• East Asian mathematical journal
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• v.36 no.4
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• pp.437-454
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• 2020

The purpose of this study is to develop a mathematical assessment and correction materials according to the mathematics learning hierarchy. The scope of the study is set to 'function' in 7th grade of middle school. The researchers developed a draft of the mathematical assessment and correction materials based on the mathematics learning hierarchy through the pilot test and the expert review. Using the results of the expert review, the researchers modified and supplemented the math assessment and correction materials to produce the final version. The mathematics assessment and correction material developed in this study is expected to build an effective guidance system for students with mathematics deficits. In addition, by presenting a mathematical assessment and correction materials to the teachers in the field, it is possible to reduce the effort for the management of underachievers and to provide guidance for the education of students with a lack of math learning.

• Design & Manufacturing
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• v.13 no.2
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• pp.6-11
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• 2019

In this study, we constructed the mathematical model to evaluate the roundness for plastic injection mold parts with complicated 3D curvatures. Mathematically we started off from the equation of circle and successfully derived an analytical solution so as to minimize the area of the residuals. On the other hand, we employed the numerical method the similar optimization process for the comparison. To verify the mathematical models, we manufactured and used a ball valve type plastic parts to apply the derived model. The plastic parts was fabricated under the process conditions of 220-ton injection mold machine with a raw material of polyester. we experimentally measured (x, y) position using 3D contact automated system and applied two mathematical methods to evaluated the accuracy of the mathematical models. We found that the analytical solution gives better accuracy of 0.4036 compared to 0.4872 of the numerical solution. The numerical method however may give adaptiveness and versatility for optional simulations such as a fixed center.

• Proceedings of the Korean Geotechical Society Conference
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• 2004.03b
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• pp.442-449
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• 2004

This paper describes a new concept of finite element analysis, which is based on neural network based material models (NNCMs) without invoking any pre-chosen mathematical framework. NNCMs have several advantages over conventional constitutive models (CCMs) and once plugged in a finite element (FE) engine, can be used for FE analysis in a manner similar to CCMs. The paper demonstrates a FE framework in which NNCMs are incorporated and also proposes a strategy for data enhancement by invoking the assumption of isotropy of the material. It is shown through some illustrative examples that this provides a better training environment for a generalized NNCM in which stress and strain components are used as effects and cause. Form this study, it appears that there is a prima facia case for developing NNCMs for materials for which mathematical theories become too complex and a large number of material parameters and constants have to be identified or determined.

• Geomechanics and Engineering
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• v.16 no.2
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• pp.141-150
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• 2018

In this current work a quasi 3D "trigonometric shear deformation theory" is proposed and discussed for the dynamic of thick orthotropic plates. Contrary to the classical "higher order shear deformation theories" (HSDT) and the "first shear deformation theory" (FSDT), the constructed theory utilizes a new displacement field which includes "undetermined integral terms" and presents only three "variables". In this model the axial displacement utilizes sinusoidal mathematical function in terms of z coordinate to introduce the shear strain impact. The cosine mathematical function in terms of z coordinate is employed in vertical displacement to introduce the impact of transverse "normal deformation". The motion equations of the model are found via the concept of virtual work. Numerical results found for frequency of "flexural mode", mode of shear and mode of thickness stretch impact of dynamic of simply supported "orthotropic" structures are compared and verified with those of other HSDTs and method of elasticity wherever considered.

• Korean Journal of Human Ecology
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• v.20 no.4
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• pp.745-757
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• 2011

