• Honam Mathematical Journal
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• v.29 no.4
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• pp.723-732
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• 2007

We investigate the existence of solutions u(x, t) for a perturbation b[$(\xi+\eta+1)^+-1$] of the hyperbolic system with Dirichlet boundary condition (0.1) = $L\xi-{\mu}[(\xi+\eta+1)^+-1]+f$ in $(-\frac{\pi}{2},\frac{\pi}{2}\;{\times})\;\mathbb{R}$, $L\eta={\nu}[(\xi+\eta+1)^+-1]+f$ in $(-\frac{\pi}{2},\frac{\pi}{2}\;{\times})\;\mathbb{R}$ where $u^+$ = max{u,0}, ${\mu},\nu$ are nonzero constants. Here $\xi,\eta$ are periodic functions.

• Honam Mathematical Journal
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• v.17 no.1
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• pp.107-118
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• 1995

We study the asymptotic behavior of nonnegative singular solutions of semilinear parabolic equations of the type $$u_t={\Delta}u-(u^q)_y-u^p$$ defined in the whole space $x=(x,y){\in}R^{N-1}{\times}R$ for t>0, with initial data a Dirac mass, ${\delta}(x)$. The exponents q, p satisfy $$1 where $q^*=max\{q,(N+1)/N\}$.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.14 no.4
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• pp.253-259
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• 1981

A study was made to find out a new method of calculating the survival rate of a fish population from length composition and growth equation. 1. In the steady state of the fish population, let the total mortality rate be z, the age of complete recruitment a, the oldest age in the catch b and the average between the age of complete recruitment and the oldest age in the catch Ut, then we have $$U_{t}\;=\;\frac{a-b\;{e xp}\{-z(b-a)\}}{1-\;{e xp}\{-z(b-a)\}}+\frac{1}{z}{\cdots}{\cdots}{\cdots}{\cdots}{\cdots}$$(1) And let b be infinite, then we obtain $$Z=\frac{1}{U_t-a}{\cdots}{\cdots}{\cdots}{\cdots}{\cdots}{\cdots}$$ (2) 2. Calculating numerical value of $U_t$ from age composition table and growth equation, and substitute in (1) for it, we may obtain the value of z and $e^{-z}$. 3. This method is applied to a case of mackerel and horse mackerel in the coastal waters of Korea, with the following results : Total mortality rate-Mackerel : 0.87909, Horse mackerel : 2.22327, Survival rate-Mackerel : 0.41516, Horse Mackerel : 0.10825, 95 percent confidence Interval of survival rate-Mackerel : $0.35966{\sim}0.47264$, Horse mackerel : $0.06897{\sim}0.14974$

• Honam Mathematical Journal
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• v.35 no.4
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• pp.707-716
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• 2013

The present paper consists of two parts. Since the recent paper [4] proved that an Alexandroff $T_0$-space is a semi-$T_{\frac{1}{2}}$-space, the first part studies semi-open and semi-closed structures of the Khalimsky nD space. The second one focuses on the study of a relation between the LS-property of ($SC^{n_1,l_1}_{k_1}{\times}SC^{n_2,l_2}_{k_2}$, k) relative to the simple closed $k_i$-curves $SC^{n_i,l_i}_{k_i}$, $i{\in}\{1,2\}$ and its normal k-adjacency. In addition, the present paper points out that the main theorems of Boxer and Karaca's paper [3] such as Theorems 4.4 and 4.7 of [3] cannot be new assertions. Indeed, instead they should be attributed to Theorems 4.3 and 4.5, and Example 4.6 of [10].

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.747-775
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• 2020

In this work we investigate the nonlocal elliptic equation with critical Hardy-Sobolev exponents as follows, $$(P)\;\{(-{\Delta}_p)^su={\lambda}{\mid}u{\mid}^{q-2}u+{\frac{{\mid}u{\mid}^{p{^*_s}(t)-2}u}{{\mid}x{\mid}^t}}{\hspace{10}}in\;{\Omega},\\u=0{\hspace{217}}in\;{\mathbb{R}}^N{\backslash}{\Omega},$$ where Ω ⊂ ℝ^N is an open bounded domain with Lipschitz boundary, 0 < s < 1, λ > 0 is a parameter, 0 < t < sp < N, 1 < q < p < p^∗_s where $p^*_s={\frac{N_p}{N-sp}}$, $p^*_s(t)={\frac{p(N-t)}{N-sp}}$, are the fractional critical Sobolev and Hardy-Sobolev exponents respectively. The fractional p-laplacian (-∆_p)^su with s ∈ (0, 1) is the nonlinear nonlocal operator defined on smooth functions by $\displaystyle(-{\Delta}_p)^su(x)=2{\lim_{{\epsilon}{\searrow}0}}\int{_{{\mathbb{R}}^N{\backslash}{B_{\epsilon}}}}\;\frac{{\mid}u(x)-u(y){\mid}^{p-2}(u(x)-u(y))}{{\mid}x-y{\mid}^{N+ps}}dy$, x ∈ ℝ^N. The main goal of this work is to show how the usual variational methods and some analysis techniques can be extended to deal with nonlocal problems involving Sobolev and Hardy nonlinearities. We also prove that for some α ∈ (0, 1), the weak solution to the problem (P) is in C^1,α(${\bar{\Omega}}$).

