• Journal of the Korean Mathematical Society
• /
• v.31 no.4
• /
• pp.633-643
• /
• 1994

Let us consider the initial-value problem of dimension m: $$ \frac{d\tau}{d}y(\tau) = f(\tau, Y(\tau)), y(0) = y_0, \tau \geq 0, (1.1) $$ Where $ = (f_1, f_2, \cdots, f_m) and y = (y_1, y_2, \cdots, y_m)$.

• Communications of the Korean Mathematical Society
• /
• v.30 no.3
• /
• pp.239-252
• /
• 2015

Motivated mainly by certain interesting extensions of the ${\tau}$-hypergeometric function defined by Virchenko et al. [11] and some ${\tau}$-Appell's function introduced by Al-Shammery and Kalla [1], we introduce here the ${\tau}$-Lauricella functions $F_A^{(n),{\tau}_1,{\cdots},{\tau}_n}$, $F_B^{(n),{\tau}_1,{\cdots},{\tau}_n}$ and $F_D^{(n),{\tau}_1,{\cdots},{\tau}_n}$ and the confluent forms ${\Phi}_2^{(n),{\tau}_1,{\cdots},{\tau}_n}$ and ${\Phi}_D^{(n),{\tau}_1,{\cdots},{\tau}_n}$ of n variables. We then systematically investigate their various integral representations of each of these ${\tau}$-Lauricella functions including their generating functions. Various (known or new) special cases and consequences of the results presented here are also considered.

• Korean Journal of Fisheries and Aquatic Sciences
• /
• v.8 no.4
• /
• pp.197-201
• /
• 1975

다랭이 주낚의 양승방식에는 방향의 양승(On-tracing retrieve)방식과 역방향의 양승(Back-tracing retrieve) 방식의 두가지 방식이 있다. 순방향의 양승은 최초에 투승된 주낙끝에서부터 양승하기 시작하여 투승한 순과 같은 순으로 양승하는 것이고 역방향의 양승은 최후에 투승된 주낚끝에서부터 양승하기 시작하며 투승한 순과 반대순으로 양승하는 것이다. 주낚의 조업소요시간을 변갱하지 않고 양승방식만 변갱한다면 주낚의 평균침지시간은 변하지 않고 다만 침지시간의 분포구간만 변한다. 투승작업시간을 $\tau_1$, 투승작업이 끝나고 양승작업을 시작하기까지의 대기시간을 $\tau_2$, 양승작업시간을 $\tau_3$하면 주낚의 침지시간분포범위는 양승방식에 따라 다음과 같이 서로 다르다. $\tau_2$부터 $\tau_1+\tau_2+\tau_3$까지의 범위 역방향으로 양승할 때 $\tau_1+\tau_2$부터 $\tau_2+\tau_3$까지의 범위 임의시의 낚시 어획성능은 $F_0\varrho-^{-zt}$ ($F_0$는 초기어획성능, z는 감소계수, t는 투승후 경과시간)으로 나타낼 수 있고 침지시간 t인 낚시 Hro의 어획미수는 $H_{F_0}\frac{1-\varrho^{-zt}}{z}$로 나타낼 수 있으므로 주낙조업에서 낚시수 $H_G$개 이고 침지시간이 $\tau_\alpha$와 $\tau_\beta$ 범위내에서 분포하면 어획미수는 $C_G$는 다음과 같이 나타낼 수 있다. $$C_G=\frac{H_G}{\tau_\beta-\tau_\alpha}{\cdot}\frac{F_0}{Z}\int^{\tau_\beta}_{\tau_\alpha}(1-\varrho^{-zt})dt$$ $\tau_\alpha,\;\tau_\beta$의 값은 순방향의 양승에 있어서는 $\tau_\alpha=\tau_1+\tau_2,\;\tau_\beta=\tau_2+\tau_3$, 역방향은 양승에 있어서는 $\tau_\alpha=\tau_2,\;\tau_\beta=\tau_1+\tau_2+\tau_3$. 따라서 다랭이 주낚의 어획미수는 그 양승방식에 따라 차가 있고 순방향의 양승으로 더 많은 어획미수를 얻을 수 있다.

• Honam Mathematical Journal
• /
• v.44 no.4
• /
• pp.521-534
• /
• 2022

In this paper, we introduce a new class 𝓡^k_λ(λ ≥ 1, k is any positive real number) of univalent complex functions, which consists of functions f of the form f(z) = z + Σ^∞_n=2 a_nzⁿ (|z| < 1) satisfying the subordination condition $$(1-{\lambda}){\frac{f(z)}{z}}+{\lambda}f^{\prime}(z){\prec}{\frac{1+r^2_kz^2}{1-k{\tau}_kz-{\tau}^2_kz^2}},\;{\tau}_k={\frac{k-{\sqrt{k^2+4}}}{2}$$, and investigate the Fekete-Szegö problem for the coefficients of f ∈ 𝓡^k_λ which are connected with k-Fibonacci numbers $F_{k,n}={\frac{(k-{\tau}_k)^n-{\tau}^n_k}{\sqrt{k^2+4}}}$ (n ∈ ℕ ∪ {0}). We obtain sharp upper bound for the Fekete-Szegö functional |a₃-𝜇a²₂| when 𝜇 ∈ ℝ. We also generalize our result for 𝜇 ∈ ℂ.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2003.07a
• /
• pp.131-134
• /
• 2003

