• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1153-1170
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• 2022

In this paper, we investigate the portfolio optimization problem under the SVCEV model, which is a hybrid model of constant elasticity of variance (CEV) and stochastic volatility, by taking into account of minimum-entropy robustness. The Hamilton-Jacobi-Bellman (HJB) equation is derived and the first two orders of optimal strategies are obtained by utilizing an asymptotic approximation approach. We also derive the first two orders of practical optimal strategies by knowing that the underlying Ornstein-Uhlenbeck process is not observable. Finally, we conduct numerical experiments and sensitivity analysis on the leading optimal strategy and the first correction term with respect to various values of the model parameters.

• Journal for History of Mathematics
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• v.23 no.2
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• pp.1-21
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• 2010

The first Korean mathematical science journal was published by Yu, Il- Sun in 1905 and the name of this journal is "Mathematical Science magazine". This monthly journal was published for 2 years. But in the existing literature, there is no information about it. We discovered its existence and studied its contents. From the historical materials, pioneering contributions of Yu, Il-Sun to mathematics were provided. In this article, the first issue of this journal was fully analyzed. We could see his affection and enthusiasm for the journal that he started. More mathematical search efforts on finding historical math materials should be continued. More efforts should be made on finding historical math literatures. Related researches will be done. Those works will be worth to be shared in ICME-12 and ICM 2014.

• The Mathematical Education
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• v.46 no.1 s.116
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• pp.53-67
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• 2007

During the recent years at a middle level Engineering School located at the local areas in Korea, more than 20 percent of freshmen had failed at their first College Mathematics. In consequence, many of them had hard time to survive at their major curriculums. The purpose of this study is to look for the main reasons of their failure and suggest an alternation of the present curriculum. Using the responses to the questionnaires and placement test scores, we studied the characteristics of the students' Mathematical abilities and analyzed how they were related to their grades of the First College Mathematics at the end of the first semester. The mathematical ability of the students at the middle level Engineering School turned out to range from bottom to top even though most of them revealed their interests towards Mathematics. The students with low scores at the placement test were more likely to fail at their first College Mathematics. Thus we suggest that the school should open a new preparation course ahead of the First College Mathematics for those who achieve low scores at the placement test and also professors should write proper books and develop ways of teaching.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.425-441
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• 2023

This paper is concerned with the value distribution for meromorphic solutions f of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions f are uniquely determined by the poles of f and the zeros of f - c, f - d (counting multiplicities) for two distinct small functions c, d.

• Communications of Mathematical Education
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• v.20 no.4 s.28
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• pp.523-535
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• 2006

We surveyed statistically the freshmen's achievement of the first year mathematics courses in Kwangwoon University, which were opened at the first semester of academic year 2006. In doing so, we classified the freshmen according to the Mathematical Area 'ga' or 'na' and the Natural Science or Social Science Area of Korean Scholastic Aptitude Test(KSAT) which they have chosen. We found that the freshmen who have chosen the Mathematical Area 'na' and the Social Science Area have the serious problem in studying the freshmen's math courses.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1113-1122
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• 2016

Let (M, g(t)) be a compact Riemannian manifold and the metric g(t) evolve by the Yamabe flow. In the paper we derive the evolution for the first eigenvalue of geometric operator $-{\Delta}_{\phi}+{\frac{R}{2}}$ under the Yamabe flow, where ${\Delta}_{\phi}$ is the Witten-Laplacian operator, ${\phi}{\in}C^2(M)$, and R is the scalar curvature with respect to the metric g(t). As a consequence, we construct some monotonic quantities under the Yamabe flow.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.47-53
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• 2017

Generalized integral formulas involving the generalized modified k-Bessel function $J^{b,c,{\gamma},{\lambda}}_{k,{\upsilon}}(z)$ of first kind are expressed in terms generalized Wright functions. Some interesting special cases of the main results are also discussed.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.683-689
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• 2000

The convergence rate of the expectation of the logarithm of the first return time R(sub)n with block length n has been investigated for Bernoulli processes. This idea is applied to check the randomness of the digits of the decimal expansion of $\pi$, e and √2.

• Journal of the Korean Mathematical Society
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• v.50 no.3
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• pp.591-605
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• 2013

The underlying field is of characteristic $p$ > 2. In this paper, we first use the method of computing the homogeneous derivations to determine the first cohomology of the so-called odd contact Lie algebra with coefficients in the even part of the generalized Witt Lie superalgebra. In particular, we give a generating set for the Lie algebra under consideration. Finally, as an application, the derivation algebra and outer derivation algebra of the Lie algebra are completely determined.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.355-363
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• 2016

By employing a refined version of the $P{\acute{o}}lya$ type integral inequality and other techniques, the authors establish some inequalities and absolute monotonicity for modified Bessel functions of the first kind with nonnegative integer order.