The purpose of this study was to explore status of mathematical interactions between parent and child and use of mathematical materials at home. For this purpose, questionnaires were developed. The framework of the questionnaires consisted of mathematics education content domains. 276 parents(4-5 year old children) in J Province responded to the questionnaires, which were analyzed according to the level of home income, the mother's work conditions and the mother's level of education. The results were as follows: First, between parent and child mathematical interaction at home showed a 2.84 score in average and frequency of mathematical interaction expressed in the domains of 'Understanding of regularity', 'Measurement', 'Growing number sense', 'Space and shapes', 'Organizing data and showing results'. The domains of 'Growing number sense', 'space and shapes', and 'measurement' showed significant difference only by mother's level of education. The higher the mother's level of education, the more frequent the mathematical interaction between parent and child. Second, the use of mathematical materials showed an average score of 1.18, which means mathematical materials were practically not used at home. Also, the use of mathematical materials showed a slightly significant difference when measures against the levels of home income and the mother's level of education. The results showed a significant difference in parent-child mathematical interactions, and the possession and use of mathematical materials when measures against by level of home income and the mother's work conditions. Therefore, the results of this study suggest that the parent education program for mathematical interaction to apply at home and mathematics curriculum to be connected early in childhood education institution and home should be developed for parents.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.161-185
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• 2016

We consider a mathematical model which describes the quasistatic frictional contact between a piezoelectric body and an electrically conductive obstacle, the so-called foundation. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with Signorini's conditions and a version of Coulomb's law of dry friction in which the adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation for the model, in the form of a system for the displacements, the electric potential and the adhesion. Under a smallness assumption which involves only the electrical data of the problem, we prove the existence of a unique weak solution of the model. The proof is based on arguments of time-dependent quasi-variational inequalities, differential equations and Banach's fixed point theorem.

• Journal of Computational Design and Engineering
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• v.2 no.4
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• pp.261-267
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• 2015

Free-form blades are widely used in different industries, such as aero-engine and steam turbine. Blades that are damaged during service or have production deficiencies are usually replaced with new ones. This leads to the waste of expensive material and is not sustainable. However, material and costs can be saved by repairing of locally damaged blades or blades with localized production deficiencies. The blade needs to be further machined after welding process to reach the aerodynamic performance requirements. This paper outlines an adaptive location approach of repaired blade for model reconstruction and NC machining. Firstly, a mathematical model is established to describe the localization problem under constraints. Secondly, by solving the mathematical model, localization of repaired blade for NC machining can be obtained. Furthermore, a more flexible method based on the proposed mathematical model and the continuity of the deformation process is developed to realize a better localization. Thirdly, by rebuilding the model of the repaired blade and extracting repair error, optimized tool paths for NC machining is generated adaptively for each individual part. Finally, three examples are given to validate the proposed method.

• Communications of Mathematical Education
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• v.29 no.4
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• pp.661-685
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• 2015

This study is to search for a program of professional development of mathematics teachers on the viewpoint of content knowledge of mathematics. To do this, we select algebraic subject as content knowledge for solution of polynomials and develop material for group study based on selected subject. We supply the developed material to teachers and discuss the possibility of application and the acceptability of it. For discussion, we collect data through tests and questionnaire. Through analysing the data, we obtain the positive result.

• Steel and Composite Structures
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• v.27 no.1
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• pp.27-33
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• 2018

In this study, a mixed-interpolated tensorial component 4 nodes method (MITC4) is treated as a numerical analysis model for topology optimization using multiple materials assigned within Reissner-Mindlin plates. Multi-material optimal topology and shape are produced as alternative plate retrofit designs to provide reasonable material assignments based on stress distributions. Element density distribution contours of mixing multiple material densities are linked to Solid Isotropic Material with Penalization (SIMP) as a design model. Mathematical formulation of multi-material topology optimization problem solving minimum compliance is an alternating active-phase algorithm with the Gauss-Seidel version as an optimization model of optimality criteria. Numerical examples illustrate the reliability and accuracy of the present design method for multi-material topology optimization with Reissner-Mindlin plates using MITC4 elements and steel materials.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.247-250
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• 1995

The development and empirical validation of a mathematical model for predicting the depth of deformed layer in a machined surface are presented. The main assumption for develioping this model is that there is a linear relationship between plastic strain and the depth to which it extends. The model relates the work required to shear the workpice material to the work needed to compress the workpiece material ahead of the cutting tool. The results show that the percent difference between the calculated and the measured depth of deformed layer ranges form 4 percent to 19 percent. An improvement of the model is suggested through application of actual distribution data of plastic strain.