• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.725-743
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• 2022

In this paper, the concepts of ω-linked homomorphisms, the ω_𝜙-operation, and DW_𝜙 rings are introduced. Also the relationships between ω_𝜙-ideals and ω-ideals over a ω-linked homomorphism 𝜙 : R → T are discussed. More precisely, it is shown that every ω_𝜙-ideal of T is a ω-ideal of T. Besides, it is shown that if T is not a DW_𝜙 ring, then T must have an infinite number of maximal ω_𝜙-ideals. Finally we give an application of Cohen's Theorem over ω-factor rings, namely it is shown that an integral domain R is an SM-domain with ω-dim(R) ≤ 1, if and only if for any nonzero ω-ideal I of R, (R/I)_ω is an Artinian ring, if and only if for any nonzero element α ∈ R, (R/(a))_ω is an Artinian ring, if and only if for any nonzero element α ∈ R, R satisfies the descending chain condition on ω-ideals of R containing a.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.1075-1087
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• 2008

We study a class of KMS-symmetric quantum Markovian semigroups on a quantum spin system ($\mathcal{A},{\tau},{\omega}$), where $\mathcal{A}$ is a quasi-local algebra, $\tau$ is a strongly continuous one parameter group of *-automorphisms of $\mathcal{A}$ and $\omega$ is a Gibbs state on $\mathcal{A}$. The semigroups can be considered as the extension of semi groups on the nontrivial abelian subalgebra. Let $\mathcal{H}$ be a Hilbert space corresponding to the GNS representation con structed from $\omega$. Using the general construction method of Dirichlet form developed in [8], we construct the symmetric Markovian semigroup $\{T_t\}{_t_\geq_0}$ on $\mathcal{H}$. The semigroup $\{T_t\}{_t_\geq_0}$ acts separately on two subspaces $\mathcal{H}_d$ and $\mathcal{H}_{od}$ of $\mathcal{H}$, where $\mathcal{H}_d$ is the diagonal subspace and $\mathcal{H}_{od}$ is the off-diagonal subspace, $\mathcal{H}=\mathcal{H}_d\;{\bigoplus}\;\mathcal{H}_{od}$. The restriction of the semigroup $\{T_t\}{_t_\geq_0}$ on $\mathcal{H}_d$ is Glauber dynamics, and for any ${\eta}{\in}\mathcal{H}_{od}$, $T_t{\eta}$, decays to zero exponentially fast as t approaches to the infinity.

• The Pure and Applied Mathematics
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• v.19 no.1
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• pp.23-35
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• 2012

Given a set ${\Omega}$ and the notion of bipolar valued fuzzy sets, the concept of a bipolar ${\Omega}$-fuzzy sub-semigroup in semigroups is introduced, and related properties are investigated. Using bipolar ${\Omega}$-fuzzy sub-semigroups, bipolar fuzzy sub-semigroups are constructed. Conversely, bipolar ${\Omega}$-fuzzy sub-semigroups are established by using bipolar fuzzy sub-semigroups. A characterizations of a bipolar ${\Omega}$-fuzzy sub-semigroup is provided, and normal bipolar ${\Omega}$-fuzzy sub-semigroups are discussed. How the homomorphic images and inverse images of bipolar ${\Omega}$-fuzzy sub-semigroups become bipolar ${\Omega}$-fuzzy sub-semigroups are considered.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.815-834
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• 1995

Let $\Omega$ be a rectangular domain in $R^2$ with boundary $\partial\Omega$, and T be a positive real number such that $0 < T < \infty$.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.787-797
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• 2012

In this paper the authors study the $L^p$ boundedness for parabolic Littlewood-Paley operator $${\mu}{\Phi},{\Omega}(f)(x)=\({\int}_{0}^{\infty}{\mid}F_{\Phi,t}(x){\mid}^2\frac{dt}{t^3}\)^{1/2}$$, where $$F_{\Phi,t}(x)={\int}_{p(y){\leq}t}\frac{\Omega(y)}{\rho(y)^{{\alpha}-1}}f(x-{\Phi}(y))dy$$ and ${\Omega}$ satisfies a condition introduced by Grafakos and Stefanov in [6]. The result in the paper extends some known results.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.715-722
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• 2006

In this paper, we show that if T is a hyponormal operator on a non-separable Hilbert space H, then $Re\;{\omega}^0_{\alpha}(T)\;{\subset}\;{\omega}^0_{\alpha}(Re\;T)$, where ${\omega}^0_{\alpha}(T)$ is the weighted Weyl spectrum of weight a with ${\alpha}\;with\;{\aleph}_0{\leq}{\alpha}{\leq}h:=dim\;H$. We also give some conditions under which the product of two ${\alpha}-Weyl$ operators is ${\alpha}-Weyl$ and its converse implication holds, too. Finally, we show that the weighted Weyl spectrum of a hyponormal operator satisfies the spectral mapping theorem for analytic functions under certain conditions.

