• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.605-620
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• 1998

This paper suggested a geometry learning model which relates an exploratory learning model with GSP applications, Such a model adopts GSP's capability of visualizing dynamic geometric figures and exploratory learning method's advantages of discovering properties and relations of geometric problem proving and concepts associated with geometric inferencing of students. The research was conducted for 3 middle school students by applying the proposed model for 6times at computer laboratory. The overall procedure was videotaped so that the collected data was later analyzed by qualitative methodology. The analysis indicated that the students with less than van Hiele 4 level took advantages of adoption our proposed model to gain concrete understandings of geometric principles and concepts with GSP. One of the lessons learned from this study suggested that the roles of students and a teacher who want to employ the proposed model need to change their roles respectively.

• Computers and Concrete
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• v.32 no.6
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• pp.543-551
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• 2023

In this article, thermal post-buckling and primary resonance of the porous functionally graded material (FGM) beams in thermal environment considering the geometric imperfection are studied, the material properties of FGM beams are assumed to vary along the thickness of the beam, meanwhile, the porosity volume fraction, geometric imperfection, temperature, and the elastic foundation are considered, using the Euler-Lagrange equation, the nonlinear vibration equations are derived, after the dimensionless processing, the dimensionless equations of motion can be obtained. Then, the two-step perturbation method is applied to solve the vibration problems, the resonance and thermal post-buckling response relations are obtained. Finally, the functionally graded index, the porosity volume fraction, temperature, geometric imperfection, and the elastic foundation on the resonance behaviors of the FGM beams are presented. It can be found that these parameters can influence the thermal post-buckling and primary resonance problems.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.2
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• pp.57-66
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• 2024

In this paper, we study how the Hilbert polynomial, associated with a reduced closed subscheme X of codimension 2 in ℙ^N, reveals geometric information about X. Although it is known that the Hilbert polynomial can tell us about the scheme's degree and arithmetic genus, we find additional geometric information it can provide for smooth varieties of codimension 2. To do this, we introduce the concept of Gotzmann coefficients, which helps to extract more information from the Hilbert polynomial. These coefficients are based on the binomial expansion of values of the Hilbert function. Our method involves combining techniques from initial ideals and partial elimination ideals in a novel way. We show how these coefficients can determine the degree of certain geometric features, such as the singular locus appearing in a generic projection, for smooth varieties of codimension 2.

• 연구논문집
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• s.23
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• pp.45-56
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• 1993

In order to acquire more comprehensive understanding of textile composites, the processing-microstructure-performance relationships for a variety of material systems, reinforcing schemes and processing technologies should be established. In this paper, emphasis is placed on the integrated analysis of three-dimensional (3-D) 2-step braided composites. The analysis includes the geometric model of unit cells, identification of key process parameters and processing windows due to limiting geometries of yarn jamming, and prediction of elastic constants of the composite. The coordinate transformation and averaging of stiffness and compliance constants are utilized in the prediction of elastic constants. Since there are several types of unit cells in the thickness and width directions of the composites, characterization of mechanical properties is based upon the macro-cell, which occupies the entire cross-section and the unit pitch length of the sample. The performance map demonstrates that a wide range of elastic properties can be achieved by varying the geometric and process parameters.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.521-533
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• 2019

In this paper, we define a mean of two positive numbers called the k-golden mean and study some properties of it. Especially, we show that the 2-golden mean refines the harmonic and the geometric means. As an application, we define the k-golden ratio and give some properties of it as an generalization of the golden ratio. Furthermore, we define the matrix k-golden mean of two positive-definite matrices and give some properties of it. This is an improvement of Lim's results [2] for which the matrix golden mean.

• Geomechanics and Engineering
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• v.35 no.4
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• pp.425-436
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• 2023

An effective tool for researching actual problems in geotechnical and mining engineering is to conduct physical modeling tests using similar materials. A reliable geometric scaled model test requires selecting similar materials and conducting tests to determine physical properties such as the mixing ratio of the mixed materials. In this paper, a method is proposed to determine similar materials that can reproduce target properties using a polynomial model based on experimental results on modeling materials using a gypsum-sand mixture (GSM) to simulate rocks. To that end, a database is prepared using the unconfined compressive strength, elastic modulus, and density of 459 GSM samples as output parameters and the weight ratio of the mixing materials as input parameters. Further, a model that can predict the physical properties of the GSM using this database and a polynomial approach is proposed. The performance of the developed method is evaluated by comparing the predicted and observed values; the results demonstrate that the proposed polynomial model can predict the physical properties of the GSM with high accuracy. Sensitivity analysis results indicated that the gypsum-water ratio significantly affects the prediction of the physical properties of the GSM. The proposed polynomial model is used as a powerful tool to simplify the process of determining similar materials for rocks and conduct highly reliable experiments in a physical modeling test.

• Journal of Computational Design and Engineering
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• v.3 no.4
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• pp.385-397
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• 2016

Scaffolds are essential in bone tissue engineering, as they provide support to cells and growth factors necessary to regenerate tissue. In addition, they meet the mechanical function of the bone while it regenerates. Currently, the multiple methods for designing and manufacturing scaffolds are based on regular structures from a unit cell that repeats in a given domain. However, these methods do not resemble the actual structure of the trabecular bone which may work against osseous tissue regeneration. To explore the design of porous structures with similar mechanical properties to native bone, a geometric generation scheme from a reaction-diffusion model and its manufacturing via a material jetting system is proposed. This article presents the methodology used, the geometric characteristics and the modulus of elasticity of the scaffolds designed and manufactured. The method proposed shows its potential to generate structures that allow to control the basic scaffold properties for bone tissue engineering such as the width of the channels and porosity. The mechanical properties of our scaffolds are similar to trabecular tissue present in vertebrae and tibia bones. Tests on the manufactured scaffolds show that it is necessary to consider the orientation of the object relative to the printing system because the channel geometry, mechanical properties and roughness are heavily influenced by the position of the surface analyzed with respect to the printing axis. A possible line for future work may be the establishment of a set of guidelines to consider the effects of manufacturing processes in designing stages.

• Communications of the Korean Mathematical Society
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• v.4 no.1
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• pp.173-185
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• 1989

• East Asian mathematical journal
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• v.17 no.2
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• pp.319-323
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• 2001

• Honam Mathematical Journal
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• v.9 no.1
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• pp.57-69
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• 1987