• Korean Journal of Mathematics
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• v.27 no.2
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• pp.515-523
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• 2019

The aim of this paper is to present some necessary and sufficient conditions for existence of solution of Sylvester operator equation involving bounded subnormal operators in a Hilbert space. Our results improve and generalize some results in the literature involving normal operators.

• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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• pp.607-615
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• 2009

In this paper, we investigate the growth of solutions and the existence of subnormal solutions for a class of higher order linear differential equations. We obtain some results which improve and extend the results of Chen-Shon [2] and Gundersen-Steinbart [5].

• The Korean Journal of Physiology
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• v.18 no.2
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• pp.151-162
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• 1984

The mechanism of the contractile response of longitudial muscle of rabbit ileum to substance P (SP) has been investigated. The contractions in rabbit ileum under various conditions were recorded isometrically The following results were obtained. 1) The contractions by SP increased according to concentrations. SP·induced contraction was not sustained but faded rapidly at $10^{-7}M$. The response to the commutative addition of SP was decreased in comparison to the response to separate administration of each concentration . 2) The response to $10^{-8}M$ SP after 5 min application cf $10^{-7}M$ SP was increased with increasing the time interval between the administration of $10^{-7}$ and $10^{-8}M$ SP. 3) The treatment of rabbit ileum by $10^{-7}M$ SP for 5 min didn't decrease the response to $10^{-6}M$ acetylcholine. 4) $10^{-6}M$ atropine had no effect of the contractile response to $10^{-7}M$ SP. The response to $10^{-7}M$ SP was normal or subnormal in the presence of 3 mM tetraethylammonium(TEA). 5) 100k solution, $10^{-4}M$ ouabain, and Na-free solution inhibited the response to $10^{-8}M$ SP and 3 mM TEA completely, and to $10^{-7}M$ SP incompletely. 3 mM TEA induced a considerable contraction in K-free solution, but $10^{-8}M$ SP didn't induce the contraction. $10^{-6}M$ norepinephrine decreased the contractile responses to SP and TEA. 6) The contractile response to $10^{-7}M$ SP was dependent on the extracellular $Ca^{2+}$ concentrations to 1.8 mM. 7) The contractile response to $10^{-7}M$ SP remained 15% of the maximal response after bathing the ileum in a Ca-free solution for 2.5 min. 8) The responsiveness to SP was completely lost within 10 min of bathing in Ca-free solution, but was restored by the exposure to $Ca^{2+}$. The restorative effect of $Ca^{2+}$ depended on the concentration of $Ca^{2+}$, and on time for which the tissue exposed to this $Ca^{2+}$ concentration. These results suggest that there are two mechanisms of the action by which the low concentrations of substance P causes the contraction of intestinal smooth muscle: the reduction of K conductance and a mechanism dependent on the extracellular $Ca^{2+}$, and that high concentration of SP may elicit a contraction by releasing $Ca^{2+}$ from an intracellular store, which is not as sensitive to removal of extracellular $Ca^{2+}$ or as easily accessible to EGTA as the extracellular space of the muscle. The location of this store is not known; it may be associated with the internal side of the cell membrane.