• Structural Engineering and Mechanics
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• v.55 no.1
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• pp.1-27
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• 2015

This article presents a theoretical parametric analysis on the ultimate torsional behaviour of axially restrained reinforced concrete (RC) beams. This analysis is performed by using a computing procedure based on a modification of the Variable Angle Truss Model. This computing procedure was previously developed to account for the influence of the longitudinal compressive stress state due to the axial restraint conditions provided by the connections of the beams to other structural members. The presented parametric study aims to check the influence of some important variable studies, namely: torsional reinforcement ratio, compressive concrete strength and axial restraint level. From the results of this parametric study, nonlinear regression analyses are performed and some design charts are proposed. Such charts allow to correct the resistance torque of RC beams (rectangular sections with small height to width ratios) to account for the favorable influence of the axial restraint.

• East Asian mathematical journal
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• v.35 no.2
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• pp.199-216
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• 2019

The purpose of this study is to analyze the needs of mathematics learning program using web or application for the development of adaptive mathematics learning program. For this study, a questionnaire survey was conducted for middle school students. The results of the 290 responses were analyzed to identify students' needs for adaptive mathematics learning. As a result, learners wanted functions to design their own learning and to support self-directed learning. The results of this study are expected to be used as basic data for the development of a adaptive mathematics learning program reflecting students' needs.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.10 no.1
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• pp.1-9
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• 2006

Three categories such as the design of a machine, control and software are necessary in the development of the photomask inspection machine with high resolution. Among them, the design of a software detects inferiority through the comparison of CAD data and real data read by camera from photomask. The block matching algorithm is used since the domain is large and the comparison of data by pixel is accomplished. To correct the error arising from the assembly of a machine, calibration algorithm is used and prefocusing algorithm is suggested to correct the surface of the photomask.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.245-261
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• 1999

Proof is an essential characteristic of mathematics and as such should be a key component in mathematics education. But, teaching proof in school mathematics have been unsuccessful for many students. The traditional approach to proofs stresses formal logic and rigorous proof. Thus, most students have difficulties of the concept of proof and students' experiences with proof do not seem meaningful to them. However, different views of proof were asserted in the reassessment of the foundations of mathematics and the nature of mathematical truth. These different views of justification need to be reflected in demonstrative geometry classes. The purpose of this study is to characterize the types of students' justification in demonstrative geometry classes taught using dynamic software. The types of justification can be organized into three categories : empirical justification, deductive justification, and authoritarian justification. Empirical justification are based on evidence from examples, whereas deductive justification are based logical reasoning. If we assume that a strong understanding of demonstrative geometry is shown when empirical justification and deductive justification coexist and benefit from each other, then students' justification should not only some empirical basis but also use chains of deductive reasoning. Thus, interaction between empirical and deductive justification is important. Dynamic geometry software can be used to design the approach to justification that can be successful in moving students toward meaningful justification of ideas. Interactive geometry software can connect visual and empirical justification to higher levels of geometric justification with logical arguments in formal proof.

• The Mathematical Education
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• v.49 no.1
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• pp.67-83
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• 2010

The purpose of this study was to analyze the research trends of elementary mathematics education with regard to the topics, methods, subjects, and mathematical contents of such research. For this purpose, the papers published in domestic journals during the recent 5 years (2004-2009) were analyzed. A total of 383 papers from 8 professional journals were analyzed with the 4 criteria. First, the frequent research topics included instructional design and methods, learners' perspectives and abilities, and analysis of curriculum and textbooks in order. Second, qualitative research methodology was used twice as many as quantitative one. Whereas a survey was the most frequent quantitative research method, content analysis and case study were for qualitative methods. Third, research subjects included mainly typical students, specifically fifth and sixth graders. Papers dealing with lower graders or low-achievers as well as pre-service teachers were rare. Lastly, whereas the research on geometry as well as number and operations was active, that of measurement as well as probability and statistics was not. On the basis of these results, this paper includes several implications for the future research direction in elementary mathematics education.

