• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.569-581
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• 2020

In this paper, we introduce the new general concept of usual expansiveness which is called "positively weak measure expansiveness" and study the basic properties of positively weak measure expansive C¹-differentiable maps on a compact smooth manifold M. And we prove that the following theorems. (1) Let 𝓟𝓦𝓔 be the set of all positively weak measure expansive differentiable maps of M. Denote by int(𝓟𝓦𝓔) is a C¹-interior of 𝓟𝓦𝓔. f ∈ int(𝓟𝓦𝓔) if and only if f is expanding. (2) For C¹-generic f ∈ C¹ (M), f is positively weak measure-expansive if and only if f is expanding.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1085-1100
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• 2023

For any given function f, we focus on the so-called prescribed mean curvature problem for the measure e^-f(|x|2)dx provided thate^-f(|x|2) ∈ L¹(ℝⁿ⁺¹). More precisely, we prove that there exists a smooth hypersurface M whose metric is ds² = dρ² + ρ²d𝜉² and whose mean curvature function is ${\frac{1}{n}}(\frac{u^p}{{\rho}^{\beta}})e^{f({\rho}^2)}{\psi}(\xi)$ for any given real constants p, β and functions f and ψ where u and ρ are the support function and radial function of M, respectively. Equivalently, we get the existence of a smooth solution to the following quasilinear equation on the unit sphere 𝕊ⁿ, $${\sum_{i,j}}({{\delta}_{ij}-{\frac{{\rho}_i{\rho}_j}{{\rho}^2+|{\nabla}{\rho}|^2}})(-{\rho}ji+{\frac{2}{{\rho}}}{\rho}j{\rho}i+{\rho}{\delta}_{ji})={\psi}{\frac{{\rho}^{2p+2-n-{\beta}}e^{f({\rho}^2)}}{({\rho}^2+|{\nabla}{\rho}|^2)^{\frac{p}{2}}}}$$ under some conditions. Our proof is based on the powerful method of continuity. In particular, if we take $f(t)={\frac{t}{2}}$, this may be prescribed mean curvature problem in Gauss measure space and it can be seen as an embedded result in Gauss measure space which will be needed in our forthcoming papers on the differential geometric analysis in Gauss measure space, such as Gauss-Bonnet-Chern theorem and its application on positive mass theorem and the Steiner-Weyl type formula, the Plateau problem and so on.

• The Korean Journal of Physiology and Pharmacology
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• v.15 no.6
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• pp.431-436
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• 2011

Vascular smooth muscle cells can obtain a proliferative function in environments such as atherosclerosis in vivo or primary culture in vitro. Proliferation of vascular smooth muscle cells is accompanied by changes in ryanodine receptors (RyRs). In several studies, the cytosolic $Ca^{2+}$ response to caffeine is decreased during smooth muscle cell culture. Although caffeine is commonly used to investigate RyR function because it is difficult to measure $Ca^{2+}$ release from the sarcoplasmic reticulum (SR) directly, caffeine has additional off-target effects, including blocking inositol trisphosphate receptors and store-operated $Ca^{2+}$ entry. Using freshly dissociated rat aortic smooth muscle cells (RASMCs) and cultured RASMCs, we sought to provide direct evidence for the operation of RyRs through the $Ca^{2+}$- induced $Ca^{2+}$ -release pathway by directly measuring $Ca^{2+}$ release from SR in permeabilized cells. An additional goal was to elucidate alterations of RyRs that occurred during culture. Perfusion of permeabilized, freshly dissociated RASMCs with $Ca^{2+}$ stimulated $Ca^{2+}$ release from the SR. Caffeine and ryanodine also induced $Ca^{2+}$ release from the SR in dissociated RASMCs. In contrast, ryanodine, caffeine and $Ca^{2+}$ failed to trigger $Ca^{2+}$ release in cultured RASMCs. These results are consistent with results obtained by immunocytochemistry, which showed that RyRs were expressed in dissociated RASMCs, but not in cultured RASMCs. This study is the first to demonstrate $Ca^{2+}$ release from the SR by cytosolic $Ca^{2+}$ elevation in vascular smooth muscle cells, and also supports previous studies on the alterations of RyRs in vascular smooth muscle cells associated with culture.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2014.05a
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• pp.86-88
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• 2014

Naive Bayes (NB) assumption has some harmful effects in classification to the real world data. To relax this assumption, we now propose approach called Naive Bayes Mutual Information Attribute Weighting with Smooth Kernel Density Estimation (NBMIKDE) that combine the smooth kernel for attribute and attribute weighting method based on mutual information measure.

• Management Science and Financial Engineering
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• v.6 no.1
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• pp.37-63
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• 2000

An important objective of pull-based production control is to achieve synchronized and smooth production flow in a multi-stage system that is subject to uncertainty. To our knowledge, previous research has not generated a performance measure that captures this objective of pull-based probased production control system. This performance material with respect to the instant when the operation is required. We examine the issue of asynchronous waste in a two-stage kanban control system.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.695-706
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• 1996

In the control system $ \dot{x} = f(t,x(t)) + g(t,x(t))\dot{u}, x(0) = \bar{x}, t \in [0,T], $ this paper shows that the map from u with $L^1(m)$-topology to $x_u$ with $L^1(\mu)$-topology is Lipschitz continuous where f is $C^1$, $\mu$ is the Stieltjes measure derived from the function g which is not smooth in the variable t and $x_u$ is the solution of the above system corresponding to u under the assumption that $\dot{u}$ is bounded.

• The Pure and Applied Mathematics
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• v.1 no.1
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• pp.19-24
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• 1994

Let P be a probability measure on the real line with Lebesque-density f. The usual estimator of the distribution function (≡df) of P for the sample $\chi$$_1$,…, $\chi$$\_$n/ is the empirical df: F$\_$n/(t)=(equation omitted). But this estimator does not take into account the smoothness of F, that is, the existence of a density f. Therefore, one should expect that an estimator which is better adapted to this situation beats the empirical df with respect to a reasonable measure of performance.(omitted)

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.193-207
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• 1999

Let ${\gamma}$ : Ilongrightarrow R2 be a sufficiently smooth curve and $\sigma$${\gamma}$ be the affine arclength measure supported on ${\gamma}$. In this paper, we study the Lp - improving properties of the convolution operators T$\sigma$${\gamma}$ associated with $\sigma$${\gamma}$ for various curves ${\gamma}$. Optimal results are obtained for all finite type plane curves and homogeneous curves (possibly blowing up at the origin). As an attempt to extend this result to infinitely flat curves we give and example of a family of flat curves whose affine arclength measure has same Lp-improvement property. All of these results will be based on uniform estimates of damping oscillatory integrals.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.935-955
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• 2020

In this paper we present a measurable version of the Smale's spectral decomposition theorem for homeomorphisms on compact metric spaces. More precisely, we prove that if a homeomorphism f on a compact metric space X is invariantly measure expanding on its chain recurrent set CR(f) and has the eventually shadowing property on CR(f), then f has the spectral decomposition. Moreover we show that f is invariantly measure expanding on X if and only if its restriction on CR(f) is invariantly measure expanding. Using this, we characterize the measure expanding diffeomorphisms on compact smooth manifolds via the notion of Ω-stability.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.129-136
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• 1996

We will investigate conditions of smooth measure ${\mu}$ for which analytic operator-valued Feynman integral associated with ${\mu}$ exist.