• 한국안광학회지
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• 제8권2호
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• pp.163-168
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• 2003

광의 세기에 따라 눈의 시감효율은 추상체와 간상체에 의해 파장에 따라 2개의 함수로 이루어진다. 광자에 대한 추상체-간상체의 반응확률을 이용하여 $P{\lambda}=A{\cdot}e^{-({\lambda}-{\lambda}_u)^2/2W^2}$의 분포함수 수식을 유도하였다. 이 식은 파장에 따른 CIE의 눈의 시감효율 곡선에 잘 적용되었다. 눈앞에 렌즈가 있는 경우 시감도는 보정 되어야 한다. 렌즈를 투과할 광은 흡수 파장에 의존하고, 최종 시감도는 추정방법은 시감도와 렌즈의 투과율 세기의 곱으로 표현된다. $$Pf({\lambda})=T({\lambda}){\cdot}P({\lambda})$$. 브라운 칼라 렌즈에 대해 시감도인 photopic과 scotopic 적용하였다.

• 천문학회지
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• 제47권2호
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• pp.77-86
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• 2014

Using a cosmological ${\Lambda}CDM$ simulation, we analyze the differences between the widely-used spin parameters suggested by Peebles and Bullock. The dimensionless spin parameter ${\lambda}$ proposed by Peebles is theoretically well-justified but includes an annoying term, the potential energy, which cannot be directly obtained from observations and is computationally expensive to calculate in numerical simulations. The Bullock's spin parameter ${\lambda}^{\prime}$ avoids this problem assuming the isothermal density profile of a virialized halo in the Newtonian potential model. However, we find that there exists a substantial discrepancy between ${\lambda}$ and ${\lambda}^{\prime}$ depending on the adopted potential model (Newtonian or Plummer) to calculate the halo total energy and that their redshift evolutions differ to each other significantly. Therefore, we introduce a new spin parameter, ${\lambda}^{\prime\prime}$, which is simply designed to roughly recover the value of ${\lambda}$ but to use the same halo quantities as used in ${\lambda}^{\prime}$. If the Plummer potential is adopted, the ${\lambda}^{\prime\prime}$ is related to the Bullock's definition as ${\lambda}^{\prime\prime}=0.80{\times}(1+z)^{-1/12}{\lambda}^{\prime}$. Hence, the new spin parameter ${\lambda}^{\prime\prime}$ distribution becomes consistent with a log-normal distribution frequently seen for the ${\lambda}^{\prime}$ while its mean value is much closer to that of ${\lambda}$. On the other hand, in case of the Newtonian potential model, we obtain the relation of ${\lambda}^{\prime\prime}=(1+z)^{-1/8}{\lambda}^{\prime}$; there is no significant difference at z = 0 as found by others but ${\lambda}^{\prime}$ becomes more overestimated than ${\lambda}$ or ${\lambda}^{\prime\prime}$ at higher redshifts. We also investigate the dependence of halo spin parameters on halo mass and redshift. We clearly show that although the ${\lambda}^{\prime}$ for small-mass halos with $M_h$ < $2{\times}10^{12}M_{\odot}$ seems redshift independent after z = 1, all the spin parameters explored, on the whole, show a stronger correlation with the increasing halo mass at higher redshifts.

• 대한수학회논문집
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• 제12권4호
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• pp.881-893
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• 1997

E. M. Silvia introduced the class $S^\lambda_\alpha$ of $\alpha$-spirallike functions f(z) satisfying the condition $$ (A) Re[(e^{i\lambda} - \alpha) \frac{zf'(z)}{f(z)} + \alpha \frac{(zf'(z))'}{f'(z)}] > 0, $$ where $\alpha \geq 0, $\mid$\lambda$\mid$ < \frac{\pi}{2}$ and $$\mid$z$\mid$ < 1$. We will generalize Silvia class of functions by formally replacing f(z) in the denominator of (A) by a spirallike function g(z). We denote the new class of functions by $Y(\alpha,\lambda)$. In this note we obtain some results for the class $Y(\alpha,\lambda)$ including integral representation formula, relations between our class $Y(\alpha,\lambda)$ and Ziegler class $Z_\lambda$, the radius of convexity problem, a few coefficient estimates and a covering theorem for the class $Y(\alpha,\lambda)$.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.471-477
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• 2007

