• 대한기계학회논문집A
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• 제41권3호
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• pp.213-218
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• 2017

리모트 용접용 2D 스캐너 F-theta 렌즈의 역설계가 광선 추적기법을 사용하여서 수행이 되었다. 렌즈의 곡면 및 렌즈간 거리를 변수로 설정하고 초점거리를 Marginal Ray Height 로 설정하여, 상용 광선추적기법 프로그램을 사용하여 무한반복 최적화를 수행 하였다. 최종목표 값을 설정 후 Merit Function에 정의된 기준에 따라, 최종 초점거리와 초점의 크기를 최종 목표 값 가중치로 설정하였다. 최적화된 렌즈는 총 4매이며, 벤치마킹된 상용렌즈의 초점거리(185mm) 보다는 다소 근거리인 137mm로 최적화 되었지만, 초점의 크기는 레이저 입사각에 따라 RMS 기준 $1.3{\mu}m$, $6.2{\mu}m$ 그리고 $16.1{\mu}m$로 계산 되었으며, 이는 상용렌즈에 근접하는 성능을 구현한다. 입사각별 왜곡도를 중첩 하여서 비교 분석한 결과, 입사각 $0^{\circ}$와 $12.5^{\circ}$에서는 기존 렌즈와 거의 유사한 형태로 나타나는 것을 볼 수가 있어, 본 연구에서 제안된 역설계기법이 사용자 환경에 따라서 효과적으로 적용되어 최적설계가 이루어질 수 있을 것으로 기대가 된다.

• 한국광학회지
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• 제3권3호
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• pp.161-166
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• 1992

회전하는 거친금속표면에 s-편극된 레이저광을 $-30^{\circ}$로 입시시켜 생긴 후방산란파중 입사광과 동일한 편극을 가지는 후방산란파에 대하여 세기의 시간상관함수 $g_{s}^{(2)}(\tau)$를 측정하였다. 이 과정에서 광전신호로부터 $g_{s}^{(2)}(0)$의 측정을 할 때 수반되는 shot noise의 영향을 제하여 줌으로써 정확한 $g_{s}^{(2)}(0)$ 값을 얻었다. 각 산란각$\theta_{s}$에서$g_{s}^{(2)}(\tau)$는 {1+exp($-\tau^2/\tau_0^2$)}함수와 거의 일치하였는데, 이는 등속으로 회전하는 간유리를 투과하여 형성된 레이저 스펙클의 경우와 같은 결과이다. 또한, 산란각에 따른 $\tau_0$의 분포에서는 $\theta_s=34^{\circ}$에서 예리하게 최대값을 가지는 것이 관찰되었다. 이 연구에서, 다중산란이 10%를 넘는 금속판산란과 다중산란이 무시될 수 있는 간유리판산란이 같은 함수꼴의 세기의 시간상관함수를 갖는다는 사실이 확인되었다.

• Kyungpook Mathematical Journal
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• 제49권3호
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• pp.435-450
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• 2009

On page 366 of his lost notebook [15], Ramanujan recorded a cubic continued fraction and several theorems analogous to Rogers-Ramanujan's continued fractions. In this paper, we derive several general formulas for explicit evaluations of Ramanujan's cubic continued fraction, several reciprocity theorems, two formulas connecting V (q) and V ($q^3$) and also establish some explicit evaluations using the values of remarkable product of theta-function.

• 대한수학회논문집
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• 제10권1호
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• pp.93-107
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• 1995

In their paper [2,3], Cameron and Storvick introduced some classes $S"+m$ and of functionals on classical Wiener spaces $C_0[a,b]$. For such functionals, they showed that the analytic Feynman integral exists and they gave some formulas for this integral. Moreover they obtained that the functionals of the form $$ (1.1) F(x) = exp {\int^b_a{\theta(s,x(x))dx} $$ are in S" where they assumbed that the potential $\delta : [a,b] \times R \to C$ satisfies (i) for each $s \in [a,b], \theta(s,\cdot)$ is the Fourier-Stieltjes transform of $\sigma_s \in M(R)$, (ii) for each Borel subset E of $[a,b] \times R, \sigma_s (E^{(s)})$ is a Borel measurable function of s on [a,b], and (iii) the total variation $\Vert \sigma_s \Vert$ of $\sigma_s$ is bounded as a function of s.tion of s.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권4호
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• pp.271-279
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• 2014

