• Korean Journal of Soil Science and Fertilizer
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• v.46 no.3
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• pp.163-172
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• 2013

The aquatic insect collected at six areas (each 2 for mountain area, plain field, and urban area) from 2009 to 2011 were classified to analyze the distribution and diversity of species. Frequency (number of aquatic insect: N), number of species (S), similarity index (C), richness index (R1, R2), variety index (V1, V2), evenness index (E1, E2, E3, E4, E5), and dominance index (D1) were investigated. Total N and S were 143 and 84, respectively. C matrix of 153 combinations was constructed with the average of 0.542. The average C of 3 years (0.659) was 9.9% P, more higher than the average C of 6 areas (0.560). The average values of the index of 18 plots were 2.28, 0.17, 1.24, 1.08, 0.07, 0.06, 0.01, 0.87, 0.31, 0.93 for R1, R2, V1, V2, E1, E2, E3, E4, E5, D1, respectively. The order in the coefficient of variation (CV) of the indicator for 18 plots was N (70.0%) > E3 (54.9%) > E1 (49.6%) > R2 (40.5%) > S (35.3%) > R1 (33.7%) > E2 (28.4%) > E5 (15.9%) > V1 (11.1%) > E4 (6.3%) > V2 (5.1%) > D1 (4.8%). The correlation matrix with 66 combinations between the indexes was constructed with statistical significance for 33 combinations. However, R1, V1, E2 and D1 were the proper indexes to represent species diversity of aquatic insect based on the correlation matrix and the theory of statistical independence. The richness index was highest in mountain, variety index in urban area, and evenness index in plain field. However, the dominance index was lowest in urban area.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.31-45
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• 2007

We prove the following theorem: Given a Varifold V in $l^{3}_{\infty}$ with the property that 0 < $lim_{r}_{\rightarrow}_{o}\;\frac{{\mu}v(C_{r}(x))}{r^{2}}\;<\;{\infty}\;for\;{\mu}v\;a.e.x\;{\in}$ SptV, then V is rectifiable.

• Journal of Food Hygiene and Safety
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• v.15 no.2
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• pp.128-136
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• 2000

Twenty-four Vibrio strains were isolated from imported frozen seafoods and identified according to their physiological and biochemical properties. They included two V cholerae non-01 sp., two V. diazotrophicus sp., one V. hollisae sp., five V. natriegens sp., eight V. fluvialis sp., and four V. nereis sp.. Two of them were not identified as Vibrio species. When these strains were tested using API-2OE kit fur identification, however, only the results for two V. cholerae and five of the V. fluvialis strains matched the results obtained previously. Due to the importance of detecting V cholerae from foods, phylogenetic identification of the strains was attempted based on restriction fragment length polymorphism (RFLP) of the 16S rDNAs amplified by PCR. The results suggested that the two strains had identical RFLP patterns which were more closely related to that of V. proteolyticus than V. cholerae. The problems associated with identification of pathogens originated from seafoods demand development of accurate and rapid identification methods.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.261-272
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• 2006

In this paper, we define the sequence spaces: $[V,{\lambda},f,p]_0({\Delta}^r,E,u),\;[V,{\lambda},f,p]_1({\Delta}^r,E,u),\;[V,{\lambda},f,p]_{\infty}({\Delta}^r,E,u),\;S_{\lambda}({\Delta}^r,E,u),\;and\;S_{{\lambda}0}({\Delta}^r,E,u)$, where E is any Banach space, and u = ($u_k$) be any sequence such that $u_k\;{\neq}\;0$ for any k , examine them and give various properties and inclusion relations on these spaces. We also show that the space $S_{\lambda}({\Delta}^r, E, u)$ may be represented as a $[V,{\lambda}, f, p]_1({\Delta}^r, E, u)$ space. These are generalizations of those defined and studied by M. Et., Y. Altin and H. Altinok [7].

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1693-1710
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• 2013

In this paper, we consider the biharmonic elliptic systems of the form $$\{{\Delta}^2u=F_u(u,v)+{\lambda}{\mid}u{\mid}^{q-2}u,\;x{\in}{\Omega},\\{\Delta}^2v=F_v(u,v)+{\delta}{\mid}v{\mid}^{q-2}v,\;x{\in}{\Omega},\\u=\frac{{\partial}u}{{\partial}n}=0,\; v=\frac{{\partial}v}{{\partial}n}=0,\;x{\in}{\partial}{\Omega},$$, where ${\Omega}{\subset}\mathbb{R}^N$ is a bounded domain with smooth boundary ${\partial}{\Omega}$, ${\Delta}^2$ is the biharmonic operator, $N{\geq}5$, $2{\leq}q$ < $2^*$, $2^*=\frac{2N}{N-4}$ denotes the critical Sobolev exponent, $F{\in}C^1(\mathbb{R}^2,\mathbb{R}^+)$ is homogeneous function of degree $2^*$. By using the variational methods and the Ljusternik-Schnirelmann theory, we obtain multiplicity result of nontrivial solutions under certain hypotheses on ${\lambda}$ and ${\delta}$.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.305-313
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• 2016