In this paper we establish some recurrence relations satisfied by the quotient moments of the upper record values from the Weibull distribution. Suppose $X{\in}WEI({\lambda})\;then\;E(\frac {X^\tau_U(m)} {X^{s+1}_{U(n)}})=\frac{1}{(s-\lambda+1)}E(\frac {X^\tau_U(m)}{X^{s-\lambda+1}_{U(n-1)}})-\frac{1}{(s-\lambda+1)}+E(\frac{X^\tau_U(m)}{X^{s-\lambda+1}_{U(n)}})\;and\;E(\frac {X^{\tau+1}_{U(m)}}{X^s_{U(n)}})=\frac{1}{(r+\lambda+1)}E(\frac{X^{\tau+\lambda+1}_{U(m)}}{X^s_{U(n-1)}})-\frac{1}{(\tau+\lambda+1)}E(\frac{X^{\tau+\lambda+1}_{U(m-1)}}{X^s_{U(n-1)}})$.

• 대한수학회보
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• 제37권1호
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• pp.191-207
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• 2000

Let R be a ommutative ring with unity and F a finite free R-module. For a nonnegative integer r, there exists a natural filtration of$S_r(S_2F)$ such that its associated graded module is isomorphic to $\Sigma_{{\lambda}{\epsilon}{\tau}_r}\;L_{\lambda}F$, where ${\Gamma}_{\gamma}$ set of partitions such that $$\mid${\lambda}$\mid$-2r,{{\widetilde}{\lambda}}-{{\widetilde}{\lambda}}_1},...,{{\widetilde}{\lambda}}_k},\;each\;{{\widetilde}{\lambda}}_t}$,is even. We call such filtrations plethysm formulas. We extend the above plethysm formula to the version of chain complexes. By plethysm formula we mean the composition of universally free functors. $Let{\emptyset}:G->F$ be a morphism of finite free R-modules. We construct the natural decomposition of $S_{r}(S_2{\emptyset})$,up to filtrations, whose associated graded complex is isomorphic to ${\Sigma}_{{\lambda}{\varepsilon}{\tau}}_r}\;L_{\lambda}{\emptyset}$.

• 대한수학회지
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• 제56권4호
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• pp.985-1000
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• 2019

Let k be an integer with $k{\geq}3$. Define $h(k)=[{\frac{k+1}{2}}]$, ${\sigma}(k)={\min}\(2^{h(k)-1},\;{\frac{1}{2}}h(k)(h(k)+1)\)$. Suppose that ${\lambda}_1,{\ldots},{\lambda}_5$ are non-zero real numbers, not all of the same sign, satisfying that ${\frac{{\lambda}_1}{{\lambda}_2}}$ is irrational. Then for any given real number ${\eta}$ and ${\varepsilon}>0$, the inequality $${\mid}{\lambda}_1p^2_1+{\lambda}_2p^2_2+{\lambda}_3p^2_3+{\lambda}_4p^2_4+{\lambda}_5p^k_5+{\eta}{\mid}<({\max_{1{\leq}j{\leq}5}}p_j)^{-{\frac{3}{20{\sigma}(k)}}+{\varepsilon}}$$ has infinitely many solutions in prime variables $p_1,{\ldots},p_5$. This gives an improvement of the recent results.