Let $T_l$ be a transformation on the interval [-1, 1] defined by Chebyshev polynomial of degree $l(l{\geq}2)$, i.e., $T_l(cos{\theta})=cos(l{\theta})$. In this paper, we consider $T_l$ as a measure preserving transformation on [-1, 1] with an invariant measure $\frac{1}{\sqrt[\pi]{1-x^2}}dx$. We show that If f(x) is a nonconstant step function with finite k-discontinuity points with k < l-1, then it satisfies the Central Limit Theorem. We also give an explicit method how to check whether it satisfies the Central Limit Theorem or not in the cases of general step functions with finite discontinuity points.

• International Journal of Reliability and Applications
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• 제12권1호
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• pp.61-77
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• 2011

One of the most important problems in the estimation of the parameter of the failure model, is the cost of experimental sampling units, which can be reduced by using any prior information available about ${\theta}$, and devising a two-stage pooling shrunken estimation procedure. We have proposed an estimator of the reliability function (R(t)) of the exponential model using two-stage time censored data when a prior value about the unknown parameter (${\theta}$) is available from the past. To compare the performance of the proposed estimator with the classical estimator, computer intensive calculations for bias, mean squared error, relative efficiency, expected sample size and percentage of the overall sample size saved expressions, were done for varying the constants involved in the proposed estimator (${\tilde{R}}$(t)).

• 대한안전경영과학회지
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• 제4권3호
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• pp.59-66
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• 2002

This paper presents accelerated life tests for Type I censoring data under probabilistic stresses. Probabilistic stress, S, is the random variable for stress influenced by test environments, test equipments, sampling devices and use conditions. The hazard rate, $\theta$ is a random variable of environments and a function of probabilistic stress. In detail, it is assumed that the hazard rate is linear function of the stress, the general stress distribution is a gamma distribution and the life distribution for the given hazard rate, $\theta$is an exponential distribution. Maximum likelihood estimators of model parameters are obtained, and the mean life in use stress condition is estimated. A hypothetical example is given to show its applicability.

• Bulletin of the Korean Chemical Society
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• 제21권12호
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• pp.1227-1232
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• 2000

Near the conical intersection for the 1,2 $^{2}A'$ states of $H_3$ the derivative coupling vector is calculated and analyzed on the plane of internal coordinates, (U,V) or its polar coordinates $(S{\theta})$, based on the squares of the internuclear distances. It is shown that in the vicinity of the conical intersection the derivative coupling vector behaves like ${\theta}/2S$, which is responsible for the sign changes of the real-valued electronic wave function when the nuclear configuration traverses a closed path enclosing a conical intersection. The analytic property of the wave functions is studied and especially the observation of the sign change in the configuration state function (CSF) coefficients of the real-valued electronic wave functions is demonstrated.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제31권2호
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• pp.189-200
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• 2024

We derive modular equations of degree 3 to find corresponding theta-function identities. We use them to find some new evaluations of $G(e^{-{\pi}{\sqrt{n}}})$ and $G(-e^{-{\pi}{\sqrt{n}}})$ for $n\,=\,\frac{25}{3{\cdot}4^{m-1}}$ and $\frac{4^{1-m}}{3{\cdot}25}$, where m = 0, 1, 2.

• Bulletin of the Korean Chemical Society
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• 제34권7호
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• pp.2063-2066
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• 2013

While many eukaryotic and some prokaryotic proteins show a phosphorylation-dependent mobility shift (PDMS) on SDS-PAGE, the molecular mechanism for this phenomenon had not been elucidated. We have recently shown that the distribution of negatively charged amino acids around the phosphorylation site is important for the PDMS of some proteins. Here, we show that replacement of the phosphorylation site with a negatively charged amino acid results in a similar degree of the mobility shift of a protein as phosphorylation, indicating that the PDMS is due to the introduction of a negative charge by phosphorylation. Compared with a protein showing no shift, one showing a retarded mobility on SDS-PAGE had a decreased capacity for SDS binding. The elucidation of the consensus sequence (${\Theta}X_{1-3}{\Theta}X_{1-3}{\Theta}$, where ${\Theta}$ corresponds to an acidic function) for a PDMS suggests a general strategy for mutagenizing a phosphorylatable protein resulting in a PDMS.