• East Asian mathematical journal
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• v.32 no.1
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• pp.61-75
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• 2016

If ${\phi}$ is a polarizable endomorphism on a projective variety, then the Weil height machine guarantees that ${\phi}$ satisfies Northcott's theorem. In this paper, we show that Northcott's theorem only holds for polarizable endomorphisms and generalize this result to arbitrary dominant endomorphisms: we introduce the height expansion and contraction coefficients which provide weak Northcott's theorem for dominant endomorphisms. We also give some applications of the height expansion and contraction coefficients.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.581-600
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• 2021

In this paper we obtain a unique common fixed point theorem for four self-maps which are involved in (𝜙, 𝜓)-weak contraction of a partially ordered b-metric space. The necessary condition has been given to a space for the existence of an unique common fixed of the maps. And our work changed conditions and nonlinear contraction, and search for the unique common fixed point of the maps.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.635-647
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• 1995

Let $H$ denote a separable, infinite dimensional complex Hilbert space and let $L(H)$ denote the algebra of all bounded linear operators on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $1_H$ and is closed in the $weak^*$ operator topology on $L(H)$. For $T \in L(H)$, let $A_T$ denote the smallest subalgebra of $L(H)$ that contains T and $1_H$ and is closed in the $weak^*$ operator topology.

• Korean Journal of Mathematics
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• v.16 no.2
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• pp.215-231
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• 2008

Let E be a uniformly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm, C a nonempty closed convex subset of E, and $T:C{\rightarrow}{\mathcal{K}}(E)$ a multivalued nonself-mapping such that $P_T$ is nonexpansive, where $P_T(x)=\{u_x{\in}Tx:{\parallel}x-u_x{\parallel}=d(x,Tx)\}$. For $f:C{\rightarrow}C$ a contraction and $t{\in}(0,1)$, let $x_t$ be a fixed point of a contraction $S_t:C{\rightarrow}{\mathcal{K}}(E)$, defined by $S_tx:=tP_T(x)+(1-t)f(x)$, $x{\in}C$. It is proved that if C is a nonexpansive retract of E and $\{x_t\}$ is bounded, then the strong ${\lim}_{t{\rightarrow}1}x_t$ exists and belongs to the fixed point set of T. Moreover, we study the strong convergence of $\{x_t\}$ with the weak inwardness condition on T in a reflexive Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm. Our results provide a partial answer to Jung's question.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.13-33
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• 2021

The aim of this paper is to establish common fixed point theorems under generalized (ψ - ϕ)-weak contractions in the setting of complete S-metric spaces and we support our result by some examples. Also an application of our results, we obtain some fixed point theorems of integral type. Our results extend Theorem 2.1 and 2.2 of Doric [5], Theorem 2.1 of Dutta and Choudhury [6], and many other several results from the existing literature.

• The Korean Journal of Physiology and Pharmacology
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• v.11 no.5
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• pp.207-213
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• 2007

This study was designed to characterize ureteral smooth muscle motility and also to study the effect of forskolin(FSK) and isoproterenol(ISO) on smooth muscle contractility in murine ureter. High $K^+$(50 mM) produced tonic contraction by $0.17{\pm}0.06mN$(n=19). Neuropeptide and neurotransmitters such as serotonin($5{\mu}M$), histamine($20{\mu}M$), and carbarchol(CCh, $10{\sim}50{\mu}M$) did not produce significant contraction. However, CCh($50{\mu}M$) produced slow phasic contraction in the presence of 25 mM $K^+$. Cyclopiazonic acid(CPA, $10{\mu}M$), SR $Ca^{2+}$-ATPase blocker, produced tonic contraction(0.07 mN). Meanwhile, inhibition of mitochondria by protonophore carbnylcyanide m-chlorophenylhydrazone(CCCP) also produced weak tonic contraction(0.01 mN). The possible involvement of $K^+$ channels was also pursued. Tetraethyl ammonium chloride(TEA, 10 mM), glibenclamide($10{\mu}M$) and quinidine($20{\mu}M$) which are known to block $Ca^{2+}$-activated $K^+$ channels($K_{Ca}$ channel), ATP-sensitive $K^+$ channels($K_{ATP}$) and nonselective $K^+$ channel, respectively, did not elicit any significant effect. However, $Ba^{2+}$($1{\sim}2mM$), blocker of inward rectifier $K^+$ channels($K_{IR}$ channel), produced phasic contraction in a reversible manner, which was blocked by $1{\mu}M$ nicardipine, a blocker of dehydropyridine-sensitive voltage-dependent L-type $Ca^{2+}$ channels($VDCC_L$) in smooth muscle membrane. This $Ba^{2+}$-induced phasic contraction was significantly enhanced by $10{\mu}M$ cyclopiazonic acid(CPA) in the frequency and amplitude. Finally, regulation of $Ba^{2+}$-induced contraction was studied by FSK and ISO which are known as adenylyl cyclase activator and $\beta$-adrenergic receptor agonist, respectively. These drugs significantly suppressed the frequency and amplitude of $Ba^{2+}$-induced contraction(p<0.05). These results suggest that $Ba^{2+}$ produces phasic contraction in murine ureteral smooth muscle which can be regulated by FSK and $\beta$-adrenergic stimulation.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.507-515
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• 2012

