• Economic and Environmental Geology
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• v.4 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1105-1127
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• 2013

Let C[0, $t$] denote the function space of real-valued continuous paths on [0, $t$]. Define $X_n\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\ldots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\ldots},x(t_n),x(t_{n+1}))$, respectively, where $0=t_0 <; t_1 <{\ldots} < t_n < t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions, which have the form $fr((v_1,x),{\ldots},(v_r,x)){\int}_{L_2}_{[0,t]}\exp\{i(v,x)\}d{\sigma}(v)$ for $x{\in}C[0,t]$, where $\{v_1,{\ldots},v_r\}$ is an orthonormal subset of $L_2[0,t]$, $f_r{\in}L_p(\mathbb{R}^r)$, and ${\sigma}$ is the complex Borel measure of bounded variation on $L_2[0,t]$. We then investigate the inverse conditional Fourier-Feynman transforms of the function and prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions can be expressed by the products of the analytic conditional Fourier-Feynman transform of each function.

• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.385-394
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• 1997

In this paper, we prove in p-uniforlmy convex space a fixed point theorem for a class of mappings T satsfying: for each x, y in the domain and for n = 1, 2, 3, $\cdots$, $$ \left\$\mid$ T^n x - T^n y \right\$\mid$ \leq a \cdot \left\$\mid$ x - y \right\$\mid$ + b(\left\$\mid$ x - T^n x \right\$\mid$ + \left\$\mid$ y - T^n y \right\$\mid$) + c(\left\$\mid$ c - T^n y \right\$\mid$ + \left\$\mid$ y - T^n x \right\$\mid$, $$ where a, b, c are nonnegative constants satisfying certain conditions. Further we establish some fixed point theorems for these mappings in a Hilbert space, in $L^p$ spaces, in Hardy spaces $H^p$ and in Sobolev spaces $H^{p,k}$ for 1 < p < $\infty$ and k $\leq$ 0. As a consequence of our main result, we also the results of Goebel and Kirk [7], Lim [8], Lifshitz [12], Xu [20] and others.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.44 no.4
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• pp.312-322
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• 2008

The age and growth of the sandfish, Arctoscopus japonicus were investigated from samples of the eastern sea danish seine and gill net fishery in the East Sea of Korea from February, 2004 to December, 2007. Ages were determined from annuli in otoliths and annuli were formed between December and February once a year. Also, the main spawning period was estimated to be between December and January, thus rings were considered to be annual marks. For the relationship between fork length and total weight, a multiplicative error structure was assumed because variability in growth increased as a function of the length. The relationship between fork length and total weight were $TW=0.0083FL^{3.01}(R^2=0.966)$ for female and $TW=0.0079FL^{3.04}(R^2=0.969)$ for male. The variability in growth was constant as a function of age, revealing an additive error structure. The von Bertalanffy growth parameters estimated by a non-linear method were $L_{\infty}=31.6cm$, K=0.266/year, $t_0=-0.835$ years for female and $L_{\infty}=27.7cm$, K=0.273/year, $t_0=-0.806$ years for male. Growth at age between male and female had a significant difference(P<0.001).

• Journal of the Korea Concrete Institute
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• v.17 no.2 s.86
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• pp.293-302
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• 2005

This study describes data from determination of the optimum mix proportion and site application of the mass concrete placed in bottom slab and side wall having a large depth and section as main structures of LNG in-ground tank. This concrete requires low heat hydration, excellent balance between workability and consistency because concreting work of LNG in-ground tank is usually classified by under-pumping, adaptation of longer vertical and horizontal pumping line than ordinary pumping condition. For this purpose, low heat Portland cement and lime stone powder as cementitious materials are selected and design factors including unit cement and water content, water-binder ratio, fine aggregate ratio and adiabatic temperature rising are tested in the laboratory and batch plant. As experimental results, the optimum unit cement and water content are selected under $270kg/m^3$ and $l55{\~}l60 kg/m^3$ separately to control adiabatic temperature rising below $30^{\circ}C$ and to improve properties of the fresh and hardened concrete. Also, considering test results of the confined water ratio($\beta$p) and deformable coefficient(Ep), $30\%$ of lime stone powder by cement weight is selected as the optimum replacement ratio. After mix proportions of 5cases are tested and compared the adiabatic temperature rising($Q^{\infty}$, r), tensile and compressive strength, modulus of elasticity, teases satisfied with the required performances are chosen as the optimum mix design proportions of the side wall and bottom slab concrete. $Q^{\infty}$ and r are proved smaller than those of another project. Before application in the site, properties of the fresh concrete and actual mixing time by its ampere load are checked in the batch plant. Based on the results of this study, the optimum mix proportions of the massive concrete are applied successfully to the bottom slab and side wall in LNG in-ground tank.