• Journal of The Korean Astronomical Society
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• v.28 no.1
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• pp.97-107
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• 1995

The stability of the geometrically thin, two-temperature hot accretion disk is studied. The general criterion for thermal instability is derived from the linear local analyses, allowing for advective cooling and dynamics in the vertical direction. Specifically, classic unsaturated Comptonization disk is analysed in detail. We find five eigen-modes: (1) Heating mode grows in thermal time scale, $(5/3)({\alpha}{\omega})^{-1}$, where alpha is the viscosity parameter and w the Keplerian frequency. (2) Cooling mode decays in time scale, $(2/5)(T_e/T_i)({\alpha}{\omega})^{-1}$, where $T_e\;and\;T_i$ are the electron and ion temperatures, respectively. (3) Lightman-Eardley viscous mode decays in time scale, $(4/3)(\Lambda/H)^2({\alpha}{\omega})^{-1}$, where $\Lambda$ is the wavelength of the perturbation and H the unperturbed disk height. (4) Two vertically oscillating modes oscillate in Keplerian time scale, $(3/8)^{1/2}\omega^{-1}$ with growth rate $\propto\;(H/\Lambda)^2$. The inclusion of dynamics in the vertical direction does not affect the thermal instability, adding only the oscillatory modes which gradually grow for short wavelength modes. Also, the advective cooling is not strong enough to suppress the growth of heating modes, at least for geometrically thin disk. Non-linear development of the perturbation is followed for simple unsaturated Compton disk: depending on the initial proton temperature perturbation, the disk can evolve to decoupled state with hot protons and cool electrons, or to one-temperature state with very cool protons and electrons.

• The Journal of Pediatrics of Korean Medicine
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• v.31 no.3
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• pp.37-45
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• 2017

Objectives Hataedock is an orally-administered herbal extract that used to treat toxic heat and help excrete meconium accumulates in the fetus from pregnancy. This study compared the effects of Hataedock using the extract of Douchi and omega-3 to control inflammation in the colonic mucosa. Methods NC/Nga mice were divided into three groups; Control group (no treatment), FGT group (given the extract of Douchi), and O3T group (given omega-3). The 3-week-old mouse from each group were given the extract of Douchi and omega-3. After 2 weeks, the colonic mucosa tissues of the mice were observed via Immunohistochemical staining for IL-4, IL-13, CD40, $Fc{\varepsilon}RI$, $p-I{\kappa}B$, EGF in the intestinal mucosa. Results In both FGT and O3T group, IL-4, IL-13, STAT-6 levels and CD40-positive reactions were decreased. However, EGF-positive responses were increased. FGT group showed 35% decrease in IL-4, 45% decrease in IL-13, 48% decrease in CD40, 50% decrease in $Fc{\varepsilon}RI$, 54% decrease in $p-I{\kappa}B$, 52% increase in EGF compared to the control group. O3T group also showed 14% decrease in IL-4, 23% decrease in IL-13, 22% decrease in CD40, 29% decrease in $Fc{\varepsilon}RI$, 41% decrease in $p-I{\kappa}B$, 39% increase in EGF compared to the control group. Conclusions Both early administration of Douchi extract and omega-3 were effective in regulating Th2, relieving inflammation and developing colonic mucosal tissues. Hataedock with Douchi extract may be more effective in modulating immune system in colonic mucosa than omega-3.

• The Korean Journal of Physiology and Pharmacology
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• v.10 no.5
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• pp.255-261
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• 2006

Melittin-induced nociceptive responses are mediated by selective activation of capsaicin-sensitive primary afferent fibers and are modulated by excitatory amino acid receptor, cyclooxygenase, protein kinase C and serotonin receptor. The present study was undertaken to investigate the peripheral and spinal actions of voltage-gated calcium channel antagonists on melittin-induced nociceptive responses. Changes in mechanical threshold and number of flinchings were measured after intraplantar (i.pl.) injection of melittin $(30\;{\mu}g/paw)$ into mid-plantar area of hindpaw. L-type calcium channel antagonists, verapamil [intrathecal (i.t.), 6 or $12\;{\mu}g$; i.pl.,100 & $200\;{\mu}g$; i.p., 10 or 30 mg], N-type calcium channel blocker, ${\omega}-conotoxin$ GVIA (i.t., 0.1 or $0.5\;{\mu}g$; i.pl., $5\;{\mu}g$) and P-type calcium channel antagonist, ${\omega}-agatoxin$ IVA (i.t., $0.5\;{\mu}g$; i.pl., $5\;{\mu}g$) were administered 20 min before or 60 min after i.pl. injection of melittin. Intraplantar pre-treatment and i.t. pre- or post-treatment of verapamil and ${\omega}-conotoxin$ GVIA dose-dependently attenuated the reduction of mechanical threshold, and melittin-induced flinchings were inhibited by i.pl. or i.t. pre-treatment of both antagonists. P-type calcium channel blocker, ${\omega}-agatoxin$ IVA, had significant inhibitory action on flinching behaviors, but had a limited effect on melittin-induced decrease in mechanical threshold. These experimental findings suggest that verapamil and ${\omega}-conotoxin$ GVIA can inhibit the development and maintenance of melittin-induced nociceptive responses.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.456-462
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• 2001

Comprehensive numerical computations are made of a homogenous spin-up in a cylindrical cavity with a time-dependent rotation rate. Numerical solutions are acquired to the governing axisymmetric cylindrical Navier-Stokes equation. A rotation rate formula is ${\Omega}_f={\Omega}_i+{\Delta}{\Omega}(1-{\exp}(-t/t_c))$. If $t_c$ is large, it implies that a rotation change rate is small. The Ekman number, E, is set to $10^{-4}$ and the aspect ratio, R/H, fixed to I. For a linear spin-up(${\epsilon}<<$), the major contributor to spin-up in the interior is not viscous-diffusion term but inviscid term, especially Coriolis term, though $t_c$ is very large. The viscous-diffusion term only works near sidewall. But for spin-up from rest, when $t_c$ is very large, viscous-diffusion term affects interior area as well as sidewall, initially. So azimuthal velocity of interior for large $t_c$ appears faster than that of interior for relatively small $t_c$. However, the viscous-diffusion term of interior decreases as time increases. Instead, inviscid term appears in the interior.