• 호남수학학술지
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• 제35권4호
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• pp.679-681
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• 2013

In this paper, we raise a question regarding existence and uniqueness of the steady-state solution of a type of Kolmogorov forward equation. We prove that the question has a positive answer for trivial vector fields, and also provide examples which show that the compactness assumption is necessary.

• 대한수학회논문집
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• 제33권3호
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• pp.1039-1048
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• 2018

In this paper we study the dynamics of a general ${\omega}-periodic$ model. Necessary and sufficient conditions for the global stability of zero steady state of the model are given. The conditions under which there exists a unique periodic solutions to the model are determined. We also show that the unique periodic solution is the global attractor of all other positive solutions. Some applications to mathematical models for cancer and tumor growth are given.

• 대한수학회보
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• 제51권5호
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• pp.1357-1368
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• 2014

This paper is concerned with a reaction-diffusion single species model with harvesting on n-dimensional isotropically growing domain. The model on growing domain is derived and the corresponding comparison principle is proved. The asymptotic behavior of the solution to the problem is obtained by using the method of upper and lower solutions. The results show that the growth of domain takes a positive effect on the asymptotic stability of positive steady state solution while it takes a negative effect on the asymptotic stability of the trivial solution, but the effect of the harvesting rate is opposite. The analytical findings are validated with the numerical simulations.

• 대한수학회보
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• 제49권6호
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• pp.1255-1262
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• 2012

A type of delayed Lotka-Volterra competition reaction-diffusion system is considered. By constructing a new Lyapunov function, we prove that the unique positive steady-state solution is globally asymptotically stable when interspecies competition is weaker than intraspecies competition. Moreover, we show that the stability property does not depend on the diffusion coefficients and time delays.

• The Korean Journal of Physiology
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• 제28권2호
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• pp.215-224
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• 1994

The presence of a calcium current $(i_{Ca^{2+}})$ passed via a specific channel was examined in the unfertilized hamster egg using the whole-cell voltage clamp technique. Pure inward current was isolated using a $Ca^{2+}-rich$ pipette solution containing 10 mM TEA. This current was independent of external $Na^+$ and was highly sensitive to the $Ca^{2+}$ concentration in the bathing solution, indicating that the inward current is carried by $Ca^{2+}$. The maximal amplitude was $-4.12{\pm}0.58nA\;(n=12)$ with 10mM $Ca^{2+}$ at -3OmV from a holding potential of -8OmV. This current reached its maximum within 20ms beyond -3OmV and decayed rapidly with an inactivation time constant $({\tau})$ of 15ms. Activation and inactivation of this $i_{Ca^{2+}}$ was steeply dependent on the membrane potential. The $i_{Ca^{2+}}$ began to activate at the lower voltage of -55 mV and reached its peak at -35 mV, being completely inactivated at potentials more positive than -40 mV. These result suggest that $i_{Ca^{2+}}$ in hamster eggs passes through channels with electrical properties similar to low voltage-activated T-type channels. Other results from the present study support this suggestion; First, the inhibitory effect of $Ni^{2+}\;(IC_{50}=13.7\;{\mu}M)$ was more potent than $Cd^{2+}\;(IC_{50}=123\;{\mu}M)$. Second, $Ba^{2+}$ conductance was equal to or below that of $Ca^{2+}$. Third, $i_{Ca^{2+}}$ in hamster eggs was relatively insensitive to nifedipine $(IC_{50}=96.6\;{\mu}M)$, known to be a specific t-type blocker. The physiological role of $i_{Ca^{2+}}$ in the unfertilized hamster eggs remains unclear. Analysis from steady-state inactivation activation curves reveals that only a small amount of this current will pass in the voltage range $(-70{\sim}-30\;mV)$ which partially overlaps with the resting membrane potential. This current has the property that it can be easily activated by a weak depolarization, thus it may trigger a certain kind of a intracellular event following fertilization which may cause oscillations in the membrane potential.

• The Korean Journal of Physiology
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• 제29권2호
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• pp.269-277
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• 1995

Membrane vesicles were prepared by differential centrifugation from epithelial cells of porcine trachea. Total activity of microsomal ATPases was measured spectrophotometrically by a coupled enzyme assay. The steady-state activity of the enzyme was $329{\pm}10$ nmol/min mg protein. Thapsigargin, a specific antagonist of intracellular $Ca^{2+}-ATPase$, inhibited about 50% of the activity, leaving $178{\pm}18\;nmol/min .mg$ protein (n=6), indicating that the $Ca^{2+}-ATPase$ is one of the major microsomal ATPases. The microsomes used in this study appeared to be tight-sealed vesicles since they showed saturation in $^{45}Ca^{2+}$ uptake experiments. Inositol 1,4,5-trisphosphate $InsP_{3}, 4\;{\mu}M$, an agonist of $InsP_{3}$-sensitive $Ca^{2+}$ release channel ($InsP_{3}$, receptor), and Ca-ionophore A23187 $(10\;{\mu}M)$ induced $^{45}Ca^{2+}$ releases of 20% and 50% of stored $^{45}Ca^{2+}$, respectively. The addition of $(10\;{\mu}M\;InsP_{3}$ also increased the microsomal ATPase activity from $282{\pm}8$ nmol/min mg protein to $334{\pm}21$ nmol/min . mg protein in the intact vesicles. Similar increase in the activity was observed by making microsomes leaky (uncoupling) using the Ca-ionophore A23187. ;$InsP_{3}-induced$ effects were blocked by either thapsigargin or heparin suggesting that: 1) the $InsP_{3}-induced$ increase in ATPase activity is mediated by microsomal $Ca^{2+}-ATPase$, and 2) dissipation of $Ca^{2+}$ gradient across the microsomal membrane is responsible for the $InsP_{3}-induced$ effect. In order to test the dependence of the $Ca^{2+}-ATPase$ activity on the activity of $InsP_{3}-induced$ the activity of ATPases was monitored in various concentrations of free $Ca^{2+}$ using $EGTA-Ca^{2+}$ buffers. The $Ca^{2+}$-dependent biphasic change is the well-known character of $InsP_{3} receptor but not of microsomal $Ca^{2+}-ATPase$ in non-excitable cells; however, the activity of microsomal ATPase appeared biphasic and a maxim진 activity of $397{\pm}36nmol/min\;.mg$ protein was obtained in the solution containing 100 nM free $Ca^{2+}$. Below or above this concentration, the activity of ATPases was lower. These results strongly support a positive correlation of microsomal $Ca^{2+}-ATPase$ to the $InsP_{3}$ receptors in epithelial microsomes.