• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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• pp.31-40
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• 2007

What is the "new paradigm"? It is impossible express it in one or two words, but if one had to; the closest might be the "holistic approach". The expression can be justified by the fact that the conclusions above lead to a greater intermixing of mathematics with engineering and natural sciences subjects, typically expressed in the form of examples of simplified real problems. They also lead to a greater intermixing of subjects within mathematics so that the courses should have less separation e.g. between symbolic and numerical mathematics. The conclusions also lead to the spreading the mathematics courses throughout all study years, not just the first two years. Of course, this should be done with great care in order to guarantee studies that are logically linked together. The new paradigm also means that the needs arising from industrial mathematics must be taken into account in the contents of engineering mathematics courses. Such topics are e.g. multivariate methods, statistics and use of mathematical software. What are we expected to gain from the paradigm shift? The primary benefit should be in obtaining more productive engineers equipped with a better degree of mathematical preparedness for engineering problems. But in addition, it should also promote more intensive use of applied mathematics and easier communication with professional mathematicians, often needed in complicated industrial problems.?Finally, it can be noted that the new paradigm is in harmony with the basic ideas of the CDIO (Conceive - Design - Implement - Operate) initiative for producing the next generation of engineers [1]. New ideas for engineering education can be found also in the homepage of SEFI (European Society for Engineering Education) [2].

• The Mathematical Education
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• v.52 no.2
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• pp.191-201
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• 2013

The theory of embodied cognition assumes that behaviors, senses and cognitions are closely connected, and there is a growing interest in investigating the significance of embodied cognition in the field of mathematics education. This study aims to applicate the embodied turtle metaphor and expressions when students visualize three-dimensional objects. We used MRT(Verdenberg & Kuse, 1978) & SVT for this research and both tests turned out that turtle schemes are useful to the students in a low level group. In addition, students found turtle schemes more useful in SVT which requires constructing three-dimensional objects, than in MRT which requires just rotating the image of three-dimensional objects in their mind. These results suggest that providing students who are less capable of spatial visualizing with the embodied schemes like turtle metaphor and expressions can be an alternative to improve their spatial visualization ability.

• Journal of The Korean Association of Information Education
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• v.22 no.1
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• pp.159-167
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• 2018

In this study, we have developed an online learning community site using Humhub social network software and promote social constructive learning through the questions and answers in subject specific learning groups. By accumulating learning contents which consist of questions and answers about specific topics, learners can acquire knowledge by searching relevant topics and questions and can create and reconstruct knowledge as well as consuming knowledge by participating in self-regulated learning community. We have developed a mathematical editor feature which enables users to enter mathematical expression such as equations and greek characters. Online learning community sites can be used for inquiry based information education.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.183-197
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• 2021

Recently several authors have extended the Beta function by using its integral representation. However, in many cases no expression of these extended functions in terms of classic special functions is known. In the present paper, we introduce a further extension by defining a family of functions G_r,s : ℝ^*₊ → ℂ, with r, s ∈ ℂ and ℜ(r) > 0. For given r, s, we prove that this function satisfies a second-order linear differential equation with rational coefficients. Solving this ODE, we express G_r,s as a combination of confluent hypergeometric functions. From this we deduce a new integral relation satisfied by Tricomi's function. We then investigate additional specific properties of G_r,1 which take the form of new non trivial integral relations involving exponential and error functions. We discuss the connection between G_r,1 and Stokes' first problem (or Rayleigh problem) in fluid mechanics which consists in determining the flow created by the movement of an infinitely long plate. For $r{\in}{\frac{1}{2}}{\mathbb{N}}^*$, we find additional relations between G_r,1 and Hermite polynomials. In view of these results, we believe the family of extended beta functions G_r,s will find further applications in two directions: (i) for improving our knowledge of confluent hypergeometric functions and Tricomi's function, (ii) and for engineering and physics problems.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.1-22
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• 2023

Let L(s, χ) be the Dirichlet L-series associated with an f-periodic complex function χ. Let P(X) ∈ ℂ[X]. We give an expression for ∑^f_n=1 χ(n)P(n) as a linear combination of the L(-n, χ)'s for 0 ≤ n < deg P(X). We deduce some consequences pertaining to the Chowla hypothesis implying that L(s, χ) > 0 for s > 0 for real Dirichlet characters χ. To date no extended numerical computation on this hypothesis is available. In fact by a result of R. C. Baker and H. L. Montgomery we know that it does not hold for almost all fundamental discriminants. Our present numerical computation shows that surprisingly it holds true for at least 65% of the real, even and primitive Dirichlet characters of conductors less than 10⁶. We also show that a generalized Chowla hypothesis holds true for at least 72% of the real, even and primitive Dirichlet characters of conductors less than 10⁶. Since checking this generalized Chowla's hypothesis is easy to program and relies only on exact computation with rational integers, we do think that it should be part of any numerical computation verifying that L(s, χ) > 0 for s > 0 for real Dirichlet characters χ. To date, this verification for real, even and primitive Dirichlet characters has been done only for conductors less than 2·10⁵.