• Kyungpook Mathematical Journal
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• 제61권3호
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• pp.671-677
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• 2021

For a distance-regular graph with valency k, second largest eigenvalue r and diameter D, it is known that r ≥ $min\{\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2},\;a_3\}$ if D = 3 and r ≥ $\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2}$ if D ≥ 4, where λ = a₁. This result can be generalized to the class of edge-regular graphs. For an edge-regular graph with parameters (v, k, λ) and diameter D ≥ 4, we compare $\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2}$ with the local valency λ to find a relationship between the second largest eigenvalue and the local valency. For an edge-regular graph with diameter 3, we look at the number $\frac{{\lambda}-\bar{\mu}+\sqrt{({\lambda}-\bar{\mu})^2+4(k-\bar{\mu})}}{2}$, where $\bar{\mu}=\frac{k(k-1-{\lambda})}{v-k-1}$, and compare this number with the local valency λ to give a relationship between the second largest eigenvalue and the local valency. Also, we apply these relationships to distance-regular graphs.

• ETRI Journal
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• 제21권2호
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• pp.31-39
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• 1999

Given two sorted lists A=(a0, a1, ${\cdots}$,a${\ell}$-1}) and B=(b0, b1, ${\cdots}$, bm-1), we are to merge these two lists into a sorted list C=(c0,c1, ${\cdots}$, cn-1), where n=${\ell}$+m. Since this is a fundamental problem useful to solve many problems such as sorting and graph problems, there have been many efficient parallel algorithms for this problem. But these algorithms cannot be performed efficiently in the postal model since the communication latency ${\lambda}$, which is of prime importance in this model, is not needed to be considered for those algorithms. Hence, in this paper we propose an efficient merge algorithm in this model that runs in $$2{\lambda}{\frac{{\log}n}{{\log}({\lambda}+1)}}+{\lambda}-1$$ time by using a new property of the bitonic sequence which is crucial to our algorithm. We also show that our algorithm is near-optimal by proving that the lower bound of this problem in the postal model is $f_{\lambda}({\frac{n}{2}})$, where $${\lambda}{\frac{{\log}n-{\log}2}{{\log}([{\lambda}]+1)}{\le}f_{\lambda}({\frac{n}{2}}){\le}2{\lambda}+2{\lambda}{\frac{{\log}n-{\log}2}{{\log}([{\lambda}]+1)}}$$.

• 한국안광학회지
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• 제1권1호
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• pp.93-102
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• 1996

렌즈의 광학계의 분광투과률을 높이기 위한 방법으로 무반사막의 다층화에 의한 광대역화와 낮은 반사률이 중요하다. 그러나 잔류반사광이 발생하여 반사색광이 미약하게 나타난다. 이런 반사색광은 두께, 굴절율, 층수, 입사광의 파장, 기판물질 등의 구조에 의한 반사광의 파장 영역을 제어할 수 있다. l층, 2층 구조에서 ${\lambda}s/{\lambda}$=1.0인 조건하에서 무반사시키면, 다른 영역에서 나온 반사광들이 색혼합된 반사색광을 얻을 수 있고, 3층 구조에서 ${\lambda}0/{\lambda}$가 $PI{\ll}1$, $P2{\gg}1$ 에서 무반사시키면 P1< ${\lambda}0/{\lambda}$

• 한국안광학회지
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• 제5권2호
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• pp.157-161
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• 2000

광원의 세기가 다른 조건하에서 눈의 시감효율은 추상체와 간상체에 의해 파장에 따라 2개의 함수로 이루어진다. 광자에 대한 추상체-간상체의 반응확률을 이용하여 $P({\lambda})=A{\cdot}e^{-({\lambda}-{\lambda}_0)^2/2W^2}$의 분포함수 수식을 유도하였다. 이 식은 파장에 따른 CIE의 눈의 시감효율 곡선에 잘 적용되며 상대 시감효율의 경우 photopic의 경우 A=106.4, ${\lambda}_0=559.2$, W=83.5이고 scotopic의 경우 A=99.3, ${\lambda}_0=502.6$, W=79.5의 값을 얻었다. 1m/W의 단위를 사용하는 시감효능 곡선에서는 photopic의 경우 $A=7.2{\times}10^4$, ${\lambda}_0=559.2$, W=86.5이고 scotopic의 경우 $A=1.6{\times}10^5$, ${\lambda}_0=502.6$, W=79.5의 값을 얻었다.