• Korean Journal of Mathematics
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• v.4 no.2
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• pp.173-178
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• 1996

In this paper, we discuss quasi-fuzzy H-closed space and introduce ${\theta}$-convergence of prefilter in fuzzy topological space. And we define ${\theta}$-closed fuzzy set using by ${\theta}$-convergence.

• The Pure and Applied Mathematics
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• v.28 no.1
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• pp.27-42
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• 2021

In this paper, we exploit some known theta function identities involving two parameters ��k,n and ��′k,n for the theta function �� to find about 54 new values of the Ramanujan's cubic continued fraction.

• Journal of Korean Ophthalmic Optics Society
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• v.6 no.2
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• pp.65-70
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• 2001

We obtained the sum of two curvature ($C_x+C_y$) in toric lens which two toroidal surface is the right angle each other. $$C_x+C_y=\frac{x^2+y^2}{2r_1}+\frac{x^2}{2}(\frac{1}{r_2}-\frac{1}{r_1})$$ and the sum of two curvature ($C_a+C_b$) in toric lens about the cross angle. $$(C_a+C_b)=\frac{x^2cos^2{\alpha}_1}{2r_1}+\frac{x^2cos^2{\alpha}_2}{2r_2}+\frac{y^2sin^2{\alpha}_1}{2r_1}+\frac{y^2sin^2{\alpha}_2}{2r_2}$$ and claculated the parameter S, C, ${\theta}$ of a combination power in toric lens of the cross angle including surface curvature ($C_x$, $C_y$) values. $$S=(n-1)\[\frac{C_x}{x^2}+\frac{C_y}{y^2}\]-\frac{C}{2},\;C=-\frac{2(n-1)}{sin2{\theta}}\[\frac{C_x}{x^2}+\frac{C_y}{y^2}\]$$ $${\theta}=\frac{1}{2}tan^{-1}\[-\frac{{C_xy^2sin2{\theta}_1}+{C_yx^2sin2{\theta}_2}}{{C_xy^2cos2{\theta}_1}+{C_yx^2cos2{\theta}_2}}\]$$.

• Journal of Korean Ophthalmic Optics Society
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• v.6 no.2
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• pp.59-63
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• 2001

Using the rotation of two polarizer plate and the area of transmittance In the visual light region measured by spectrophotometer, we obtained the luminance to measure the Contrast Sensitivity, and calculated the values of $L_{min}$ and ${\theta}_{min}$ after fixed the average contrast, $L_{max}$ and ${\theta}_{max}$ values from the values of two contrasts. Then, when it was fixed by $L_{max}=4000(T%nm)$ and ${\theta}_{max}=44.1^{\circ}$, $L_{min}$ and ${\theta}_{min}$ values were respectively given by 1333, 2666, 3920(T%nm) and 56.6, 54.3, $45^{\circ}$ in Cs values of 2.5, 100.

• 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$.

• Journal of Integrative Natural Science
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• v.7 no.4
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• pp.253-259
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• 2014

Protein kinase C theta (PKC-${\theta}$) is a serine/threonine specific protein kinase. It is largely expressed in the T-cells and CD28 signaling. PKC-${\theta}$ phosphorylates diverse proteins that are involved in the various cellular signaling pathways. Activated PKC-${\theta}$ in turn activates other transcription factors that control the proliferation and differentiation of T- cells. PKC-${\theta}$ is considered to be an interesting therapeutic target due to its crucial role in the proliferation, differentiation and survival of T-cells. In the present study, we have performed ligand-based CoMFA study on a series of pyridylpyrazolopyridine derivatives as PKC-${\theta}$ inhibitors. An acceptable CoMFA model ($q^2$=0.544; ONC=4; $r^2$=0.876) was developed and validated by Bootsrapping and progressive sampling. The CoMFA contour map suggested the regions to increase the activity. Bulky substitutions in R2 position of the piperizine ring could increase the activity. Similarly positive, small substitution in the R1 position of the Pyridine ring could considerably increase the activity. Our work could assist in designing more potent PKC-${\theta}$ inhibitors of pyridylpyrazolopyridine derivatives.

• Publications of The Korean Astronomical Society
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• v.15 no.1
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• pp.15-19
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• 2000

The lens mass determined from the photometrically obtained Einstein time scale suffers from large uncertainty due to the lens parameter degeneracy. The uncertainty can be substantially reduced if the mass is determined from the lens proper motion obtained from astrometric measurements of the source image centroid shifts, ${\delta}{\theta}_c$, by using high precision interferometers from space-based platform such as the Space Interferometry Mission (SIM), and ground-based interferometers soon available on several 8-10m class telescopes. However, for the complete resolution of the lens parameter degeneracy it is required to determine the lens parallax by measuring the parallax-induced deviations in the centroid shifts trajectory, ${\Delta}{\delta}{\theta}_c$ aloe. In this paper, we investigate the detectabilities of ${\delta}{\theta}_c$ and ${\Delta}{\delta}{\theta}_c$ by determining the distributions of the maximum centroid shifts, $f({\delta}{\theta}_{c,max})$, and the average maximum deviations, $(<{\Delta}{\delta}_{c,max}>)$, for different types of Galactic microlensing events caused by various masses. From this investigation, we find that as long as source stars are bright enough for astrometric observations it is expected that $f({\delta}{\theta}_c)$ for most events caused by lenses with masses greater than 0.1 $M_\bigodot$ regardless of the event types can be easily detected from observations by using not only the SIM (with a detection threshold but also the ${\delta}{\theta}_{th}\;\~3{\mu}as)$ but also the ground-based interferometers $(with\;{\delta}{\theta}_{th}\;\~3{\mu}as)$. However, from ground-based observations, it will be difficult to detect ${\Delta}{\delta}{\theta}_c$ for most Galactic bulge self-lensing events, and the detection will be restricted only for small fractions of disk-bulge and halo-LMC events for which the deviations are relatively large. From observations by using the SIM, on the other hand, detecting ${\Delta}{\delta}{\theta}_c$ will be possible for majority of disk and halo events and for a substantial fraction of bulge self-lensing events. For the complete resolution of the lens parameter degeneracy, therefore, SIM observations will be essential.

