• 대한수학회논문집
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• 제19권2호
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• pp.307-319
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• 2004

In this paper, we establish some new oscillation criteria for the functional differential equations of the form $\frac{d}{dt}$$\frac{1}{a_{n-1}(t)}$$\frac{d}{dt}(\frac{1}{{a_{n-2}(t)}\frac{d}{dt}(...(\frac{1}{a_1(t)}\frac{d}{dt}x(t))...)))^\alpha$ + $\delta[f_1(t,s[g_1(t)],\frac{d}{dt}x[h_1(t)])$ + $f_2(t,x[g_2(t)],\frac{d}{dt}x[h_2(t)])]=0$ via comparing it with some other functional differential equations whose oscillatory behavior is known.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권2호
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• pp.163-179
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• 2016

Let $M_1f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_2f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$ Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_1f(x,y)-{\rho}M_2f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ and (0.2) $N(M_2f(x,y)-{\rho}M_1f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ in fuzzy Banach spaces, where ρ is a fixed real number with ρ ≠ 1.

• Current Research on Agriculture and Life Sciences
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• 제4권
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• pp.77-86
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• 1986

재현기간(再現期間)에 따른 단시간(短時間) 강우강도특성(降雨强度特性)을 분석고찰(分析考察)하여 도시하수도(都市下水道) 및 중소유역(中小流域)의 배수계획(排水計劃)과 같은 수리구조물(水理構造物)의 설계(設計)에 필요(必要)한 최적강우강도식(最適降雨强度式)을 대구(大邱)와 포항(浦項)을 대표지점(代表地點)으로 분석(分析)한 결과(結果) 다음과 같은 결론(結論)을 얻었다. 1. 각종(各種) 확률강우강도식(確率降雨强度式) 산정(算定)에 있어서 대구(大邱)는 lwai 법(法), 포항(浦項)은 Gumbel-Chow 법(法)에 의한 결과치(結果値)를 확률강우강도(確率降雨强度)로 채택(採擇)함이 타당(妥當)하다고 생각된다. 2. 최적강우강도식(最適降雨强度式)을 유도(誘導)함에 있어서 표준편차비교결과(標準偏差比較結果) 대구(大邱)는 2.52~4.17, 포항(浦項)은 1.86~4.54로 공(共)히 Japanese 형(型) ($I=\frac{a}{\sqrt{t}+b}$)이 적합(適合)한 것으로 나타났으며, 재현기간별(再現期間別) 강우강도식(降雨强度式)은 다음과 같다. 대구(大邱) T : 200년(年) - $I=\frac{824}{\sqrt{t}+1.5414}$ T : 100년(年) - $I=\frac{751}{\sqrt{t}+1.4902}$ T : 30년(年) - $I=\frac{623}{\sqrt{t}+1.4017}$ T : 20년(年) - $I=\frac{580}{\sqrt{t}+1.3721}$ T : 10년(年) - $I=\frac{502}{\sqrt{t}+1.3145}$ T : 5년(年) - $I=\frac{418}{\sqrt{t}+1.2515$ 포항(浦項) T : 200년(年) - $I=\frac{468}{\sqrt{t}+1.1468}$ T : 100년(年) - $I=\frac{429}{\sqrt{t}+1.1605}$ T : 50년(年) - $I=\frac{391}{\sqrt{t}+1.1852}$ T : 30년(年) - $I=\frac{362}{\sqrt{t}+1.2033}$ T : 20년(年) - $I=\frac{339}{\sqrt{t}+1.2229}$ T : 10년(年) - $I=\frac{229}{\sqrt{t}+1.2578}$ T : 5년(年) - $I=\frac{257}{\sqrt{t}+1.3026}$ 3. 각(各) 지방(地方)에 따르는 재현기간별(再現期間別) 강우강도(降雨强度)를 쉽게 이용(利用)할 수 있도록 I.D.F. 상관도(相關圖)를 작성(作成)한 바 그 이용도(利用度)의 가치(價値)가 크게 있을 것으로 기대(期待)된다.

• 충청수학회지
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• 제20권3호
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• pp.261-267
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• 2007

We show the existence of the positive solution for the system of the following nonlinear wave equations with Dirichlet boundary conditions $$u_{tt}-u_{xx}+av^+=s{\phi}_{00}+f$$, $$v_{tt}-v_{xx}+bu^+=t{\phi}_{00}+g$$, $$u({\pm}\frac{\pi}{2},t)=v({\pm}\frac{\pi}{2},t)=0$$, where $u_+=max\{u,0\}$, s, $t{\in}R$, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}=1$ of the eigenvalue problem $u_{tt}-u_{xx}={\lambda}_{mn}u$ with $u({\pm}\frac{\pi}{2},t)=0$, $u(x,t+{\pi})=u(x,t)=u(-x,t)=u(x,-t)$ and f, g are ${\pi}$-periodic, even in x and t and bounded functions in $[-\frac{\pi}{2},\frac{\pi}{2}]{\times}[-\frac{\pi}{2},\frac{\pi}{2}]$ with $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}f{\phi}_{00}=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}g{\phi}_{00}=0$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권3호
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• pp.247-263
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• 2016

Let $M_{1}f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}f(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_{2}f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$. Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_{1}f(x,y),t){\geq}N({\rho}M_{2}f(x,y),t)$ where ρ is a fixed real number with |ρ| < 1, and (0.2) $N(M_{2}f(x,y),t){\geq}N({\rho}M_{1}f(x,y),t)$ where ρ is a fixed real number with |ρ| < $\frac{1}{2}$.

