• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1229-1240
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• 2014

In this paper we provide three results involving large Schr$\ddot{o}$der paths. First, we enumerate the number of large Schr$\ddot{o}$der paths by type. Second, we prove that these numbers are the coefficients of a certain symmetric function defined on the staircase skew shape when expanded in elementary symmetric functions. Finally we define a symmetric function on a Fuss path associated with its low valleys and prove that when expanded in elementary symmetric functions the indices are running over the types of all Schr$\ddot{o}$der paths. These results extend their counterparts of Kreweras and Armstrong-Eu on Dyck paths respectively.

• Journal of Yeungnam Medical Science
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• v.12 no.2
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• pp.246-259
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• 1995

This study aimed to investigate the mechanism of action of baclofen on the detrusor muscle isolated from rat. Rats (Sprague-Dawley) were sacrificed by decapitation and exsanguination. Horizontal muscle strips of $2mm{\times}15mm$ were prepared for isometric myography in isolated muscle chamber bubbled with 95% / 5%-$O_2$ / $CO_2$ at $37^{\circ}C$, and the pH was maintained at 7.4. Detrusor strips contracted responding to the electrical field stimulation (EFS) by 2 Hz, 20 msec, monophasic square wave of 60 VDC. The initial peak of EFS-Induced contraction was tended to be suppresed by ${\alpha},{\beta}$-methylene-adenosine 5'-triphosphate (mATP), a partial agonist of purinergic receptor, and baclofen, a $GABA_B$ receptor agonist (statistically nonsignificant). The late sustained contraction by EFS was suppressed significantly (p < 0.05) by additions of atropione, a cholinergic muscarinic receptor antagonist and baclofen. The adenosine 5'-triphosphate-induced contraction was completely abolished by mA TP but not by baclofen. In the presence of atropine, the subsequent addition of acetylcholine could not contract the muscle strips: but the addition of acetylcholine in the presence of baclofen evoked a contraction to a remarkable extent. These results suggest that in the condition of present study, the cholinergic innervation may play a more important role than the purinergic one, and baclofen suppresses the contractility of rat detrusor by the stimulation of the $GABA_B$ receptors to inhibit the release of neurotransmitter from the cholinergic nerve ending.