• Journal of the Korea Society of Computer and Information
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• v.24 no.1
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• pp.257-263
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• 2019

This paper is a study on mathematical aspects that can be basic for understanding and applying the contents of machine learning. If you are familiar with mathematics in the field of computer science, you can create algorithms that can diversify researches and implement them faster, so you can implement many real-life ideas. There is no curriculum standard for mathematics in the field of machine learning, and there are many absolutely lacking mathematical contents that are taught in the curriculum presented at existing universities. Machine learning now includes speech recognition systems, search engines, automatic driving systems, process automation, object recognition, and more. Many applications that you want to implement combine a large amount of data with many variables into the components that the programmer generates. In this course, the mathematical areas required for computer engineer (CS) practitioners and computer engineering educators have become diverse and complex. It is important to analyze the mathematical content required by engineers and educators and the mathematics required in the field. This paper attempts to present an effective range design for the essential processes from the basic education content to the deepening education content for the development of many researches.

• Journal of the Korean School Mathematics Society
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• v.18 no.2
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• pp.223-240
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• 2015

This paper deals with how to design and develop white-box based e-learning contents which are equipped with conceptual understanding and step-by-step computational procedures for studying vector calculus for science-engineering majors who might need supplementary mathematics learning. Noting that rewriting rules are often used in school mathematics for students' problem solving, the theoretical aspects of rewriting rules are reviewed for developing supplementary e-learning contents for them. The software design of step-by-step problem solving requires careful arrangement of rewriting rules and pattern matching techniques for white-box procedures using a computer algebra system such as Mathematica. Several modules for step-by-step problem solving as well as producing dynamic display of e-learning contents was coded by Mathematica in order to find the length of a curve in vector calculus after implementing several rules for differentiation and integration. The developed contents are equipped with diagnostic modules and immediate feedback for supplementary learning in terms of a tutorial. At the end, this paper indicates the strengths and features of the developed contents for college students who need to increase math learning capabilities, and suggests future research directions.

• School Mathematics
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• v.8 no.3
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• pp.327-339
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• 2006

In this study, a teaching units for teaching and learning of secondary preservice teachers' mathematising is designed, focusing on reinvention of Bretschneider's formula. preservice teachers can obtain the following through this teaching units. First, preservice teachers can experience mathematising which invent a noumenon which organize a phenomenon, They can make an experience to invent Bretscheider's formula as if they invent mathematics really. Second, preservice teachers can understand one of the mechanisms of mathematics knowledge invention. As they reinvent Brahmagupta's formula and Bretschneider's formula, they understand a mechanism that new knowledge is invented Iron already known knowledge by analogy. Third, preservice teachers can understand connection between school mathematics and academic mathematics. They can understand how the school mathematics can connect academic mathematics, through the relation between the school mathematics like formulas for calculating areas of rectangle, square, rhombus, parallelogram, trapezoid and Heron's formula, and academic mathematics like Brahmagupta's formula and Bretschneider's formula.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.265-275
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• 2004

In this paper, multi-objective models for designing 3D trajectory of horizontal wells are developed in a fuzzy environment. Here, the objectives of minimizing the length of the trajectory and the error of entry target point are fuzzy in nature. Some parameters, such as initial value, end value, lower bound and upper bound of the curvature radius, tool-face angle and the arc length of each curve section, are also assumed to be vague and imprecise. The impreciseness in the above objectives have been expressed by fuzzy linear membership functions and that in the above parameters by triangular fuzzy numbers. Models have been solved by the fuzzy non-linear programming method based on Zimmermann [1] and Lee and Li [2]. Models are applied to practical design of the horizontal wells. Numerical results illustrate the accuracy and efficiency of the fuzzy models.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.405-413
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• 2004

Rational parameterization of curves and surfaces is one of the main topics in computer-aided geometric design because of their computational advantages. Pythagorean hodograph (PH) curves and Minkowski Pythagorean hodograph (MPH) curves have attracted many researcher's interest because they provide for rational representation of their offset curves in Euclidean space and Minkowski space, respectively. In [10], Kim presented the characterization of the PH curves in the Euclidean space and analyzed the relation between the class of PH curves and the class of rational curves. In this paper, we extend the characterization of PH curves in [10] into that of MPH curves in the general Minkowski space and consider some generalized MPH curves satisfying this characterization.