of mathematical modelling on primary students and methods of improving their mathematical modelling skills; and (3) methods used to assess the modelling skills of primary school teachers and students. The results indicate that professional development interventions can enhance the teaching quality of mathematical modelling. The components of the interventions should include an introduction to the pedagogy of mathematical modelling, clarifying the role of the teacher and the student in mathematical modelling activities. Through mathematical modelling, students can generate mathematical ideas, explore mathematical theorems independently, develop critical thinking, and improve their metacognitive and communicative skills. The competency of mathematical modelling is often determined using formative assessments of teachers and students. Because limitations still exist in conducting primary-level modelling activities, schools should utilise more standardised assessment methods, provide universal teacher training, and grant more opportunities for primary school students to participate in mathematical modelling activities. The lack of research on cross-cultural contexts should draw the attention of future research.

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Symak, Dmytro, Vira Sabadash, Jaroslaw Gumnitsky, and Zoriana Hnativ. "Kinetic Regularities and Mathematical Modelling of Potassium Chloride Dissolution." Chemistry & Chemical Technology 15, no. 1 (February 15, 2021): 148–52. http://dx.doi.org/10.23939/chcht15.01.148.

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Abstract (sommario):

The dissolution process of potassium chloride particles in the apparatus with two-blade mechanical stirrer was investigated and the mass transfer coefficient was determined. The experimental results were generalized by criterion dependence. The independence of the mass transfer coefficient from the solid particles diameter was confirmed. A countercurrent process of potassium salt dissolution in two apparatuses with a mechanical stirring was considered. A mathematical model for countercurrent dissolution was developed and the efficiency of this process was determined.

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