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.507-517
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• 2004

Let (2,2,2,2) be ramification indices for the Riemann sphere. It is well known that the regular branched covering map corresponding to this, is the Weierstrass P function. Lattes [7] gives a rational function R(z)= ${\frac{z^4+{\frac{1}{2}}g2^{z}^2+{\frac{1}{16}}g{\frac{2}{2}}$ which is chaotic on ${\bar{C}}$ and is induced by the Weierstrass P function and the linear map L(z) = 2z on complex plane C. It is also known that there exist regular branched covering maps from $T^2$ onto ${\bar{C}}$ if and only if the ramification indices are (2,2,2,2), (2,4,4), (2,3,6) and (3,3,3), by the Riemann-Hurwitz formula. In this paper we will construct regular branched covering maps corresponding to the ramification indices (2,4,4), (2,3,6) and (3,3,3), as well as chaotic maps induced by these regular branched covering maps.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.9 no.1
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• pp.1-7
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• 1976

1) The decrease in strength of netting twines at the knot may be regarded to be due mainly to the frictional force acting on the tip of the knot. The knot strength T may be given by $$T=\frac{T_0}{1+{\mu}\frac{s}{\rho}\varrho^{\mu\theta}$$ were $T_0$ is the tensile strength of unknotted netting twines, $\mu$ the coefficient of friction beween two netting twines forming a knot, s the contact length between the tip and the netting twine compressing it, $\rho$ the radius of curvature of the compressing, and $\theta$ the angle at which the compressing rubs with another one in the vicinity of the opposite tip. 2) Knots are arranged in order of strength as follows : the reef knot pulled lengthwise $\risingdotseq$ the trawler knot pulled breadtwise the reef knot pulled breadthwise.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.635-646
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• 2024

In this research work, we introduce and investigate four innovative types of soft spaces, pushing the boundaries of traditional spatial concepts. These new types of soft spaces are named as soft T_b space, soft T^#_b space, soft T^##_b space and soft_αT^#_b space. Through rigorous analysis and experimentation, we uncover and propose distinct characteristics that define and differentiate these spaces. In this research work, we have established that every soft $T_{\frac{1}{2}}$ space is a soft _αT^#_b space, every soft T_b space is a soft _αT^#_b space, every soft T^#_b space is a soft _αT^#_b space, every soft T_b space is a soft T^#_b space, every soft T^#_b space is a soft T^##_b space, every soft $T_{\frac{1}{2}}$ space is a soft ^#T_b space and every soft T_b space is a soft #T_b space.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1649-1654
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• 2014

A tournament T is an orientation of a complete graph and an arc in T is called pancyclic if it is contained in a cycle of length l for all $3{\leq}l{\leq}n$, where n is the cardinality of the vertex set of T. In 1994, Moon [5] introduced the graph parameter h(T) as the maximum number of pancyclic arcs contained in the same Hamiltonian cycle of T and showed that $h(T){\geq}3$ for all strong tournaments with $n{\geq}3$. Havet [4] later conjectured that $h(T){\geq}2k+1$ for all k-strong tournaments and proved the case k = 2. In 2005, Yeo [7] gave the lower bound $h(T){\geq}\frac{k+5}{2}$ for all k-strong tournaments T. In this note, we will improve his bound to $h(T){\geq}\frac{2k+7}{3}$.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1643-1653
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• 2019

This paper shows that if $1<p<{\infty}$, ${\alpha}{\geq}-n-2$, ${\alpha}>-1-{\frac{p}{2}}$ and f is holomorphic on the unit ball ${\mathbb{B}}_n$, then $${\int_{{\mathbb{B}}_n}}{\mid}Rf(z){\mid}^p(1-{\mid}z{\mid}^2)^{p+{\alpha}}dv_{\alpha}(z)<{\infty}$$ if and only if $${\int_{{\mathbb{B}}_n}}{\int_{{\mathbb{B}}_n}}{\frac{{\mid}f(z)-F({\omega}){\mid}^p}{{\mid}1-(z,{\omega}){\mid}^{n+1+s+t-{\alpha}}}}(1-{\mid}{\omega}{\mid}^2)^s(1-{\mid}z{\mid}^2)^tdv(z)dv({\omega})<{\infty}$$ where s, t > -1 with $min(s,t)>{\alpha}$.