We investigate the number of the solutions for the elliptic boundary value problem. We obtain a theorem which shows the existence of six weak solutions for the elliptic problem with jumping nonlinearity crossing three eigenvalues. We get this result by using the geometric mapping defined on the finite dimensional subspace. We use the contraction mapping principle to reduce the problem on the infinite dimensional space to that on the finite dimensional subspace. We construct a three dimensional subspace with three axis spanned by three eigenvalues and a mapping from the finite dimensional subspace to the one dimensional subspace.

• Journal of Yeungnam Medical Science
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• v.8 no.2
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• pp.138-149
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• 1991

This study was aimed at investigation of the stimulatory innervations on the rat urinary bladder. Detrusor muscle strips of 15 mm long were suspended in isolated muscle chambers containing 1 ml of PSS maintained at $37^{\circ}C$ and aerated with 95% $O_2/5%CO_2$. Isometric myography was perfomed, and the results were as followings : Muscle strips showed "on-contraction" by electric field stimulation (EFS) frequency-dependently. The EFS-induced contraction was not affected by hexamethonium, a ganglion blocker, but abolished, by tetrodotoxin, a nerve conduction blocker. Physostigmine, a cholinesterase inhibitor enhanced the EFS-induced contraction which was inhibited by hemicholinium, an inhibitor of choline uptake at the cholinergic nerve ending. Such an EFS-induced contraction was antagonized by atropine only partially, and the atropine-resistant portion was completely abolished by the desensitization of purinergic receptors by prolonged incubatin of the strips in the presence of high concentratin of ATP. Bethanechol, a cholinergic agonist, elicited concentration-dependent contraction. Adenosine triphosphate (ATP), a purinergic agonist, induced a weak but concentration-dependent contraction of short duration. Bethanechol-induced contraction was not affected by ATP-desensitization, and ATP-induced contraction was not affected by tetrodotoxin. These results suggest that there are at least two main stimulatory components of innervations in the detrusor muscle, cholinergic muscarinic and purinergic ; and those receptors are independent each other.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.11 no.5
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• pp.738-747
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• 2000

In this paper it is shown that the meander line at the low frequency can be thought as the single transmission line whose characteristic impedance is approximately equal to that without coupling. But the length is contracted from that without coupling. The approximate contraction ratio is derived for weak coupling and is compared with the circuit simulation results and the EM simulation results. The formula are in good agreement with the simulation results in weak coupling.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.13-18
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• 2004

We defined Cantor dimensions of a perturbed Cantor set, and investigated a relation between these dimensions and Hausdorff and packing dimensions of a perturbed Cantor set. In this paper, we introduce another expressions of the Cantor dimensions. Using these, we study some informations which can be derived from power equations induced from contraction ratios of a perturbed Cantor set to give its Hausdorff or packing dimension. This application to a deranged Cantor set gives us an estimation of its Hausdorff and packing dimensions, which is a generalization of the Cantor dimension theorem.