[ $ZnWO_4$ ] shows excellent frequency selectivity due to its high quality factor($Q{\times}f$) at microwave frequencies. However, in order to use $ZnWO_4$ as multilayered wireless communication components, its other properties such as sintering temperature($1050^{\circ}C$), ${\tau}_f$ ($-70ppm/^{\circ}C$) and ${\varepsilon}_r(15.5)$ should be modified. In present study, $TiO_2$ and LiF were used to improve the microwave dielectric and sintering properties of $ZnWO_4$. $TiO_2$ additions to $ZnWO_4$ changed ${\tau}_f$ from negative to positive value, and also increased ${\varepsilon}_r$ due to its high ${\tau}_f$ ($+400ppm/^{\circ}C$) and ${\varepsilon}_r$(100). At 20 mol% $TiO_2$ addition, ${\tau}_f$ was controlled to near zero $ppm/^{\circ}C$ with ${\varepsilon}_r=19.4$ and $Q{\times}f=50000GHz$. However, the sintering temperature was still high to $1100^{\circ}C$. LiF addition to the $ZnWO_4+TiO_2$ mixture was greatly reduced the sintering temperature from $1100^{\circ}C$ to $850^{\circ}C$ due to liquid phase formation. Also LiF addition decreased the ${\tau}_f$ value due to its high negative ${\tau}_f$ value. Therefore, by controlling the $TiO_2$ and LiF amount, temperature stable LTCC material in the $ZnWO_4$-TiO_2-LiF$ system could be fabricated.

• The Korean Journal of Applied Statistics
• /
• v.29 no.3
• /
• pp.425-435
• /
• 2016

In this paper, we analyze the inverse statistics of rainfall for 12 regions from 1973 to 2014. We obtain a probability density function f(x) of daily rainfall x, and $f({\tau}_{\rho})$ of the first passage time ${\tau}_{\rho}$ for a given ${\rho}$. Lastly, we derive the relation between ${\rho}$ and ${\tau}_{mean}({\rho})$, i.e., the averaged value of ${\tau}_{\rho}$. The analyses result in the x and ${\tau}_{\rho}$ have stretched exponential distributions. Also, ${\tau}_{mean}({\rho})$ has the form of a stretched exponential function. We derive the shape parameter ${\beta}$ of the distribution, and analyze the characteristics of 12 regional rainfalls.

• The Mathematical Education
• /
• v.31 no.2
• /
• pp.133-140
• /
• 1992

The problem of estimating a smooth distribution function F at a point $\tau$ based on randomly right censored data is treated under certain smoothness conditions on F . The asymptotic performance of a certain class of kernel estimators is compared to that of the Kap lan-Meier estimator of F($\tau$). It is shown that the .elative deficiency of the Kaplan-Meier estimate. of F($\tau$) with respect to the appropriately chosen kernel type estimate. tends to infinity as the sample size n increases to infinity. Strong uniform consistency and the weak convergence of the normalized process are also proved.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.4
• /
• pp.815-823
• /
• 2010

Let ${\tau}\;{\neq}\;\delta_0$ be either a power bounded radial measure with compact support on the unit disc D with $\tau(D)\;=\;1$ such that there is a $\delta$ > 0 so that ${\mid}\hat{\tau}(s){\mid}\;{\neq}\;1$ for every $s\;{\in}\;\Sigma(\delta)$ \ {0,1}, or just a radial probability measure on D. Here, we provide a decomposition of the set X = {$h\;{\in}\;L^{\infty}(D)\;{\mid}\;lim_{n{\rightarrow}{\infty}}\;h\;*\;\tau^n$ exists}. Let $\tau_1$, ..., $\tau_n$ be measures on D with above mentioned properties. Here, we prove that if $f\;{in}\;L^{\infty}(D^n)$ satisfies an invariant volume mean value property with respect to $\tau_1$, ..., $\tau_n$, then f is n-harmonic.

• Nuclear Engineering and Technology
• /
• v.6 no.1
• /
• pp.14-22
• /
• 1974

Effects of anodization voltage on frequency characteristics of anodic oxide films on tantalum were analyzed based on the following impedance equatious : (equation omitted) Here $R_{f}$, $C_{f}$ and tan $\delta$$_{f}$ are equivalent series resistance in ohm, equivalent Belies capacitance in farad and dielectric loss, of anodic oxide films respectively Parameters P, $\tau$$_{ο}$, $\tau$$_{\omega}$, and Co are defined as follows: P=(d-w)/w, $\tau$$_{ο}$=$textsc{k}$$\rho$$_{ο}$, $\tau$$_{\omega}$=$textsc{k}$$\rho$$_{\omega}$, $C_{ο}$=$textsc{k}$A/d where d is the thickness of oxide film, $\omega$ is the diffusion layer thickness. $\rho$$_{ο}$ is the resistivity of oxide film at the interface of metal and the oxide, $\rho$$_{\omega}$ is the resistivity of oxide film at intrinsic region and A is the area of the film and $textsc{k}$=0.0885$\times$10$^{-12}$ $\times$dielectric constant, (in farad/cm). It was shown that dielectric loss and frequency dependence of equivalent series capacitance decrease as anodization voltage increases. This is a consequence of the fact that the thickness of diffusion layer increases a little with increasing anodization voltage whereas the total oxide thickness is proportional to the anodization voltage. The ngative deviation of measured values from tile relation, tan $\delta$$_{f}$=0.682 $\Delta$ $C_{f}$, was also discussed based on the Impedance equations given above. Here $\Delta$ $C_{f}$ is the change in capacitance between 0.1 and 1 KHZ.KHZ.Z.

• Journal of The Korean Astronomical Society
• /
• v.3 no.1
• /
• pp.13-16
• /
• 1970

A hyperbolic orbit is expanded in terms of F analogous to the eccentric anomaly of an elliptical orbit: ${\tau}^p\;sinq{\upsilon}\;and\;{\tau}^p\;cosq{\upsilon}$ are expressed in terms of F. The true anomaly ${\upsilon}$ is expressed in terms of F, and F in terms of ${\upsilon}$.