• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.623-636
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• 2023

In this paper, we prove some vanishing theorems under the assumptions of weighted BiRic curvature or m-Bakry-Émery-Ricci curvature bounded from below.

• Journal of the Korean Data and Information Science Society
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• v.18 no.1
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• pp.237-245
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• 2007

Nonlinear asymmetric time series models have the growing interest in econometrics and finance. Threshold model is one of the successful asymmetric model. We consider a smooth transition ARMA model which converges a.s. to a threshold ARMA model and show that the smooth transition ARMA model admits a stationary measure, provided a suitable condition on the coefficients of the autoregressive parts of the different regimes is satisfied. Stationarity of a smooth transition GARCH model is also obtained.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.525-538
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• 1998

Recently, a stability theorem for the Feynman integral as a bounded linear operator on$ L_2$($R^{d}$ /) with respect to measures whose positive and negative variations are in the generalized Kato class was proved. We study a stability theorem for the Feynman integral with respect to measures whose positive variations are in the class of $\sigma$-finite smooth measures and negative variations are in the generalized Kato class. This extends the recent result in the sense that the class of $\sigma$-finite smooth measures properly contains the generalized Kato class.

• Journal of Advanced Marine Engineering and Technology
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• v.28 no.4
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• pp.611-617
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• 2004

Pixel classification is one of basic image processing issues. The general characteristics of the pixels belonging to various classes are discussed and the radical principles of pixel classification are given. At the same time. a pixel classification scheme based on image direction measure is proposed. As a typical application instance of pixel classification, an adaptive multi-level median filter is presented. An image can be classified into two types of areas by using the direction information measure, that is. smooth area and edge area. Single direction multi-level median filter is used in smooth area. and multi-direction multi-level median filter is taken in the other type of area. What's more. an adaptive mechanism is proposed to adjust the type of the filters and the size of filter window. As a result. we get a better trade-off between preserving details and noise filtering.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1359-1380
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• 2018

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Hardy type inequality with the same exponent n ($n{\geq}3$), then it has exactly the n-dimensional volume growth. Besides, three interesting applications of this fact have also been given. The first one is that we prove that complete noncompact smooth metric measure space with non-negative weighted Ricci curvature on which the Hardy type inequality holds with the best constant are isometric to the Euclidean space with the same dimension. The second one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then its flag curvature is identically zero. The last one is an interesting rigidity result, that is, we prove that if a complete n-dimensional Berwald space of non-negative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then it is isometric to the Minkowski space of dimension n.

• International Journal of Concrete Structures and Materials
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• v.6 no.2
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• pp.101-110
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• 2012

This paper focuses on the finite element (FE) response sensitivity and reliability analyses considering smooth constitutive material models. A reinforced concrete frame is modeled for FE sensitivity analysis followed by direct differentiation method under both static and dynamic load cases. Later, the reliability analysis is performed to predict the seismic behavior of the frame. Displacement sensitivity discontinuities are observed along the pseudo-time axis using non-smooth concrete and reinforcing steel model under quasi-static loading. However, the smooth materials show continuity in response sensitivity at elastic to plastic transition points. The normalized sensitivity results are also used to measure the relative importance of the material parameters on the structural responses. In FE reliability analysis, the influence of smoothness behavior of reinforcing steel is carefully noticed. More efficient and reasonable reliability estimation can be achieved by using smooth material model compare with bilinear material constitutive model.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.3
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• pp.171-180
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• 2023

Investigating local dynamics requires precise control to effectively manage the subtle differences that distinguish it from global dynamics. This paper aims to study the localized perspective of the recently proposed continuum-wise expansive measures [13]. Let f : M → M be a diffeomorphism on a closed smooth manifold M and let p be a hyperbolic periodic point of f. We prove that if the homoclinic class H_f (p) of f associated to p is C¹-robustly measure continuum-wise expansive then it is hyperbolic.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1131-1142
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• 2018

A notion of measure expansivity for homeomorphisms was introduced by Morales recently as a generalization of expansivity, and he obtained many interesting dynamic results of measure expansive homeomorphisms in [8]. In this paper, we introduce a concept of weak measure expansivity for homeomorphisms which is really weaker than that of measure expansivity, and show that a diffeomorphism f on a compact smooth manifold is $C^1$-stably weak measure expansive if and only if it is ${\Omega}$-stable. Moreover we show that $C^1$-generically, if f is weak measure expansive, then f satisfies both Axiom A and the no cycle condition.

• Proceedings of the Korean Institute of Building Construction Conference
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• 2020.06a
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• pp.191-192
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• 2020

The purpose of this study is to measure the electrical conductivity of cementitious composites as an early step to obtain shielding performance by mixing various type of steel fiber into cementitious composites, the main building material of protection facility, to shield electromagnetic pulse (EMP) damage. Fiber such as conductors as amorphous metallic fiber, hooked steel fiber, and smooth steel fiber are mixed into cementitious composites to give electrical conductivity and measure the impedance of concrete using LCR meter. By doing this, the electrical conductivity of each type of steel fiber reinforced cementitious composites (FRCC) is compared.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.543-551
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• 1997

We prove a norm inequality of the form $\left\$\mid$ \upsilon \right\$\mid$ \leq (r - 1) \left\$\mid$ u \right\$\mid$_p, 1 < p < \infty$, between a non-negative subharmonic function u and a smooth function $\upsilon$ satisfying $$\mid$\upsilon(0)$\mid$ \leq u(0), $\mid$\nabla\upsilon$\mid$ \leq \nabla u$\mid$$ and $\mid$\Delta\upsilon$\mid$ \leq \alpha\Delta u$, where $\alpha$ is a constant with $0 \leq \alpha \leq 1$. This inequality extends Burkholder's inequality where $\alpha = 1$.