• 대한수학회보
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• 제60권3호
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• pp.677-685
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• 2023

For n ≥ 2 and a real Banach space E, 𝓛(ⁿE : E) denotes the space of all continuous n-linear mappings from E to itself. Let Π (E) = {[x^*, (x₁, . . . , x_n)] : x^*(x_j) = ||x^*|| = ||x_j|| = 1 for j = 1, . . . , n }. An element [x^*, (x₁, . . . , x_n)] ∈ Π(E) is called a numerical radius point of T ∈ 𝓛(ⁿE : E) if |x^*(T(x₁, . . . , x_n))| = v(T), where the numerical radius v(T) = sup_{[y^*,y1,...,yn]∈Π(E)}|y^*(T(y₁, . . . , y_n))|. For T ∈ 𝓛(ⁿE : E), we define Nradius(T) = {[x^*, (x₁, . . . , x_n)] ∈ Π(E) : [x^*, (x₁, . . . , x_n)] is a numerical radius point of T}. T is called a numerical radius peak n-linear mapping if there is a unique [x^*, (x₁, . . . , x_n)] ∈ Π(E) such that Nradius(T) = {±[x^*, (x₁, . . . , x_n)]}. In this paper we present explicit formulae for the numerical radius of T for every T ∈ 𝓛(ⁿE : E) for E = c₀ or l_∞. Using these formulae we show that there are no numerical radius peak mappings of 𝓛(ⁿc₀ : c₀).

• 한국수산과학회지
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• 제38권4호
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• pp.257-264
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• 2005

We studied age and growth of the sea urchin, Pseudocentrotus depressus, to obtain some informations regarding its sustainable production and appropriate resources reinforcement. The samples were collected at two locations (Ongpo and Bubhwan) in Jeju, Korea. Annual rings were formed from October to January, and this period was well matched with the time just prior to or during their reproduction. Two population regression lines generated by using Walford's plotting with mean radius of each age group showed significant differences in their growth rate between the two sampling locations (p<0.0l). When the regression equations were calculated using either madreporite's radius (R) and test diameter (L) or body weight (W) and test diameter (L), the results were L=23.830+ 11.735R and $W=0.0004L^3$, and no statistically significant differences were detected between the two populations (p>0.2). Based on the data of madreporite's radius and test diameters, two estimated growth equations were $L_t(mm)=72.988(1-e^{-0.412(t-0.596)}\;and\;L_t(mm)=70.195(1-e{-0.365(t-0.51l)}$ in Ongpo and Bubhwan population, respectively. Three distinct annulus groups were recognizable within the distribution of the radii of the annual rings measured from age I to age 5. The mean radii calculated from the same annulus group were all identical even though they were from different age groups.

• 한국농공학회지
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• 제35권2호
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• pp.57-64
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• 1993

A modified kinematic wave model of the overland flow in vegetated filter strips was developed. The model can predict both flow depth and hydraulic radius of the flow. Existing models can predict only mean flow depth. By using the hydraulic radius, erosion, deposition and flow's transport capacity can be more rationally computed. Spacing hydraulic radius was used to compute flow's hydraulic radius. Numerical solution of the model was accomplished by using both a second-order nonlinear scheme and a linear solution scheme. The nonlinear portion of the model ensures convergence and the linear portion of the model provides rapid computations. This second-order nonlinear scheme minimizes numerical computation errors that may be caused by linearization of a nonlinear model. This model can also be applied to golf courses, parks, no-till fields to route runoff and production and attenuation of many nonpoint source pollutants.

• Journal of Ship and Ocean Technology
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• 제3권2호
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• pp.1-16
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• 1999

The incompressible Reynolds-Averaged Navier-Stokes(RANS) equations are solved using the standard $\textsc{k}-\varepsilon$ turbulence model and a finite volume method(FVM)with an O-type grid system. The computed results for its performance test are in good agreement with the published experimental data. The present method is applied to the study on the leading edge radius of a hydrofoil section Calculated results suggest that the leading edge radius has some effects on cavitation performances of a 2-D foil. A natural leading edge radius for the NACA66 section is determined from this study.

• 한국수산과학회지
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• 제3권3호
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• pp.154-160
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• 1970

우리나라 서해안의 참조기를 대상으로 1967년 6월부터 1968년 5월 사이의 자료에서 체장, 체중 및 인문(鱗紋)조사를 실시하며 다음의 결과를 얻었다. 1. 윤문은 연 1회 형성되고, 형성 시기는 $4\~7$월로, Bae(1960)가 발표한 산란기와 일치되고 있다. 2. 윤군(輪群)별 각 윤경(輪徑)적 평균 성장률은 0.73이었다. 3. 체장(total length)과 인경(鱗徑)과의 관계는 직선 회귀로, 그 관계식은 다음과 같다. L=61.350R+50.184 4. 체중과 체장(total length)과의 관계는 지수 곡선으로 다음과 같다. $$W=4.298L^{3.227}\times10^{-3}$$ 5. Walford의 정차도에 의하여 산출된 이론적인 최대 체강은 346.9mm이었고, 그 관계식은 다음과 같다. $$L_{n+1}=0.6866L_n+10.8730$$ 6. 연령과 체장(total length)과의 관계를 von Bertalanffy의 성장 방정식에 적응시킨 결과 다음과 같았다. $$L_t=346.9(1-e^{-0.376(t+0.609)})$$

• 호남수학학술지
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• 제34권1호
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• pp.103-111
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• 2012

Wetzel[5] proved if ${\Gamma}$ is a closed curve of length L in $E^n$, then ${\Gamma}$ lies in some ball of radius [L/4]. In this paper, we generalize Wetzel's result to the non-Euclidean plane with much stronger version. That is to develop a lower bound of length of a triangle inscribed in a circle in non-Euclidean plane in terms of a chord of the circle.