• Journal of Biosystems Engineering
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• v.13 no.3
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• pp.1-10
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• 1988

Fraser, Dombrowski, Tanasawa 그리고 Momono 등(等)이 분구(噴口)에 대(對)한 중자도구(中子導溝) 단면적(斷面積)의 비(比)에 기초을 두고 있는 Nozzle Parameter가 클수록 유량계수(流量係數)는 증가(增加)한다고 보고(報告)하였다. 그러나 노즐의 구조(構造)는 중자도구(中子導溝) 및 와실(渦室)의 형상(形狀)에 따라서 특성(特性)을 가지고 있고 구조(構造)의 특성(特性)은 유량계수(流量係數), 분무각(噴霧角) 및 살포도(撒布度)에 지대한 영향을 미친다. 노즐구조(構造)에 관(關)한 이론분석(理論分析)의 결과(結果)는 다음과 같다. 중자도구변(中子導溝邊)(d), 중자(中子)두께(t) 및 중자도구각(中子導溝角)(${\theta}$) 등(等)의 관계(關係)가 와실유선각(渦室流線角)(${\theta}_c$)에 미치는 영향은 $$tan({\theta}_c)=\frac{t{\cdot}sin^2{\theta}}{d-t{\cdot}sin{\theta}{\cdot}(1-cos{\theta})}$$ 또한 와실유선각(渦室流線角)(${\theta}_c$)이 중자도구각(中子導溝角)(${\theta}$)과 일치(一致)하는 관계(關係)는 $\frac{d}{t}=sin{\theta}$이다. 와실유선각(渦室流線角)과 와실형상(渦室形狀)과의 관계(關係)는 $$tan({\theta}_c){\qeq_-}\frac{r_c-r_g}{L_c}$$ 이며 와실유선각(渦室流線角)은 와실유선회전반경(渦室流線回轉半徑)과 와실(渦室)길이의 비(比)에 의(依)하여 변화(變化)함을 시사(示唆)한다. Swirl core가 Swirl plate보다는 생산비(生産費)의 고려없이 압력손실(壓力損失) 및 마찰손실 면(面)에서 더욱 합리적(合理的)으로 고려(考慮)된다.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.135-149
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• 2011

Using (r, s)-preopen sets [14] and pre-${\omega}_t$-closures [6], a new kind of covering property $P^t_{({\omega}_r,s)}$-closedness is introduced in a bitopological space and several characterizations via filter bases, nets and grills [30] along with various properties of such concept are investigated. Two new types of cluster sets, namely pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets and (r, s)t-${\theta}_f$-precluster sets of functions and multifunctions between two bitopological spaces are introduced. Several properties of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets are investigated and using the degeneracy of such cluster sets, some new characterizations of some separation axioms in topological spaces or in bitopological spaces are obtained. A sufficient condition for $P^t_{({\omega}_r,s)}$-closedness has also been established in terms of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets.

• 한국해양학회지
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• v.5 no.2
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• pp.41-51
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• 1970

Periodic characters of water temperature in the regions of the Mishima and the Okinoshima were derived through the analysis of the five days interval data during 1914 to 1970 mainly. In terms of ten days mean temperatures, annual variation function of the Mishima region, Korea Strait, is F($\theta_d$)=17.45-5.34 cos $\theta_d$-3.77 sin $\theta_d$+0.62 sin $2\theta_d$ -0.52 sin $3\theta_d$, where $\theta_d$=$\frac{\pi}{18}$(d-2), d is the order of ten days period 1 to 36. And in the region of Okinoshima, Tsushima Strait, we find F($\theta_d$)=18.88-5.39 cos $\theta_d$-3.60 sin $\theta_d$+0.52 sin $2\theta_d$. The annual mean temperature is 17.4$^{\circ}C$ in the Mishima region, 18.9$^{\circ}C$ in the Okinoshima region, and the amplitudes of annual variation functions are 7$^{\circ}C$ in both regions with minimum temperature in the middle ten days of February, maximum in the middle ten days of August. The long term variations of surface water temperature with 12 5 years period were observed in the annual mean temperature, monthly mean temperatures and the fixed day temperatures of every year. In addition to these, relatively short term variations were also found significant periods of 3 years, 4 years and 2 years, respectively.