In this paper, we give several sufficient conditions ensuring that any positive radial solution (u, v) of the following ${\gamma}$-Laplacian systems in the whole space ${\mathbb{R}}^n$ has the components symmetry property $u{\equiv}v$ $$\{\array{-div({\mid}{\nabla}u{\mid}^{{\gamma}-2}{\nabla}u)=f(u,v)\text{ in }{\mathbb{R}}^n,\\-div({\mid}{\nabla}v{\mid}^{{\gamma}-2}{\nabla}v)=g(u,v)\text{ in }{\mathbb{R}}^n.}$$ Here n > ${\gamma}$, ${\gamma}$ > 1. Thus, the systems will be reduced to a single ${\gamma}$-Laplacian equation: $$-div({\mid}{\nabla}u{\mid}^{{\gamma}-2}{\nabla}u)=f(u)\text{ in }{\mathbb{R}}^n$$. Our proofs are based on suitable comparation principle arguments, combined with properties of radial solutions.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1753-1769
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• 2016

This paper is concerned with the quasilinear $Schr{\ddot{o}}dinger$ system $$(0.1)\;\{-{\Delta}u+a(x)u-{\Delta}(u^2)u=Fu(u,v)+h(x)\;x{\in}{\mathbb{R}}^N,\\-{\Delta}v+b(x)v-{\Delta}(v^2)v=Fv(u,v)+g(x)\;x{\in}{\mathbb{R}}^N,$$ where $N{\geq}3$. The potential functions $a(x),b(x){\in}L^{\infty}({\mathbb{R}}^N)$ are bounded in ${\mathbb{R}}^N$. By using mountain pass theorem and the Ekeland variational principle, we prove that there are at least two solutions to system (0.1).

• Korean Journal of Fisheries and Aquatic Sciences
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• v.30 no.5
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• pp.691-699
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• 1997

In order to find out the properties in flow resistance of trawlR=1.5R=1.5\;S\;v^{1.8}\;S\;v^{1.8} nets and the exact expression for the resistance R (kg) under the water flow of velocity v(m/sec), the experimental data on R obtained by other, investigators were pigeonholed into the form of $R=kSv^2$, where $k(kg{\cdot}sec^2/m^4)$ was the resistance coefficient and $S(m^2)$ the wall area of nets, and then k was analyzed by the resistance formular obtained in the previous paper. The analyzation produced the coefficient k expressed as $$k=4.5(\frac{S_n}{S_m})^{1.2}v^{-0.2}$$ in case of bottom trawl nets and as $$k=5.1\lambda^{-0.1}(\frac{S_n}{S_m})^{1.2}v^{-0.2}$$ in midwater trawl nets, where $S_m(m^2)$ was the cross-sectional area of net mouths, $S_n(m^2)$ the area of nets projected to the plane perpendicular to the water flow and $\lambda$ the representitive size of nettings given by ${\pi}d^2/2/sin2\varphi$ (d : twine diameter, 2l: mesh size, $2\varphi$ : angle between two adjacent bars). The value of $S_n/S_m$ could be calculated from the cone-shaped bag nets equal in S with the trawl nets. In the ordinary trawl nets generalized in the method of design, however, the flow resistance R (kg) could be expressed as $$R=1.5\;S\;v^{1.8}$$ in bottom trawl nets and $$R=0.7\;S\;v^{1.8}$$ in midwater trawl nets.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.287-291
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• 1997

Assume $H_i : R_+ \times R_+ \to R_+ (i = 1, 2)$ are monotonically increasing (in both variables), homogeneous mapping for which $H_1(tu, tv) = t^p(H_1(u, v) (p > 0)$ and $H_2(u, v)^{t^q} (q \leq 1)$ hold for $t, u, v \geq 0$. Using an idea from the paper of Baker, Lawrence and Zorzitto [2], the superstability problems of the functional inequalities $\Vert f(x+y) - f(x)f(y) \Vert \leq H_i (\Vert x \Vert, \Vert y \Vert)$ shall be investigated.