• Journal of Korean Ophthalmic Optics Society
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• v.5 no.1
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• pp.43-48
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• 2000

It was to adjust the luminance of light by the rotation angle of the polarizes and analyzer. The luminance value Lmax, Lmin of Contrast Sensitivity could be obtained from the rotation angle ${\theta}_m$ of the average luminance($L_m$), the rotation angle(${\theta}_{max}$, ${\theta}_{min}$) of the maximum and the minimum's amplitude. $$L_{max}=I(0)e^{-2at}{\cdot}cos^2{\theta}_m(1+C_s^{-1})$$ $$L_{min}=I(0)e^{-2at}{\cdot}cos^2{\theta}_m(1-C_s^{-1})$$ We obtained the rotation angle(${\theta}_{max}$, ${\theta}_{min}$) of the polarizes and analyzer from the rotation angle ${\theta}_m$ of the average luminance($L_m$) and the Contrast Sensitivity($C_s$). $${\theta}_{max}=cos^{-1}[cos{\theta}_m{\cdot}(1+C_s^{-1})^{1/2}]$$ $${\theta}_{min}=cos^{-1}[cos{\theta}_m{\cdot}(1-C_s^{-1})^{1/2}]$$.

• Publications of The Korean Astronomical Society
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• v.7 no.1
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• pp.25-30
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• 1992

Recent redshift surveys suggest that most galaxies may be distributed on the surfaces of bubbles surrounding large voids. To investigate the quantitative consistency of this qualitative picture of large-scale structure, we study analytically the clustering properties of galaxies in a universe filled with spherical shells. In this paper, we report the results of the calculations for the spatial and angular two-point correlation functions of galaxies. With ${\sim}20%$ of galaxies in clusters and a power law distribution of shell sizes, $n_{sh}(R){\sim}R^{-{\alpha}}$, ${\alpha}\;{\simeq}\;4$, the observed slope and amplitude of the spatial two-point correlation function ${\xi}_{gg}(r)$ can be reproduced. (It has been shown that the same model parameters reproduce the enhanced cluster two-point correlation function, ${\xi}_{cc}(r)$). The corresponding angular two-point correlation function $w({\theta})$ is calculated using the relativistic form of Limber's equation and the Schecter-type luminosity function. The calculated w(${\theta}$) agrees with the observed one quite well on small separations (${\theta}{\lesssim}2deg$).

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.377-383
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• 1996

We consider in this paper the following nonlinear regression model $$ (1.1) y_t = f(x_t, \theta_o) + \in_t, t = 1, \ldots, n, $$ where $y_t$ is the tth response, $x_t$ is m-vector imput variable, $\theta_o$ is a p-vector of unknown parameter belong to a parameter space $\Theta, f:R^m \times \Theta \ to R^1$ is a nonlinear known function, and $\in_t$ are independent unobservable random errors with finite second moment.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1269-1289
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• 2014

We first find a sufficient condition for a product of theta constants to be a Siegel modular function of a given even level. And, when $K_{(2p)}$ denotes the ray class field of $K=\mathbb{Q}(e^{2{\pi}i/5})$ modulo 2p for an odd prime p, we describe a subfield of $K_{(2p)}$ generated by the special value of a certain theta constant by using Shimura's reciprocity law.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.553-564
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• 2007

In this paper we establish several integration by parts formulas involving integral transforms of functionals of the form $F(y)=f(<{\theta}_1,\;y>),\ldots,<{\theta}_n,\;y>)$ for s-a.e. $y{\in}C_0[0,\;T]$, where $<{\theta},\;y>$ denotes the Riemann-Stieltjes integral ${\int}_0^T{\theta}(t)\;dy(t)$.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.173-184
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• 2016

Mock theta functions are the most interesting topic mentioned in Ramanujan's Lost Notebook, due to its emerging application in the field of Number theory, Quantum invariants theory and etc. In the present research articles we have made an attempt to develop continued fractions representation of all the existing Mock theta functions.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.31-43
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• 2022

In his notebooks, Srinivasa Ramanujan recorded several modular equations that are useful in the computation of class invariants, continued fractions and the values of theta functions. In this paper, we prove some new modular equations of signature 2 by well-known and useful theta function identities of composite degrees. Further, as an application of this, we evaluate theta function identities.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.249-258
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• 2006

The weakened forms of the (${\theta},s$)-continuous function are introduced and their basic properties are investigated in concern with the other weakened continuous function. The open property of a function and the extremal disconnectedness of the spaces are crucial tools for the survey of these functions.

• Korean Journal of Applied Biomechanics
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• v.25 no.3
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• pp.241-248
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• 2015

Objective : The purpose of this study was to investigate the theta on the components of ground reaction force according to the ground conditions during gait. Method : Six healthy women(mean age: 22 yrs, mean height: $166.14{\pm}2.51cm$, mean body weights: $56.61{\pm}4.58kg$) participated in this study. The medial-lateral GRF(Fx 1), anterior-posterior GRF(Fy 1, Fy 2), vertical GRF(Fz 1, Fz 2, Fz 3), and impact loading rate were determined from time function and frequency domain. Also, GRF theta were time function and forces. Results : Fx 1, Fy 1 and Fy 2 of stair descending showed significant statistically higher forces than that of level walking, and ascending. Fz 1 of stairs descending showed significant statistically higher forces than that of level walking and stairs ascending(theta $88.62^{\circ}$). Also, Fz 2 of level walking showed significant statistically higher forces than that of stairs ascending and descending(theta $65.78^{\circ}$). Fz 3 of stairs ascending showed significant statistically higher forces than that of level walking and stairs descending($65.26^{\circ}$). Impact loading rate of stairs descending showed significant statistically higher forces than that of level and ascending walking. The GRF showed similar correlation with GRF theta(r=.603) according to the ground conditions during gait. Conclusion : These results suggest that the GRF theta can be used in conjunction with a gait characteristics, prediction of loading rate and dynamic stability.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.127-131
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• 2003

Let X$_1$, X$_2$,... be a sequence of independent and identically distributed random variables with continuous cumulative distribution function F(x). X$_j$ is an upper record value of this sequence if X$_j$ > max {X$_1$,X$_2$,...,X$_{j-1}$}. We define u(n)=min{j$\mid$j> u(n-1), X$_j$ > X$_{u(n-1)}$, n $\geq$ 2} with u(1)=1. Then F(x) = 1-x$^{\theta}$, x > 1, ${\theta}$ < -1 if and only if (${\theta}$+1)E[X$_{u(n+1)}$$\mid$X$_{u(m)}$=y] = ${\theta}E[X_{u(n)}$\mid$X_{u(m)}=y], (\theta+1)^2E[X_{u(n+2)}$\mid$X_{u(m)}=y] = \theta^2E[X_{u(n)}$\mid$X_{u(m)}=y], or (\theta+1)^3E[X_{u(n+3)}$\mid$X_{u(m)}=y] = \theta^3E[X_{u(n)}$\mid$X_{u(m)}=y], n $\geq$ M+1$.