• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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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).

• Korean Journal of Fisheries and Aquatic Sciences
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• v.38 no.4
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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.

• Magazine of the Korean Society of Agricultural Engineers
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• v.35 no.2
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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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• v.3 no.2
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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.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.3 no.3
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• pp.154-160
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• 1970

The present paper deals with the growth of yellow croaker by scale age reading. This study is based on material from 596 specimens caught by the Danish seine in the Yellow Sea during the period from June 1967 to April 1968. Ring marks of the scale were formed from April to July, corresponding to the spawning season of the fish reported by Bae (1960). Growth rate of each radius of the ring was approximately 0.73. The relationship between the total length and radius of scales, and the relationship between the body weight and total length are represented by the following equations respectively: L=61.350R+50.184 $$W=4.298L^{3.227}\times10^{-3}$$ Maximum total length calculated by the diagram of Walford's growth transformation, $$L_{n+1}=0.6866L_n+10.8730$$, was 346.9mm. Growth curve of the fish can be expressed by the following von Bertalanffy's equation : $$L_t=346.9(1-e^{-0.376(t+0.609)})$$

• Honam Mathematical Journal
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• v.34 no.1
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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.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.31 no.4
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• pp.529-534
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• 1998

Age and growth of the yellow goosefish, Lophius litulon, were studied using samples collected from the southwestern waters of Korea. Vertebrae of the fish had relatively clear annuli on their surface. The opaque zone of vertebrae was formed once a year between March and April. The oldest fish observed in this study was 8 years old for females and 5 years old for males. The relationship between the radius (R) of vertebral centrum and total length (L) was as follows: L=12.7+4.8R for females and L=9.8+5.6R for males. The relationship between total length and body weight (W) was as follows : $W=0.0089L^{3.0311}$ for females and $W=0.0329L^{2.7752}$ for males. Growth in length of the fish was expressed by the von Bertalanffy's equation as $L_t=127.60(1-e^{-0.1228(t+0.3851)})$ for females and $L_t=82.23(1-e^{-0.1832(t+0.6431)})$ for males.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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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 ${\in}L^1(\mathbb{Q}_p^d)$.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.37 no.1
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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: $$L_t=44.54(1-e^{-0.16(t+2.69)})\;for\;females\;and\;L_t=41.52(1-e^{-0.15(t+3.34)})\;for\;males$$.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.37 no.4
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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.