• Journal of the Korean School Mathematics Society
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• v.8 no.1
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• pp.101-116
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• 2005

The purpose of this study is to survey mathematics teacher's cognition of proof along with their proof forms of expression and proof ability, and to explore the relationship between their proof scheme and teaching practice. This study shows that mathematics teachers tend to regard proof as a deduction from assumption to conclusion and that they prefer formal proof with mathematical symbols. Mathematics teachers also recognize that prof is an important area in school mathematics but they reveal poor understanding of teaching methods of proof. Teachers tend to depend on the proof style employed in mathematics textbooks. This study demonstrates that a proof scheme is a major factor of determining the teaching method of proof.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.6
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• pp.19-24
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• 1998

In this paper, a new closed form expression for the average symbol error rate(SER) of generalized selection combining(SC), whereby the two(three) signals with the two(three) largest amplitudes are combined from the original diversity branches in the channel, for MPSK signals in a frequency-nonselective slowly m-distributed Nakagami fading channel is derived. In order to analyze the error performance for a generalized SC, the Order-Statistics is applied. To derive the SER of MPSK signals with SC, the new expression of pdf is introduced and many other mathematical methods are used. Comparing the derived SER with that of MRC, we find adequate diversity branch number from total Lth-order diversity branches.

• Education of Primary School Mathematics
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• v.12 no.2
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• pp.117-132
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• 2009

The purpose of this study was analysis on types of strategies and errors when the sixth grade students were solving proportion problems of mathematics textbooks. For this study, proportion problems in mathematics textbooks were investigated and 17 representative problems were chosen. The 277 students of two elementary schools solved the problems. The types of strategies and errors in solving proportion problems were analyzed. The result of this study were as follows; The percentage of correct answers is high if the problems could be solved by proportional expression and the expression is in constant rate. But the percentage of correct answers is low, if the problems were expressed with non-constant rate.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.13 no.1
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• pp.47-52
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• 2002

It was virtually declared that measurement science must abandon the error analysis of measurement when ISO had published "Guide to Expression of uncertainty in Measurement" International inclination of measurement field in order to guarantee the traceability and confidence of measurement results discards the error concept and instead analyzes the measurement uncertainty. In this paper we establish a mathematical model of measurement and analyze all uncertainty factors as possible as for yielding the measurement uncertainty in the course of the calibration of RF multimeter using Transfer Standard, Thermal Voltage Converter We produce the expanded uncertainty by analyzing cable effects, correlation of thermocoupler and DC meter, DC source, RF source, attenuator, reflection coefficients and DUT.s and DUT.

• Korean Institute of Interior Design Journal
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• v.17 no.3
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• pp.156-164
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• 2008

Through staggering advancements of technology and network as we know them as digital revolution, we have established a foundation of space in which we can express reality by eliminating the boundaries between expression, space, and movement. There are many ongoing approaches that aim to overcome the physically-fixed property of space where the mathematical-geometric notion of Voronoi Diagram is one of them. Although the repetitive increment based on self-organization during the process in which space is generated by the Voronoi Diagram forms a pattern and focuses on the formation, its pattern is not restricted to a single method of expression but evolves over self-control. The result of having analyzed spaces generated by the Voronoi Diagram in this study can be summarized as follows. First, the Voronoi computation method with self-organization property creates multiple levels, increments, and evolves through feedbacks among changes with the slightest order and in the absence of control. Secondly, after forming a pattern through such feedbacks comes the differentiation phase due to the presence of different properties. Thirdly, a space that has gone through the generation process retransforms through active interaction between changes and it obtains ambiguous boundaries and a repetitive pattern. This leads to an evolution of space through repetitive increments based on self-organization. Such flexible space creation is supported by various digital technologies where we believe a converging application of these studies, sciences, engineering concepts, and space design is and effective and new method in terms of space creation.