• Journal of Korean Ophthalmic Optics Society
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• v.8 no.2
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• pp.163-168
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• 2003

The eye sensitivity in the difference conditions of a light source intensity consists of two functions by the receptor of cone and rod according to a wavelength. We derived a distribution function of $P{\lambda}=A{\cdot}e^{-({\lambda}-{\lambda}_u)^2/2W^2}$ using a respond probability of the receptor of cone-rod for a photon. It was well applied for a CIE eye's sensitivity curve of a wavelength. When there is lens In front of eye, luminous efficiency should be corrected. Transmission light which permeate to depends on absorption wavelength, and relationship of final luminous efficiency's estimation method is expressed by multiplication of luminous efficiency and transmittance intensity of lens. $$Pf({\lambda})=T({\lambda}){\cdot}P({\lambda})$$. The theory was applied to photopic and scopic vision with brown color lens.

• Journal of The Korean Astronomical Society
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• v.47 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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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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• v.23 no.1_2
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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 $X{\in}WEI({\lambda})\;then\;E(\frac {X^\tau_U(m)} {X^{s+1}_{U(n)}})=\frac{1}{(s-\lambda+1)}E(\frac {X^\tau_U(m)}{X^{s-\lambda+1}_{U(n-1)}})-\frac{1}{(s-\lambda+1)}+E(\frac{X^\tau_U(m)}{X^{s-\lambda+1}_{U(n)}})\;and\;E(\frac {X^{\tau+1}_{U(m)}}{X^s_{U(n)}})=\frac{1}{(r+\lambda+1)}E(\frac{X^{\tau+\lambda+1}_{U(m)}}{X^s_{U(n-1)}})-\frac{1}{(\tau+\lambda+1)}E(\frac{X^{\tau+\lambda+1}_{U(m-1)}}{X^s_{U(n-1)}})$.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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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 ${\Sigma}_{{\lambda}{\varepsilon}{\tau}}_r}\;L_{\lambda}{\emptyset}$.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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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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• v.61 no.3
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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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• v.21 no.2
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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 $${\lambda}{\frac{{\log}n-{\log}2}{{\log}([{\lambda}]+1)}{\le}f_{\lambda}({\frac{n}{2}}){\le}2{\lambda}+2{\lambda}{\frac{{\log}n-{\log}2}{{\log}([{\lambda}]+1)}}$$.

• Journal of Korean Ophthalmic Optics Society
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• v.1 no.1
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• pp.93-102
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• 1996

The optical system of lens must be designed to tramsmit light over wide wavelength range and to have lower reflectivity in order to obtain higher spectral transmittance. However, the reflection color light appears due to the remain-reflection light in any optical system of lens. The wavelength of the reflection color light can be controlled by the structure of the number of layers, thickness of layer, reflective index, wavelength of incidence, and substrate etc. In the optical systems of the single layer and the double layers, the reflection color light appears in the condition of the anti-reflection of ${\lambda}s/{\lambda}$ = 1.0 by the color mixture of the remain-reflection lights in the ranges of the longer wavelength side and the shorter one of the ${\lambda}s/{\lambda}$ = 1.0, and of the double layers and triple layers, the reflection color light positioned at P1 < ${\lambda}s/{\lambda}$ < P2 appears in the condition of the antireflection of ${\lambda}s/{\lambda}$ = $PI{\ll}1$ and $P2{\gg}1$. In the optical system of the multi-layers, many antireflection points are existed at the various s/ values, and the reflection color light by the color mixture of the remain-reflection lights in the ranges except for the antireflection points.

• Journal of Korean Ophthalmic Optics Society
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• v.5 no.2
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• pp.157-161
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• 2000

The Eye sensitivity in the difference conditions of a light source intensity consists of two functions by the receptor of cone and rod according to a wavelength. We derived a distribution function of $P({\lambda})=A{\cdot}e^{-({\lambda}-{\lambda}_0)^2/2W^2}$ using a respond probability of the receptor of cone-rod for a photon. It was well applied for a CIE eye's sensitivity curve of a wavelength, we obtained values in case of a relative sensitivity. A = 106.4, ${\lambda}_0=559.2$, W = 83.5 for a photopic and A = 99.3 ${\lambda}_0=502.6$, W = 79.5 for a scotopic, and in case of a sensitivity curve using 1m/W units. $A=7.2{\times}10^4$, ${\lambda}_0=559.2$, W = 83.5 for a photopic and $A=1.6{\times}10^5$, ${\lambda}_0=502.6$. W = 79.5 for a scotopic.