• Korean Journal of Mathematics
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• 제16권3호
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• pp.355-362
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• 2008

We prove the existence of a unique positive solution for a class of systems of the following nonlinear suspension bridge equation with Dirichlet boundary conditions and periodic conditions $$\{{u_{tt}+u_{xxxx}+\frac{1}{4}u_{ttxx}+av^+={\phi}_{00}+{\epsilon}_1h_1(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,\\{v_{tt}+v_{xxxx}+\frac{1}{4}u_{ttxx}+bu^+={\phi}_{00}+{\epsilon}_2h_2(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,$$ where $u^+={\max}\{u,0\},\;{\epsilon}_1,\;{\epsilon}_2$ are small number and $h_1(x,t)$, $h_2(x,t)$ are bounded, ${\pi}$-periodic in t and even in x and t and ${\parallel} h_1{\parallel}={\parallel} h_2{\parallel}=1$. We first show that the system has a positive solution, and then prove the uniqueness by the contraction mapping principle on a Banach space

• 대한핵의학회지
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• 제4권2호
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• pp.55-66
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• 1970

Reappraisal measurements of apparent half survival time of red cell by $^{51}Cr$ method was made and effects of blood-letting over red cell survival were observed. The study was performed on 53 normal male subjects under three different experimental conditions. 1. Group 1 Mean $^{51}Cr$ red cell half survival by ACD wash method was 29.7 days. $T\frac{1}{2}$ of Ascorbic acid method was 29.0 days in group with 100 mg dose and 29.1 days in group with 50 mg dose respectively. There was no difference between these two methods in regards to red cell half survival. No difference were noted in amount of ascorbic acid administered. 2. Group 2 As daily amount of blood loss is increased the shortening of red cell half survival was noted. Rapid phase was seen when blood loss ranged 10 to 25 ml per day, while slow phase noted when more loss amounted 25 ml or more daily. Thus, it was clear that there was more than an exponential relation between $T\frac{1}{2}$ and the amount of blood loss. 3. Group 3 $T\frac{1}{2}$ measured by cpm per whole blood was within normal range and $T\frac{1}{2}$ measured by cpm per red cell mass showed shortening tendency when compared with the former in the group measured after blood loss (from 25 ml daily up to 100 ml daily in 10 days). In the group with rather constant blood loss of 100 ml daily for 10 consecutive days revealed the significant difference in two measurements (P<0.01). 4. $T\frac{1}{2}$ in non-steady state When red cell production is increased compared with red cell destruction, $T\frac{1}{2}$ measured by cpm per red cell mass being shorter than that by cpm per whole blood. Shortening of $T\frac{1}{2}$ measured by cpm per whole blood is more prominent. if red cell destrction is enhanced and exceeds production. 5. It is clear that when expressing red cell destruction rate, $T\frac{1}{2}$ measured by cpm per whole blood is more adequate and production more consistent with cpm red cell mass. 6. $T\frac{1}{2}$ measured during blood-letting, when corrected by amount of blood loss, it remains normal. It is erroneous to use conventional equational when measuring $T\frac{1}{2}$ in non-steady. $T\frac{1}{2}$ measured by cpm per whole blood is considred more applicable in clinical evaluation.

• 대한수학회논문집
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• 제25권4호
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• pp.655-669
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• 2010

In this paper we propose new primal-dual interior point methods (IPMs) for $P_*(\kappa)$ linear complementarity problems (LCPs) and analyze the iteration complexity of the algorithm. New search directions and proximity measures are defined based on a class of kernel functions, $\psi(t)=\frac{t^2-1}{2}-{\int}^t_1e{^{q(\frac{1}{\xi}-1)}d{\xi}$, $q\;{\geq}\;1$. If a strictly feasible starting point is available and the parameter $q\;=\;\log\;\(1+a{\sqrt{\frac{2{\tau}+2{\sqrt{2n{\tau}}+{\theta}n}}{1-{\theta}}\)$, where $a\;=\;1\;+\;\frac{1}{\sqrt{1+2{\kappa}}}$, then new large-update primal-dual interior point algorithms have $O((1\;+\;2{\kappa})\sqrt{n}log\;n\;log\;{\frac{n}{\varepsilon}})$ iteration complexity which is the best known result for this method. For small-update methods, we have $O((1\;+\;2{\kappa})q{\sqrt{qn}}log\;{\frac{n}{\varepsilon}})$ iteration complexity.

