• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.515-526
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• 2021

Denote by ��+ the set of probability measures supported on ℝ+. Suppose V�� is the variance function of the Cauchy-Stieltjes Kernel (CSK) family ��-(��) generated by a non degenerate probability measure �� ∈ ��+. We determine the formula for variance function under boolean multiplicative convolution power. This formula is used to identify the relation between variance functions under the map ${\nu}{\mapsto}{\mathbb{M}}_t({\nu})=({\nu}^{{\boxtimes}(t+1)})^{{\uplus}{\frac{1}{t+1}}}$ from ��+ onto itself.

• Bulletin of the Korean Chemical Society
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• v.33 no.8
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• pp.2657-2668
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• 2012

We obtain the general formulation which can handle the rotational preionization spectrum of $H_2$ in the region above its ${H_2}^+$ ionization threshold, ($^2{\sum}_g^+$, ${\nu}^+=0$, $N^+=0$) converging toward its rotationally excited (${\nu}^+=0$, $N^+=2$) limit and perturbed by the vibrationally excited levels $7p{\pi}$ ${\nu}=1$ and $5p{\pi}$ ${\nu}^=2$. The formulation is based on phase-shifted multichannel quantum-defect theory. With this formulation, resonance structures are analyzed in detail.

• The Mathematical Education
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• v.45 no.4 s.115
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• pp.507-518
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• 2006

There is a great need to find new topics which are good to evaluate and to encourage the mathematical creativity of gifted students, For the purpose to find such a topic, we study Ho-bak-go-nu game that is one of Korean traditional games and a typical alignment game. By analyzing patterns of possible alignment, the author gives a complete solution to win or not to lose according to the rules chosen by players. The author also poses several class-models including a test for the class of gifted students based on the analysis of real classes on Ho-bak-go-nu game.

• Proceedings of the Korean Nuclear Society Conference
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• 1997.05a
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• pp.77-82
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• 1997

The CANDU-6 transition core refuelled from 37-element fuel to CANFLEX-NU fuel has been evaluated by an 100full power day time-dependent fuel-management simulation to find the core compatibility with the CANFLEX fuel loading. The simulation calculations for the transition core were carried out with the RFSP code, provided by the cell averaged fuel properties obtained from the POWDERPUFS-V code. The simulation results were compared with those of the current 37-element fuel loading only. The results show that the CANFLEX-NU fuel bundles will be compatible with the CANDU-6 reactor because the core physics characteristics of CANFLEX-NU fuel are very similar to those of the 37-element fuel bundle.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.279-290
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• 1996

In the present paper we study the Cauchy problem in a Banach space E for an abstract nonlinear differential equation of form $$\frac{d^2u}{dt^2}=-A{\frac{du}{dt}}+B(t)u+f(t, W)$$ where W=($A_1$(t)u, A_2(t)u)..., A_{\nu}(t)u), A_{i}(t),\;i=1,2,...{\nu}$,(B(t), t{\in}I$=[0, b]) are families of closed operators defined on dense sets in E into E, f is a given abstract nonlinear function on $I{\times}E^{\nu}$ into E and -A is a closed linar operator defined on dense set in e into E which generates a semi-group. Further the existence and uniqueness of the solution of the considered Cauchy problem is studied for a wide class of the families ($A_{i}$(t), i =1.2...${\nu}$), (B(t), $t{\in}I$) An application and some properties are also given for the theory of partial diferential equations.

• Journal of the Korean Chemical Society
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• v.6 no.2
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• pp.170-175
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• 1962

The ultraviolet and visable absorption spectra of trans, cis-azoxybenzene, substituted azoxybenzenes and their conjugate acids have been studied. The 320-350$m{\mu}$ main bands of free-base of azoxybenzenes are due to ${\pi}{\to}{\pi}^{\ast}$ transition. These bands of their conjugate acids shown bathochromic shift into visible range. The following emperical relationship between absorption maxima of the main bands was found. ${\lambda}_{max}={\lambda}^{\circ}_{max}+{\Delta}{\lambda}_x+{\Delta}{\lambda}_y$ This relationship in terms of wave number is also hold in good agreement. ${\nu}={\nu}_{\circ}-({\Delta}{\nu}_x+{\Delta}{\nu}_y)$