• Journal of Aquaculture
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• v.11 no.2
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• pp.193-201
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• 1998

This study was carried out to investigate the enviromental quality and the growth of transplanted pen shell, Atrinna pectinata japonica. Followings are the results of growth of transplanted pen shell with respect to the shell size groups from the natural habitat (Usando) in May 1995, and cultivated upto November in the transplantated area (Soomoonri). The water depth of transplantated area andnatural habitat were 3m, 20~25m, respectively. The seawater temperature of the two culturing farms were ranged of 10.9~$27.8^{\circ}C.$, 8.5~$30.0^{\circ}C.$, respectively at the lowest in November adn the highest in July. The seawater salinity of the two areas were ranged of 29.54~35.26$^0\prime\infty$, 28.75~36.31$^0\prime\infty$, respectively at the lowest in July and the highest in November. The phosphoric acid ($PO_4$-P) of the two areas were 0.09~$1.14 ^{\mu}$g-at/l, 0.23~$1.33 ^{\mu}$g-at/l, respectively at the lowest in June and the highest in September. The bottom type of the two areas was a silty mud, 85.23% (82.17~87.26%) in natural habitat and 92.12% (90.76~92.94$^0\prime\infty$) in transplanted area. In this study area, phytoplankton were composed of 19 species. Of these 19 species, Skeletonema costatum was dominant species in seawater between natural habitat and transplantatied area, and 157 cells/ml, 165 cells/ml at August respectively. Stock of phytoplankton in transplantated area were more than those of natural habitat except June and November. The growth of shell length, shell height, total weight, soft part weight and posterior adductor muscle weight of pen shell on different size groups (SL 10, 10~15, 15~20, 20cm) were excellent in shell length of 10cm group, and 99.32%, 107.66%, 871.09%, 951.26% and 1,223.76%, respectively. The survival rate of pen shell was 98.10% in the shell length of 10cm groups, 90.35~94.76% in the others groups. The growth of shell length, total weight, soft part weight and posterior adductor muscle weight of pen shell in transplantated area were more 1.3, 2.6, 2.7 and 4.5 times than those of natural habitat.

• KSBB Journal
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• v.15 no.2
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• pp.174-180
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• 2000

Pichia pastoris and Hansenula polymorpha, the methylotrophic yeasts have been widely used as a host for the production of e eudaryotic proteins due to the advantages related to their inherited characters. This paper describes the method to enhance t the productivity of recombinant proteins by P. pastoris and H. po$\psi$morpha. In the production of recombinant proteins using a f fed batch fermentation system, the effects of specific growth rate on the specific expression rate of re$\infty$mbinant proteins w were studied. In both species, the expression system of recombinant proteins using the fed batch fermentation was optimezed.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.65-72
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• 2012

Let T > 0 be given. Let $(C[0,T],m_{\varphi})$ be the analogue of Wiener measure space, associated with the Borel proba-bility measure ${\varphi}$ on ${\mathbb{R}}$, let $(L_{2}[0,T],\tilde{\omega})$ be the centered Gaussian measure space with the correlation operator $(-\frac{d^{2}}{dx^{2}})^{-1}$ and ${\el}_2,\;\tilde{m}$ be the abstract Wiener measure space. Let U be the space of all sequence $<c_{n}>$ in ${\el}_{2}$ such that the limit $lim_{{m}{\rightarrow}\infty}\;\frac{1}{m+1}\;\sum{^{m}}{_{n=0}}\;\sum_{k=0}^{n}\;c_{k}\;cos\;\frac{k{\pi}t}{T}$ converges uniformly on [0,T] and give a set function m such that for any Borel subset G of $\el_2$, $m(\mathcal{U}\cap\;P_{0}^{-1}\;o\;P_{0}(G))\;=\tilde{m}(P_{0}^{-1}\;o\;P_{0}(G))$. The goal of this note is to study the relationship among the measures $m_{\varphi},\;\tilde{\omega},\;\tilde{m}$ and $m$.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.323-342
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• 2013

Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $Xn:C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}:C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\cdots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\cdots},x(t_n),x(t_{n+1}))$, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n$ < $t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions which have the form $${\int}_{L_2[0,t]}{{\exp}\{i(v,x)\}d{\sigma}(v)}{{\int}_{\mathbb{R}^r}}\;{\exp}\{i{\sum_{j=1}^{r}z_j(v_j,x)\}dp(z_1,{\cdots},z_r)$$ for $x{\in}C[0,t]$, where $\{v_1,{\cdots},v_r\}$ is an orthonormal subset of $L_2[0,t]$ and ${\sigma}$ and ${\rho}$ are the complex Borel measures of bounded variations on $L_2[0,t]$ and $\mathbb{R}^r$, respectively. We then investigate the inverse transforms of the function with their relationships and finally prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the products of the conditional Fourier-Feynman transforms of each function.

• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.709-723
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• 2016

Let C[0, t] denote a generalized Wiener space, the space of real-valued continuous functions on the interval [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}{\mathbb{R}}^n$ by $Zn(x)=(\int_{0}^{t_1}h(s)dx(s),{\cdots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $t_n$ < t is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. In this paper we will introduce a simple formula for a generalized conditional Wiener integral on C[0, t] with the conditioning function $Z_n$ and then evaluate the generalized analytic conditional Wiener and Feynman integrals of the cylinder function $F(x)=f(\int_{0}^{t}e(s)dx(s))$ for $x{\in}C[0,t]$, where $f{\in}L_p(\mathbb{R})(1{\leq}p{\leq}{\infty})$ and e is a unit element in $L_2[0,t]$. Finally we express the generalized analytic conditional Feynman integral of F as two kinds of limits of non-conditional generalized Wiener integrals of polygonal functions and of cylinder functions using a change of scale transformation for which a normal density is the kernel. The choice of a complete orthonormal subset of $L_2[0,t]$ used in the transformation is independent of e and the conditioning function $Z_n$ does not contain the present positions of the generalized Wiener paths.