• 한국수산과학회지
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• 제31권4호
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• pp.529-534
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• 1998

1995년 1월부터 12월까지 한국 남서해역 (제주도 부근)에서 매월 어획된 황아귀를 대상으로 연령과 성장을 조사하였다. 연령사정은 척추골을 이용하였다. 황아귀 척추골의 추체에 윤문이 형성되는 시기는 3$\~$4월경으로 산란시기와 거의 일치하였다. 암컷의 연령은 8세까지, 그리고 수컷은 5세까지 나타났다. 추체경 (R)과 전장 (L) 사이에는 암컷의 경우 L=12.7+4.8R, 그리고 수컷의 경우 L=9.8+5.6R의 관계식을 보였다 전장과 체중 (W) 사이에는 암컷의 경우 $W=0.0089L^{3.0311}$, 그리고 수컷의 경우 $W=0.0329L^{2.7752}$의 관계식을 보였다 황아귀의 성장식은 암컷의 경우 $L_t=127.60(1-e^{-0.1228(t+0.3851)})$ 이었으며, 수컷은 $L_t=82.23(1-e^{-0.1832(t+0.6431)})$ 이었다.

• 대한수학회논문집
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• 제24권3호
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• pp.367-379
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• 2009

For a prime number p, let $\mathbb{Q}_p$ denote the p-adic field and let $\mathbb{Q}_p^d$ denote a vector space over $\mathbb{Q}_p$ which consists of all d-tuples of $\mathbb{Q}_p$. For a function f ${\in}L_{loc}^1(\mathbb{Q}_p^d)$, we define the Hardy-Littlewood maximal function of f on $\mathbb{Q}_p^d$ by $$M_pf(x)=sup\frac{1}{\gamma{\in}\mathbb{Z}|B_{\gamma}(x)|H}{\int}_{B\gamma(x)}|f(y)|dy$$, where |E|$_H$ denotes the Haar measure of a measurable subset E of $\mathbb{Q}_p^d$ and $B_\gamma(x)$ denotes the p-adic ball with center x ${\in}\;\mathbb{Q}_p^d$ and radius $p^\gamma$. If 1 < q $\leq\;\infty$, then we prove that $M_p$ is a bounded operator of $L^q(\mathbb{Q}_p^d)$ into $L^q(\mathbb{Q}_p^d)$; moreover, $M_p$ is of weak type (1, 1) on $L^1(\mathbb{Q}_p^d)$, that is to say, |{$x{\in}\mathbb{Q}_p^d:|M_pf(x)|$>$\lambda$}|$_H{\leq}\frac{p^d}{\lambda}||f||_{L^1(\mathbb{Q}_p^d)},\;\lambda$ > 0 for any f ${\in}L^1(\mathbb{Q}_p^d)$.

• 한국수산과학회지
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• 제37권1호
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• pp.51-56
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• 2004

Age and growth of three-lined tonguefish (Cynoglossus abbreviatus) were studied using samples from the waters off Yosu, Korea, from June to December, 2001. Sagittal otoliths had relatively clear annuli. Each annulus was formed once a year in April. The peak of the gonadosomatic index occurred also in April. The oldest fish observed in this study was 5 years old for females and 4 years old for males. The relationship between the otolith radius (R) and total length (L) was as follows: L=14.921R-2.5318 for females and L=13.527R-0.5584 for males. The relationship between total length and body weight (W) was as follows: $W=0.0008L^{3.54}$ for females and $W=0.0029L^{3.14}$ for males. The growth in length of the fish was expressed by the von Bertalanffy's growth equation as: $$L_t=44.54(1-e^{-0.16(t+2.69)})\;for\;females\;and\;L_t=41.52(1-e^{-0.15(t+3.34)})\;for\;males$$.

• 한국수산과학회지
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• 제37권4호
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• pp.307-311
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• 2004

Age and growth of red tongue sole (Cynoglossus joyneri), were studied using samples from the coastal waters off Yeosu, Korea, from January to December, 2001. Sagittal otoliths had relatively clear annuli. Marginal index of otolith dropped sharhly in August suggesting that each annulus was formed once a year In August. Monthly changes in the gonadosomatic index indicated that spawning peaked between July and September. The oldest fish observed in this study was 4 years old for both of females and males. Relationships between the otolith radius (R) and total length (L) were: L=14.1R-0.098 for females, and L=11.9R+1.83 for males. Relationships between total length and body weight $(W)\;were:\;W=0.0021L^{3.24}\;for\;females,\;and\;W=0.0014L^{3.39}$ for males. Growth in length of the fish was expressed by the von Bertalanffy's growth equation as:$L_{t}=29.06\;(1-e^{-0.19(t+2.40)})\;for\;females\;and\;L_{t}=27.44 (1-e^{-0.17(t+2.84)})$ for males.