• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.479-497
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• 2018

This paper deals with an optimal control on semilinear stochastic functional differential equations with Poisson jumps in a Hilbert space. The existence of an optimal control is derived by the solution of proposed system which satisfies weakly sequentially compactness. Also the stochastic maximum principle for the optimal control is established by using spike variation technique of optimal control with a convex control domain in Hilbert space. Finally, an application of retarded type stochastic Burgers equation is given to illustrate the theory.

• 전기의세계
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• v.24 no.5
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• pp.103-106
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• 1975

This Paper deals with an applicatoin of Luenberger Observer to the Linear Stochastic Systems. The basic technique is the use of a matrix version of the Maximum Principle of Pontryagin coupled with the use of gradient matrices to derive the gain matix for minimum error covariance. The optimal observer which is derived turns out to be identical to the well-known Kalman-Bucy Filter.

• Interaction and multiscale mechanics
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• v.3 no.4
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• pp.333-342
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• 2010

The Pseudo-Excitation Method (PEM) is applied to study the stochastic space vibration responses of train-bridge coupling system. Each vehicle is modeled as a four-wheel mass-spring-damper system with two layers of suspension system possessing 15 degrees-of- freedom. The bridge is modeled as a spatial beam element, and the track irregularity is assumed to be a uniform random process. The motion equations of the vehicle system are established based on the d'Alembertian principle, and the motion equations of the bridge system are established based on the Hamilton variational principle. Separate iteration is applied in the solution of equations. Comparisons with the Monte Carlo simulations show the effectiveness and satisfactory accuracy of the proposed method. The PSD of the 3-span simply-supported girder bridge responses, vehicle responses and wheel/rail forces are obtained. Based on the $3{\sigma}$ rule for Gaussian stochastic processes, the maximum responses of the coupling system are suggested.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.337-345
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• 2004

In allelic model X = ($\chi_1\chi$_2ㆍㆍㆍ, \chi_d$), M_f(t) = f(p(t)) - ${{\int^t}_0}\;Lf(p(t))ds$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we can show existence and uniqueness of solution for stochastic differential equation and martingale problem associated with mean vector. Also, we examine that if the operator related to this martingale problem is connected with Markov processes under certain circumstance, then this operator must satisfy the maximum principle.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.311-330
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• 2020

This paper investigates infinite horizon optimal control problems driven by a class of backward stochastic delay differential equations in Hilbert spaces. We first obtain a prior estimate for the solutions of state equations, by which the existence and uniqueness results are proved. Meanwhile, necessary and sufficient conditions for optimal control problems on an infinite horizon are derived by introducing time-advanced stochastic differential equations as adjoint equations. Finally, the theoretical results are applied to a linear-quadratic control problem.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.455-460
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• 2007

In allelic model $X=(x_1,\;x_2,\;{\cdots},\;x_d)$, $$M_f(t)=f(p(t))-{\int}_0^t\;Lf(p(t))ds$$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we try to apply diffusion processes for countable-allelic model in population genetic model and we can define a new diffusion operator $L^*$. Since the martingale problem for this operator $L^*$ is related to diffusion processes, we can define a integral which is combined with operator $L^*$ and a bilinar form $<{\cdot},{\cdot}>$. We can find properties for this integral using maximum principle.

• Computers and Concrete
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• v.26 no.2
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• pp.127-136
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• 2020

There is an inherent randomness for concrete microstructure even with the same manufacturing process. Meanwhile, the concrete material under the aqueous environment is usually not fully saturated by water. This study aimed to develop a stochastic micromechanical framework to investigate the probabilistic behavior of the unsaturated concrete from microscale level. The material is represented as a multiphase composite composed of the water, the pores and the intrinsic concrete (made up by the mortar, the coarse aggregates and their interfaces). The differential scheme based two-level micromechanical homogenization scheme is presented to quantitatively predict the concrete's effective properties. By modeling the volume fractions and properties of the constituents as stochastic, we extend the deterministic framework to stochastic to incorporate the material's inherent randomness. Monte Carlo simulations are adopted to reach the different order moments of the effective properties. A distribution-free method is employed to get the unbiased probability density function based on the maximum entropy principle. Numerical examples including limited experimental validations, comparisons with existing micromechanical models, commonly used probability density functions and the direct Monte Carlo simulations indicate that the proposed models provide an accurate and computationally efficient framework in characterizing the material's effective properties. Finally, the effects of the saturation degrees and the pore shapes on the concrete macroscopic probabilistic behaviors are investigated based on our proposed stochastic micromechanical framework.

• Journal of Korea Water Resources Association
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• v.30 no.3
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• pp.269-278
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• 1997

Operating rules, the basic principle of reservoir operation, are mostly developed from maximum or minimum, mean inflow series so that those rules cannot be used in practical operating situations to estimate the expected benefits or provide the operating policies for uncertainty conditions. Many operating rules based on the deterministic method that considers all operation variables including inflows as known variables can not reflect to uncertainties of inflow variations. Explicit operating rules can be developed for improving the weakness. In this method, stochastic trend of inflow series, one of the reservoir operation variables, can be directly method, the stochastic technique was applied to develop reservoir operating rule. In this study, stochastic dynamic programming using the concepts was applied to develop optimal operating rule for the Chungju reservoir system. The developed operating rules are regarded as a practical usage because the operating policy is following up the basic concept of Lag-1 Markov except for flood season. This method can provide reservoir operating rule using the previous stage's inflow and the current stage's beginning storage when the current stage's inflow cannot be predicted properly.

• Geomechanics and Engineering
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• v.14 no.5
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• pp.499-507
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• 2018

In this paper splitting failure on rock pillars among the underground caverns has been studied. The damaged structure is considered to be thin plates and then the failure mechanism of rock pillars has been studied consequently. The critical load of buckling failure of the rock plate has also been obtained. Furthermore, with a combination of the basic energy dissipation principle, generalized formulas in estimating the number of splitting cracks and in predicting the maximum deflection of thin plate have been proposed. The splitting criterion and the mechanical model proposed in this paper are finally verified with numerical calculations in FLAC 3D.