• The Mathematical Education
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• v.54 no.1
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• pp.65-81
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• 2015

The purpose of this study is to investigate the international trends of how the core competencies are reflected in mathematics curriculum, and to find the implications for the revision of Korean mathematics curriculum. For this purpose, the curriculum of the 9 countries including the U.S., Canada(Ontario), England, Australia, Poland, Singapore, China, Taiwan, and Hong Kong were thoroughly reviewed. It was found that a variety of core competencies were reflected in mathematics curricula in the 9 countries such as problem solving, reasoning, communication, mathematical knowledge and skills, selection and use of tools, critical thinking, connection, modelling, application of strategies, mathematical thinking, representation, creativity, utilization of information, and reflection etc. Especially the four most common core competencies (problem solving, reasoning, communication, and creativity) were further analyzed to identify their sub components. Consequently, it was recommended that new mathematics curriculum should consider reflecting various core competencies beyond problem solving, reasoning, and communication, and these core competencies are supposed to combine with mathematics contents to increase their feasibility. Finally considering the fact that software education is getting greater attention in the new curriculum, it is necessary to incorporate computational thinking into mathematics curriculum.

• Structural Engineering and Mechanics
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• v.21 no.5
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• pp.539-551
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• 2005

Finite elements based on isoparametric formulation are known to suffer spurious stiffness properties and corresponding stress oscillations, even when care is taken to ensure that completeness and continuity requirements are enforced. This occurs frequently when the physics of the problem requires multiple strain components to be defined. This kind of error, commonly known as locking, can be circumvented by using reduced integration techniques to evaluate the element stiffness matrices instead of the full integration that is mathematically prescribed. However, the reduced integration technique itself can have a further drawback - rank deficiency, which physically implies that spurious energy modes (e.g., hourglass modes) are introduced because of reduced integration. Such instability in an existing stiffness matrix is generally detected by means of an eigenvalue test. In this paper we show that a knowledge of the dimension of the solution space spanned by the column vectors of the strain-displacement matrix can be used to identify the instabilities arising in an element due to reduced/selective integration techniques a priori, without having to complete the element stiffness matrix formulation and then test for zero eigenvalues.

• Coupled systems mechanics
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• v.10 no.1
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• pp.1-19
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• 2021

Composite nature of the masonry structures in general causes complex and non-linear behaviour, especially in intense vibration conditions. The presence of different types and forms of structural elements and different materials is a major problem for the analysis of these type of structures. For this reason, the analysis of the behaviour of masonry structures requires a combination of experimental tests and non-linear mathematical modelling. The famous UNESCO Heritage Old Bridge in Mostar was selected as an example for the analysis of the global behaviour of reinforced stone arch masonry bridges. As part of the experimental research, a model of the Old Bridge was constructed in a scale of 1:9 and tested on a shaking table platform for different levels of seismic excitation. Non-linear mathematical modelling was performed using a combined finite-discrete element method (FDEM), including the effect of connection elements. The paper presents the horizontal displacement of the top of the arch and the failure mechanism of the Old Bridge model for the experimental and the numerical phase, as well as the comparison of the results. This research provided a clearer insight into the global behaviour of stone arch masonry structures reinforced with steel clamps and steel dowels, which is significant for the structures classified as world cultural heritage.

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.657-677
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• 2014

The present qualitative case study explored the ways in which three middle school students constructed and refined their mathematical models and modeling processes, and factors that had influenced such refinement. The results suggest that students' modeling processes are non-sequential in that the participant students reformulated their initial problem from the real-world problem situation and revised the model when they could not get a satisfactory solution or the acquired solution did not make sense. Moreover, the students' model refinement processes were affected by the following four elements: the types of real-word problem situations, students' metacognitive thinking, communications between teachers and peers, and the role of teachers.

• Proceedings of the Korea Institute of Fire Science and Engineering Conference
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• 1997.11a
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• pp.112-119
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• 1997

The modelling of carbon substances obtaining, for instance, carbon fibers which have high fire resistance, has been realized on the example of the polyacrylonitrile pyrolysis modelling. The pyrolysis is considered as a double step process when the formation of a liquid phase and the oxidation of substance are excluded. Three main reactions are considered: a) with the evolution of ammonia; b) with the evolution of hydrogen cyanide; c) with the evolution of hydrogen. Reactions b) and c) are sequential, and a) and b) are parallel. The problem is formulated as one-dimensional. The equations of energy, masses or concentrations, porosity and thermal conductivity are proposed. The mathematical model of the carbonization process is designed using tile kinetic characteristics of the above reactions and the thermodynamic parameters of reagents and products in these reactions. The equations received are calculated by Runge-Cutta method and by Adams method of the fourth order accuracy.