• Kyungpook Mathematical Journal
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• 제28권2호
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• pp.129-139
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• 1988

Let $T^{\alpha}_{\lambda}$(p, A, B) denote the class of functions $$f(z)=z^p-{\sum\limits^{\infty}_{k=1}}{\mid}a_{p+k}{\mid}z^{p+k}$$ which are regular and p valent in the unit disc U = {z: |z| <1} and satisfying the condition $\left|{\frac{{e^{ia}}\{{\frac{f^{\prime}(z)}{z^{p-1}}-p}\}}{(A-B){\lambda}p{\cos}{\alpha}-Be^{i{\alpha}}\{\frac{f^{\prime}(z)}{z^{p-1}}-p\}}}\right|$<1, $z{\in}U$, where 0<${\lambda}{\leq}1$, $-\frac{\pi}{2}$<${\alpha}$<$\frac{\pi}{2}$, $-1{\leq}A$<$B{\leq}1$, 0<$B{\leq}1$ and $p{\in}N=\{1,2,3,{\cdots}\}$. In this paper, we obtain sharp results concerning coefficient estimates, distortion theorem and radius of convexity for the class $T^{\alpha}_{\lambda}$(p, A, B). It is further shown that the class $T^{\alpha}_{\lambda}$(p, A, B) is closed under "arithmetic mean" and "convex linear combinations". We also obtain class preserving integral operators of the form $F(z)=\frac{p+c}{z^c}{\int^z_0t^{c-1}}f(t)dt$, c>-p, for the class $T^{\alpha}_{\lambda}$(p, A, B). Conversely when $F(z){\in}T^{\alpha}_{\lambda}$(p, A, B), radius of p valence of f(z) has also determined.

• 자원환경지질
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• 제4권4호
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• pp.225-234
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• 1971

With the advance of civilization and steadily increasing population rivalry and competition for the use of the sewage, culverts, farm irrigation and control of various types of flood discharge have developed and will be come more and more keen in the future. The author has tried to calculated a formula that could adjust these conflicts and bring about proper solutions for many problems arising in connection with these conditions. The purpose of this study is to find out effective sewage, culvert, drainage, farm irrigation, flood discharge and other engineering needs in the Taegu area. If demands expand further a new formula will have to be calculated. For the above the author estimated methods of control for the probable expected rainfall using a formula based on data collected over a long period of time. The formula is determined on the basis of the maximum daily rainfall data from 1921 to 1971 in the Taegu area. 1. Iwai methods shows a highly significant correlation among the variations of Hazen, Thomas, Gumbel methods and logarithmic normal distribution. 2. This study obtained the following major formula: ${\log}(x-2.6)=0.241{\xi}+1.92049{\cdots}{\cdots}$(I.M) by using the relation $F(x)=\frac{1}{\sqrt{\pi}}{\int}_{-{\infty}}^{\xi}e^{-{\xi}^2}d{\xi}$. ${\xi}=a{\log}_{10}\(\frac{x+b}{x_0+b}\)$ ($-b<x<{\infty}$) ${\log}(x_0+b)=2.0448$ $\frac{1}{a}=\sqrt{\frac{2N}{N-1}}S_x=0.1954$. $b=\frac{1}{m}\sum\limits_{i=1}^{m}b_s=-2.6$ $S_x=\sqrt{\frac{1}{N}\sum\limits^N_{i=1}\{{\log}(x_i+b)\}^2-\{{\log}(x_0+b)\}^2}=0.169$ This formule may be advantageously applicable to the estimation of flood discharge, sewage, culverts and drainage in the Taegu area. Notation for general terms has been denoted by the following. Other notations for general terms was used as needed. $W_{(x)}$ : probability of occurranec, $W_{(x)}=\int_{x}^{\infty}f_{(n)}dx$ $S_{(x)}$ : probability of noneoccurrance. $S_{(x)}=\int_{-\infty}^{x}f_(x)dx=1-W_{(x)}$ T : Return period $T=\frac{1}{nW_{(x)}}$ or $T=\frac{1}{nS_{(x)}}$ $W_n$ : Hazen plot $W_n=\frac{2n-1}{2N}$ $F_n=1-W_x=1-\(\frac{2n-1}{2N}\)$ n : Number of observation (annual maximum series) P : Probability $P=\frac{N!}{{t!}(N-t)}F{_i}^{N-t}(1-F_i)^t$ $F_n$ : Thomas plot $F_n=\(1-\frac{n}{N+1}\)$ N : Total number of sample size $X_l$ : $X_s$ : maximum, minumum value of total number of sample size.