• Journal of the Korean Mathematical Society
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• v.61 no.3
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• pp.461-494
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• 2024

We prove the Sobolev continuity of maximal commutator and its fractional variant with Lipschitz symbols, both in the global and local cases. The main result in global case answers a question originally posed by Liu and Wang in [29].

• Journal of the Korea Academia-Industrial cooperation Society
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• v.10 no.12
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• pp.3702-3707
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• 2009

In this paper, a new approximated MAP algorithm for soft bit decision from QAM symbols is proposed for Gray Coded QAM signals, based on the Max-Log-MAP and a Gray coded QAM signal can be separated into independent two Gray coded PAM signal, M-PAM on I axis with M symbols and N-PAM on Q axis with N symbols. The Max-Log-MAP used distance comparisons between symbols to get the soft bit decision instead of mathematical exponential or logarithm functions. But in accordance with the increase of the number of symbols, the number of comparisons also increase with high complexity. The proposed algorithm is used with the Euclidean distance and constituted with plain arithmetic functions, thus we can know intuitively that the algorithm has low implementing complexity comparing to conventional ones.

• The Journal of Korean Association of Computer Education
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• v.3 no.1
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• pp.65-74
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• 2000

Based on recent fast development of computer and telecommunication technologies, the Distance Education System(DES) was introduced and utilized widely in the area of education. For an immediate and fluent communication between the teacher and the student under DES, the chatting subsystem was effectively used. However, the current chatting systems are not able to receive and transmit the mathematical symbols despite their indispensability in the process of problem and solution setting under remote mathematical education. In this study, thus, Equation Chatting System that can receive and send the mathematical symbols under the graphical user interface was designed and implemented.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.287-304
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• 2017

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] by means of the incomplete Pochhammer symbols $({\lambda};{\kappa})_{\nu}$ and $[{\lambda};{\kappa}]_{\nu}$, we first introduce incomplete Fox-Wright function. We then define the families of incomplete extended Hurwitz-Lerch Zeta function. We then systematically investigate several interesting properties of these incomplete extended Hurwitz-Lerch Zeta function which include various integral representations, summation formula, fractional derivative formula. We also consider an application to probability distributions and some special cases of our main results.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.349-361
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• 2002

The ill-posed elliptic wave propagation problems can be transformed into well-posed initial value problems of the reflection and transmission operators characterizing the material structure of the given model by the combination of wave field splitting and invariant imbedding methods. In general, the derived scattering operator equations are of first-order in range, nonlinear, nonlocal, and stiff and oscillatory with a subtle fixed and movable singularity structure. The phase space and path integral analysis reveals that construction and reconstruction algorithms depend crucially on a detailed symbol analysis of the scattering operators. Some information about the singularity structure of the scattering operator symbols is presented and analyzed in the transversely homogeneous limit.

• Journal for History of Mathematics
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• v.31 no.3
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• pp.127-150
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• 2018

In spite of important researches and translational works of the Joseon mathematical treatises in the 80's and on, these results were almost out of reach to the school teachers as well as students due to the antiquity of their contents and the terms used. In order to make our traditional mathematics approachable to the middle and high school students, it will be educationally meaningful to reinterpret them tuned at the student's level using modern terminology and symbols. In this study, we reinterpreted 9 problems from Cheukryang Dohae, which is one of the representative mathematical books of Joseon Dynasty. We used the terminology and symbols from the school curriculum. We also reconstructed two of them using modern metrologies adapted to modern situations adding illustrations and photos, so that they are useful at the teaching site.

• Journal for History of Mathematics
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• v.28 no.4
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• pp.167-179
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• 2015

We study the solution of truncated series of Lee Sang-hyeog with the aspect of visualization. Lee Sang-hyeog solved a problem of truncated series by 4 ways: Shen Kuo' series method, splitting method, difference sequence method, and Ban Chu Cha method. As the structure and solution of truncated series in tertiary number is already clarified with algebraic symbols in some previous research, we express and explain it by visual representation. The explanation and proof of algebraic symbols about truncated series is clear in mathematical aspects; however, it has a lot of difficulties in the aspects of understanding. In other words, it is more effective in the educational situations to provide algebraic symbols after the intuitive understanding of structure and solution of truncated series with visual representation.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1137-1147
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• 2018

In this paper, we discovered a sufficient condition ensuring the weighted composition operators $C_{{\omega}_1,{\varphi}_1},{\cdots},C_{{\omega}_N,{\varphi}_N}$ were disjoint supercyclic on $H({\Omega})$ endowed with the compact open topology. Besides, we provided a condition on inducing symbols to guarantee the disjoint supercyclicity of non-constant adjoint multipliers $M^*_{{\varphi}_1},M^*_{{\varphi}_2},{\cdots},M^*_{{\varphi}_N}$ on a Hilbert space ${\mathcal{H}}$.

• Communications of Mathematical Education
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• v.28 no.3
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• pp.375-394
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• 2014

The purpose of this study is to examine the transition of mathematical representation in Joseon mathematics, which is focused on numbers and operations, letters and expressions. In Joseon mathematics, there had been two numeral systems, one by chinese character and the other by counting rods. These systems were changed into the decimal notation which used Indian-Arabic numerals in the late 19th century passing the stage of positional notation by Chinese character. The transition of the representation of operation and expressions was analogous to that of representation of numbers. In particular, Joseon mathematics represented the polynomials and equations by denoting the coefficients with counting rods. But the representation of European algebra was introduced in late Joseon Dynasty passing the transitional representation which used Chinese character. In conclusion, Joseon mathematics had the indigenous representation of numbers and mathematical symbols on our own. The transitional representation was found before the acceptance of European mathematical representations.

• East Asian mathematical journal
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• v.24 no.5
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• pp.527-545
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• 2008

One of the education purpose of the section "Figures" in the eighth grade is to develop students' deductive reasoning ability, which is basic and essential for living in a democratic society. However, most or middle school students feel much more difficulty or even frustration in the study of formal arguments for geometric situations than any other mathematical fields. It is owing to the big gap between inductive reasoning in elementary school education and deductive reasoning, which is not intuitive, in middle school education. Also, it is very burden for students to describe geometric statements exactly by using various appropriate symbols. Moreover, Usage of the same symbols for angle and angle measurement or segments and segments measurement makes students more confused. Since geometric relations is mainly determined by the measurements of geometric objects, students should be able to interpret the geometric properties to the algebraic properties, and vice verse. In this paper, we first compare and contrast inductive and deductive reasoning approaches to justify geometric facts and relations in school curricula. Convincing arguments are based on experiment and experience, then are developed from inductive reasoning to deductive proofs. We introduce teaching methods to help students's understanding for deductive reasoning in the textbook by using stepwise visualization materials. It is desirable that an effective proof instruction should be able to provide teaching methods and visual materials suitable for students' intellectual level and their own intuition.