• Communications of Mathematical Education
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• v.28 no.3
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• pp.423-429
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• 2014

It is necessary to realize in advance the lessons and knowhow about how to live, which humankind have developed, through learning to decrease the number of trial and error in our first trip to life. The big problem that present mathematical education is faced with is just only to place much importance on doing microscopic research ignoring macroscopic perspective, which results in the ineffectiveness of mathematics for contributing to life. The purpose of present study is to examine the way of living, classify methods of gaining an insight into life using macroscopic perspective, and develop a life model which can suggest a way of gaining an insight into life from external perspective. Also, this study explores a way of building a creative mathematical model for effective insight about life.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2009.11a
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• pp.459-468
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• 2009

Analysis of the uncertainty to have engineering solution of gas-dynamic and hydrodynamic problems is based on the comparison the prospective engineering solution with experimental result. In this paper, the mathematical model to estimate heat flux along gas-dynamic channel wall and the solution sequence are shown. Statistical information and generalizing experimental characteristics about gas- and hydro-dynamic channels were applied to the mathematical model. As the results, it is possible to draw a conclusion that models of the integrated approach, using the averaged statistical data of generalizing characteristics for a turbulent flow, without consideration of the turbulent mechanism (characteristic pulsations), can predict a nominal operating regime for gas-dynamic and hydrodynamic systems. The probable deviation of operating regime for newly designed the gas-dynamic channel can achieve 20% from a regime predicted on a basis 1-D or 3-D modelling irrespective of a kind of used models.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.125-135
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• 1992

In various viscus flow problems it has been the custom to replace the convective derivative by the ordinary partial derivative in problems for which the data are small. In this paper we consider the Benard Convection problem with small data and compare the solution of this problem (assumed to exist) with that of the linearized system resulting from dropping the nonlinear terms in the expression for the convective derivative. The objective of the present work is to derive an estimate for the error introduced in neglecting the convective inertia terms. In fact, we derive an explicit bound for the L$_{2}$ error. Indeed, if the initial data are O(.epsilon.) where .epsilon. << 1, and the Rayleigh number is sufficiently small, we show that this error is bounded by the product of a term of O(.epsilon.$^{2}$) times a decaying exponential in time. The results of the present paper then give a justification for linearizing the Benard Convection problem. We remark that although our results are derived for classical solutions, extensions to appropriately defined weak solutions are obvious. Throughout this paper we will make use of a comma to denote partial differentiation and adopt the summation convention of summing over repeated indices (in a term of an expression) from one to three. As reference to work of continuous dependence on modelling and initial data, we mention the papers of Payne and Sather [8], Ames [2] Adelson [1], Bennett [3], Payne et al. [9], and Song [11,12,13,14]. Also, a similar analysis of a micropolar fluid problem backward in time (an ill-posed problem) was given by Payne and Straughan [10] and Payne [7].

• Smart Structures and Systems
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• v.22 no.3
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• pp.259-276
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• 2018

This paper studies the energies and energy release rate (ERR) for the initially rotationally symmetric compressed (or stretched) in the inward (outward) radial direction of the PZT/Elastic/PZT sandwich circular plate with interface penny-shaped cracks. The investigations are made by utilizing the so-called three-dimensional linearized field equations and relations of electro-elasticity for piezoelectric materials. The quantities related to the initial stress state are determined within the scope of the classical linear theory of piezoelectricity. Mathematical formulation of the corresponding problem and determination of the quantities related to the stress-strain state which appear as a result of the action of the uniformly normal additional opening forces acting on the penny-shaped crack's edges are made within the scope of the aforementioned three-dimensional linearized field equations solution which is obtained with the use of the FEM modelling. Numerical results of the energies and ERR and the influence of the problem parameters on these quantities are presented and discussed for the PZT- 5H/Al/PZT-5H, PZT-4/Al/PZT-4, $BaTiO_3/Al/BaTiO_3$ and PZT-5H/StPZT-5H sandwich plates. In particular, it is established that the magnitude of the influence of the piezoelectricity and initial loading on the ERR increases with crack radius length.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.227-245
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• 2011

In this paper, we introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a ${\beta}$inverse-strongly monotone mapping and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Ces$\`{a}$ro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mind conditions. Our results improve and extend the corresponding results of Kumam and Katchang [A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mapping, Nonlinear Analysis: Hybrid Systems, 3(2009), 475-86], Peng and Yao [Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems, Mathematical and Computer Modelling, 49(2009), 1816-828], Shimizu and Takahashi [Strong convergence to common fixed points of families of nonexpansive mappings, Journal of Mathematical Analysis and Applications, 211(1) (1997), 71-83] and some authors.