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.89-99
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• 2009

Let $\mu$ be a finite positive Borel measure on the unit ball $B{\subset}\mathbb{C}^n$ and $\nu$ be the Euclidean volume measure such that ${\nu}(B)=1$. For the unit sphere $S=\{z:{\mid}z{\mid}=1\}$, $\sigma$ is the rotation-invariant measure on S such that ${\sigma}(S)=1$. Let $\mathcal{P}[f]$ be the invariant Poisson integral of f. We will show that there is a constant M > 0 such that $\int_B{\mid}{\mathcal{P}}[f](z){\mid}^{p}d{\mu}(z){\leq}M\;{\int}_B{\mid}{\mathcal{P}}[f](z)^pd{\nu}(z)$ for all $f{\in}L^p({\sigma})$ if and only if ${\parallel}{\mu}{\parallel_r}\;=\;sup_{z{\in}B}\;\frac{\mu(E(z,r))}{\nu(E(z,r))}\;<\;\infty$.

• Journal for History of Mathematics
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• v.24 no.2
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• pp.31-46
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• 2011

[ ${\ll}$ ]n divisions of figures(${\pi}{\varepsilon}{\rho}{\acute{\iota}}\;{\delta}{\iota}{\alpha}{\iota}{\rho}{\acute{\varepsilon}}{\sigma}{\varepsilon}{\omega}{\nu}\;{\beta}{\iota}{\beta}{\lambda}{\acute{\iota}}o{\nu}$)${\gg}$ is one of the works written by Euclid, but little known to us. In this paper, we introduce this Euclid's book on divisions of figures with its brief history, analyse its contents, and discuss how to use it in mathematics education.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.81-84
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• 2003

$\varepsilon$-SVR(e-Support Vector Regression)학습방법은 SV(Support Vector)들을 이용하여 함수 근사(Regression)하는 방법으로 최근 주목받고 있는 기법이다. SVM(SV machine)의 한 가지 방법으로, 신경망을 기반으로 한 다른 알고리즘들이 학습과정에서 지역적 최적해로 수렴하는 등의 문제를 한계로 갖는데 반해, 이러한 구조들을 대체할 수 있는 학습방법으로 사용될 수 있다. 일반적인 $\varepsilon$-SVR에서는 학습 데이터와 관사 함수 f사이에 허용 가능한 에러범위 $\varepsilon$값이 학습하기 전에 정해진다. 그러나 Nu-SVR(ν-version SVR)학습방법은 학습의 결과로 최적화 된 $\varepsilon$값을 얻을 수 있다. 정해진 기저함수가 포함되는 $\varepsilon$-SVR 학습방법(Sermparametric SVR)은 정해진 독립 기저함수를 사용하여 함수를 근사하는 방법으로, 일반적인 $\varepsilon$-SVR 학습방범에 비해 우수한 결과를 나타내는 것이 성공적으로 입증된 바 있다. 이에 따라, 본 논문에서는 정해진 기저함수가 포함된 ν-SVR 학습 방법을 제안하고, 이에 대한 수식을 유도하였다. 그리고, 모의 실험을 통하여 제안된 Sermparametric ν-SVR 학습 방법의 적용 가능성을 알아보았다.

• Proceedings of the Korean Nuclear Society Conference
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• 1998.05a
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• pp.169-174
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• 1998

An 1200-day time-dependent fuel-management for the transition from 37-element fuel to CANFLEX-NU fuel in a CANDU 6 reactor has been simulated to show the compatibility of the CANFLEX-NU fuel with the reactor operation. The simulation calculation were carried out with the RFSP code, provided by cell averaged hel properties obtained from the POWDERPUFS-V code. The refueling scheme for both fuels was an eight bundle shift art a time. The simulation results show that the maximum channel and bundle powers were maintained below the licence limit of the CANDU 6. This indicates that the CANFLEX-NU fuel bundle is compatible with the CANDU 6 reactor operation during the transition period.