• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.135-144
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• 2005

We consider the stochastic differential inclusion of the form $dX_t{\in}{\sigma}(t, X_t)dB_t+b(t, X_t)dt$, where ${\sigma}$, b are set-valued maps, B is a standard Brownian motion. We prove that the set of solutions is closed.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.807-816
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• 2007

For the stochastic differential inclusion on infinite dimensional space of the form $dX_t{\in}\sigma(X_t)dW_t+b(X_t)dt$, where ${\sigma}$, b are set-valued maps, W is an infinite dimensional Hilbert space valued Q-Wiener process, we prove the boundedness and continuity of solutions under the assumption that ${\sigma}$ and b are closed convex set-valued satisfying the Lipschitz property using approximation.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.159-165
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• 2003

We consider the stochastic differential inclusion of the form $dX_t\;\in\;\sigma(t,\;X_t)db_t+b(t,\;X_t)dt$, where $\sigma$, b are set-valued maps, B is a standard Brownian motion. We prove the boundedness of solutions under the assumption that $\sigma$ and b satisfy the local Lipschitz property and linear growth.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.41-59
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• 2013

In this paper, we investigate the existence and controllability results for a class of abstract stochastic evolution differential inclusions with nonlocal conditions where the linear part is nondensely defined and satisfies the Hille-Yosida condition. The results are obtained by using integrated semigroup theory and a fixed point theorem for condensing map due to Martelli.

• Proceedings of the KIEE Conference
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• 1995.07b
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• pp.901-903
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• 1995

The ordinary differential equation (ODE) method has been widely used for the convergence analysis of stochastic recursive algorithms. The principal objective of this method is to associate to a given algorithm a differential equation with continuous righthand side. Usually some assumptions should be imposed to get such a differential equation. If any of assumptions fails, then the ODE method cannot be used. Recently a new method using differential inclusions (DIs) was introduced in [3], which is useful to deal with those cases. The DI method shares the same idea with the ODE method, but it is different in that a differential inclusion is identified instead of a differential equation with continuous righthand side. In this paper, we briefly review the DI method and then analyze a Robbins and Monro (RM)-type algorithm. Our focus is placed on the projected algorithm.

• KDI Journal of Economic Policy
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• v.36 no.3
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• pp.1-23
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• 2014

This paper has studied the monetary policy in Korea with a time varying VAR model using four key macroeconomic variables. First, inclusion of the exchange rate was a crucial factor in evaluating Korean monetary policy since the monetary policy demonstrated sensitivity to exchange rate movements during the crisis periods of both the Asian financial crisis of 1997 and the global financial crisis of 2008. Second, a specification of the stochastic volatilities in TVP-VAR model is important in explaining excessive movements of all variables in the sample. The overall moderation of variables in 2000s was more or less due to a reduction of the stochastic volatilities but also somewhat due to the macroeconomic fundamental structures captured by impulse response functons. Third, the degree of the monetary policy effectiveness of inflation was mitigated in recent periods but with increased persistence. Lastly, the monetary policy stance towards inflation stabilization has advanced ever since the inflation targeting scheme was adopted. However, there still seems to be a room for improvement in this aspect since the degree of the monetary policy stance towards inflation stabilization was relatively weaker than to output stabilization.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1691-1701
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• 2018

New inclusion sets are obtained for the eigenvalues of real matrices for which the all 1's vector is an eigenvector, i.e., the constant row-sum real matrices. A number of examples are provided. This paper builds upon the work of the authors in [7]. The results of this paper are in terms of $Ger{\check{s}}gorin$ discs of the second type. An application of the main theorem to bounding the algebraic connectivity of connected simple graphs is obtained.

• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.369-387
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• 2016

In this work, random homogenization analysis for the effective thermal properties of a three-dimensional composite material with unidirectional fibers is presented by combining the equivalent inclusion method with Random Factor Method (RFM). The randomness of the micro-structural morphology and constituent material properties as well as the correlation among these random parameters are completely accounted for, and stochastic effective thermal properties as thermal expansion coefficients as well as their correlation are then sought. Results from the RFM and the Monte-Carlo Method (MCM) are compared. The impact of randomness and correlation of the micro-structural parameters on the random homogenized results is revealed by two methods simultaneously, and some important conclusions are obtained.

• Geophysics and Geophysical Exploration
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• v.7 no.1
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• pp.14-18
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• 2004

High levels of ambient noise and safety factors often limit the use of 'active-source' seismic methods for geotechnical investigations in urban environments. As an alternative, shear-wave velocity-depth profiles can be obtained by treating the background microtremor wave field as a stochastic process, rather than adopting the traditional approach of calculating velocity based on ray path geometry from a known source. A recent field test in Melbourne demonstrates the ability of the microtremor method, using only Rayleigh waves, to resolve a velocity inversion resulting from the presence of a hard, 12 m thick basalt flow overlying 25 m of softer alluvial sediments and weathered mudstone. Normally the presence of the weaker underlying sediments would lead to an ambiguous or incorrect interpretation with conventional seismic refraction methods. However, this layer of sediments is resolved by the microtremor method, and its inclusion is required in one-dimensional layered-earth modelling in order to reproduce the Rayleigh-wave coherency spectra computed from observed seismic noise records. Nearby borehole data provided both a guide for interpretation and a confirmation of the usefulness of the passive Rayleigh-wave microtremor method. Sensitivity analyses of resolvable modelling parameters demonstrate that estimates of shear velocities and layer thicknesses are accurate to within approximately $10\%\;to\;20\%$ using the spatial autocorrelation (SPAC) technique. Improved accuracy can be obtained by constraining shear velocities and/or layer thicknesses using independent site knowledge. Although there exists potential for ambiguity due to velocity-thickness equivalence, the microtremor method has significant potential as a site investigation tool in situations where the use of traditional seismic methods is limited.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.34 no.1
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• pp.43-50
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• 2001

In order to analyze the dynamic motions of fish cage systems made of a frame and a netting under the conditions of waves and current, the hydraulic model experiment at towing tank and the numerical computation using boundary integral element method based on linear potential theory were carried out on a square and a circular type of fish cage, The computed and measured results for the dynamic motions of model fish cage systems showed that the heave and pitch motions were almost unaffected by the inclusion of nets, while the surge motions were very reduced by drag force acting on them. In addition, irregular wave-induced motions of fish cages included non-negligible 2nd order harmonic components at high frequency nearly twice the wave frequency. The reason why these motions were considered was due to resonance or structural components of frames being overflown and out of water during a wave cycle. It was found that circular type was more desirable structure in the open sea than square one only in the respect of dynamic motions due to waves and current. Further verifications were needed considering hydrodynamic forces, fatigue life, and structure analysis based on long term stochastic waves including frequency and time domain for the purpose of analyzing and designing fish cage systems.