• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.39-69
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• 2004

This paper investigates the teaching and learning of Linear function relating functional contexts and suggests the improved methods of representation-shift through this analysis. The methods emphasize the link between students' preacquired knowledge of mathematical representations and the way of using those. This methods are explanatory teaching, teaching and teaming based on modelling perspectives or tasks (interpretation, prediction, translation and scaling). We categorize the 8th grade middle school students' errors on the linear function relating real contexts and make a comparative study of the error-remedial effects and the teaching and teaming methods. We present the results of a study in which representation-shift methods based on modelling perspectives and tasks are more effective in terms of flexible connection of representations and error remediation. Also, We describe how students used modelling perspective-taking to explain and justify their conceptual models, to assess the quality of their models and to make connection to other mathematical representation during the problem solving focusing on the students' self-diagnosis.

• International Journal of Computer Science & Network Security
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• v.21 no.7
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• pp.211-220
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• 2021

The aim of the study is to implement a factor analysis of the determinants of pricing in a state-regulated competitive market using economic and mathematical modelling methods and to develop ways to improve the pricing environment of the market under study. The purpose of the work defines the main objectives: (i) to investigate the features of the competitive model of the Ukrainian flour market; (ii) to analyse the current price conjuncture of the flour market and the dynamics of the main determinants of pricing; (iii)to develop ways of improving the price situation on the flour market on the basis of the factor analysis on the results of economic and mathematical modelling. In order to ensure the reliability and validity of the research results, the following methods were applied: the logical-dialectical method of scientific knowledge in the study of the main theoretical aspects of flour market functioning, the method of logical generalisation and synthesis, comparison, factor analysis, correlation and regression analysis, the graphical method, etc. It has been shown that pricing in a state-regulated competitive market has its own characteristics. For example, in the flour market the price of goods cannot be influenced by producers (sellers) by any methods, therefore determinants of pricing by indirect influence have been taken into account. The five-factor power model of wheat flour price has been constructed. It was substantiated that the price of wheat flour in Ukraine is mostly influenced by consumer price index (0.92 %). The received complex model of wheat flour price may be used also for medium-term forecasting and working out the ways of price formation optimization in the flour market.

• Proceedings of the Korean Society for Agricultural Machinery Conference
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• 1996.06a
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• pp.170-173
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• 1996

• Proceedings of the Korean Society of Life Science Conference
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• 2004.10a
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• pp.30-32
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• 2004

• East Asian mathematical journal
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• v.37 no.1
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• pp.141-147
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• 2021

In [1], we studied the PDE system with time-varing delay. Time delay occurs due to loosening in a high-speed moving axially directed membrane (string, belt, or plate) at production. Our purpose in this work derives a mathematical model with internal time delay. First, we consider the physical phenomenon of axially moving membrane with respect to kinetic energy, potential energy and work done. By the energy conservation law in physics, we get the second order nonlinear PDE system with internal time delay.

• Applied Science and Convergence Technology
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• v.23 no.5
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• pp.240-247
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• 2014

Modelling and measurements of normal and lateral stiffness for atomic force microscopy (AFM) are presented in this work. Important issues, such as element discretisation, stiffness calibration, and deflection angle are explored using the finite element (FE) model. Elements with various dimension ratios are investigated and comparisons with several mathematical models are reported to verify the accuracy of the model. Investigation of the deflection angle of a cantilever is also shown. Moreover, AFM force measurement experiments with conical and colloid probe tips are demonstrated. The relationships between force and displacement, required for stiffness measurement, in normal and lateral directions are acquired for the conical tip and the limitations of the colloid probe tip are highlighted.

• Advances in Computational Design
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• v.8 no.2
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• pp.179-190
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• 2023

In this paper, building information modelling (BIM) associated to the principle of significant items emerged at quantities and costs in the optimization of productivity related to the rehabilitation of the building where proposed and discussed. A quantitative and qualitative study related to the field of application based on some parameters such as pathology diagnosis, projects documents and bills of quantities were used for model development at the preliminary stage of this work. The study identified 14 quantities significant items specified to cost value based on the use of the 80/20 Pareto rule, through the integration of building information modelling (BIM) in the optimisation of labour productivity for rehabilitation of buildings. The results of this study reveal the reliability and the improvement of labour productivity using building information modelling process integrating quantities and cost significant items.

• Journal of Educational Research in Mathematics
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• v.20 no.1
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• pp.73-84
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• 2010

Mathematical modeling is an important part of mathematics education since it can be used or created to find mathematical models to understand real life various situations. Most of mathematical modeling tasks taught and learned currently in secondary school mathematics classes need simple mathematical modelling with one or two variables and produce fixed solutions to the real life problems. But many real life problems involve various and complex variables which can be used to get more proper solutions. Constructing mathematical models to get more appropriate solutions from the real problems having various and complex variables is not easy. In this paper the researcher suggested a model to fit mathematical models to get more appropriate solutions and showed three examples to apply the model in solving real life problems which can be treated in the secondary school mathematics classrooms.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1095-1106
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• 2020

The purpose of this paper is to introduce a new class of rings that is closely related to the class of pseudo-Krull domains. Let 𝓗 = {R | R is a commutative ring and Nil(R) is a divided prime ideal of R}. Let R ∈ 𝓗 be a ring with total quotient ring T(R) and define 𝜙 : T(R) → R_Nil(R) by ${\phi}({\frac{a}{b}})={\frac{a}{b}}$ for any a ∈ R and any regular element b of R. Then 𝜙 is a ring homomorphism from T(R) into R_Nil(R) and 𝜙 restricted to R is also a ring homomorphism from R into R_Nil(R) given by ${\phi}(x)={\frac{x}{1}}$ for every x ∈ R. We say that R is a 𝜙-pseudo-Krull ring if 𝜙(R) = ∩ R_i, where each R_i is a nonnil-Noetherian 𝜙-pseudo valuation overring of 𝜙(R) and for every non-nilpotent element x ∈ R, 𝜙(x) is a unit in all but finitely many R_i. We show that the theories of 𝜙-pseudo Krull rings resemble those of pseudo-Krull domains.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.2
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• pp.89-95
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• 1999

This study investigates the population model of the spread of HIV/AIDS which the infection is generated by an infectious individual in a population of susceptible. A mathematical model is presented for the transmission dynamics of HIV infection within the communities of homosexual males. The pattern on the epidemic character of HIV, the causative agent of AIDS, was analysed by the mathematical model of AIDS system which is derived according to the ecological relationship between five epidemilogic states of individuals. The computer simulation was performed using real data and the following conclusions are drawn on the basis of the simulations. 1. The model structure and the algorithm described n the thesis is good. 2. In proportion to increase Ro, the population of AIDS patient increases and the time of its widespread reaches earlier. 3. The AIDS patients will be maximum between 7 and 21 years after an attack of AIDS and widespread between 10 and 20 years. 4. Considering the properties of the incubation periods, the maximum number of infected person is increased, and the attack rate is decreased.