• Structural Engineering and Mechanics
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• v.28 no.3
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• pp.281-294
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• 2008

In this paper, linear elastic isotropic structures under the effects of both stochastic operators and stochastic excitations are studied. The analysis utilizes the spectral stochastic finite elements (SSFEM) with its two main expansions namely; Neumann and Homogeneous Chaos expansions. The random excitation and the random operator fields are assumed to be second order stochastic processes. The formulations are obtained for the system solution of the two dimensional problems of plane strain and plate bending structures under stochastic loading and relevant rigidity using the previously mentioned expansions. Two finite element programs were developed to incorporate such formulations. Two illustrative examples are introduced: the first is a reinforced concrete culvert with stochastic rigidity subjected to a stochastic load where the culvert is modeled as plane strain problem. The second example is a simply supported square reinforced concrete slab subjected to out of plane loading in which the slab flexural rigidity and the applied load are considered stochastic. In each of the two examples, the first two statistical moments of displacement are evaluated using both expansions. The probability density function of the structure response of each problem is obtained using Homogeneous Chaos expansion.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.607-618
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• 2017

In this paper, we introduce a quadratic stochastic operators on the set of all probability measures of a measurable space. We study the dynamics of the Lebesgue quadratic stochastic operator on the set of all Lebesgue measures of the set [0, 1]. Namely, we prove the regularity of the Lebesgue quadratic stochastic operators.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.813-837
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• 2022

In this paper we consider inverse problem for a general class of nonlinear stochastic differential equations on Hilbert spaces whose generating operators (drift, diffusion and jump kernels) are unknown. We introduce a class of function spaces and put a suitable topology on such spaces and prove existence of optimal generating operators from these spaces. We present also necessary conditions of optimality including an algorithm and its convergence whereby one can construct the optimal generators (drift, diffusion and jump kernel).

• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.167-178
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• 2016

In this paper, we study the stochastic integral of processes taking values of generalized operators based on a triple E ⊂ H ⊂ E^∗, where H is a Hilbert space, E is a countable Hilbert space and E^∗ is the strong dual space of E. For our purpose, we study E-valued Wiener processes and then introduce the stochastic integral of L(E, F^∗)-valued process with respect to an E-valued Wiener process, where F^∗ is the strong dual space of another countable Hilbert space F.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.311-319
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• 2001

We show that it is possible to associate diffusion processes to second order perturbations of the Ornstein-Uhlenbeck operator L on the Wiener space of the form L = L + 1/2∑L$^2$(sub)ξ(sub)$\kappa$ where the ξ(sub)$\kappa$ are "tangent processes" (i.e., semimartingales with antisymmetric diffusion coefficients).

• Journal of Korea Trade
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• v.26 no.3
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• pp.23-44
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• 2022

Purpose - Recent issues such as vessel enlargement, strengthening of environmental regulations, and port smartization are expected to increase costs and intensify competition in the port industry. In the new normal era, when external growth has reached its limit, the efficient operation of ports is becoming indispensable for achieving sustainable growth. This study aims to identify the determinants of inefficiency by examining the cost structure and efficiency of container terminals in Korea and furthermore propose the political implications to derive the maximization of efficiency. Design/methodology - This study estimates the cost function of container terminal operators and identifies the efficiency of container terminals using stochastic cost frontier (SCF) in the first stage. In the second step, the SCF results are compared with the data envelopment analysis (DEA). Last, this paper proposes efficiency determinants on container terminal operation to establish appropriate strategies. Out of the 29 container terminal operators in South Korea, 13 operators participated in the survey. The translog cost function was estimated utilizing a total of 116 observations collected over the 2007-2017 period. Findings - Empirical analysis shows that economies of scale exist in Korea's container ports, which provides a rationale for the government's policy to establish the global terminal operator by integrating small terminal operators to enhance competitiveness. In addition, as a result of the determinants analysis, container throughput, weight of direct employment costs, and labour cost share have positive effects on improving cost efficiency, while inefficiency increases as the length of quay increases. More specifically, cost efficiency improves as the proportion of direct employment costs to outsourcing service costs increases. Originality/value - This study contributes to analyzing the inefficiency factors of container terminals through efficiency analysis with respect to a cost function. In addition, this study proposes the practical and political implications, such as establishing a long-term manpower pool, the application of the hybrid liner terminal system, and the construction of a statistical data system, to improve the cost inefficiency of terminal operators.

• East Asian mathematical journal
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• v.33 no.3
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• pp.271-289
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• 2017

It is our purpose in this paper to introduce the concept of best random proximity pair for subsets A and B of a separable Banach space E. We prove some best random approximation and best random proximity pair theorems of certain classes of random operators, which is the stochastic verse of the deterministic results of Eldred et al. [22], Eldred et al. [18] and Eldred and Veeramani [19]. Furthermore, our results generalize and extend recent results of Okeke and Abbas [42] and Okeke and Kim [43]. Moreover, we shall apply our results to study nonlinear stochastic integral equations of the Hammerstein type.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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• pp.355-368
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• 2021

In this paper, we investigate necessary and sufficient conditions for the approximate controllability for semilinear stochastic functional differential equations with delays in Hilbert spaces without the strict range condition on the controller even though the equations contain unbounded principal operators, delay terms and local Lipschitz continuity of the nonlinear term.

• Environmental and Resource Economics Review
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• v.30 no.4
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• pp.557-579
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• 2021

Collective energy is an intermediate stage in energy conversion and has a great influence on the power structure as a distributed power source. However, the problem of the collective energy business has recently emerged due to the worsening profitability of some collective energy operators. This study measured the technical efficiency of major operators through the estimation of the production efficiency of Korean collective energy operators, and based on this, we looked at ways to improve the profit structure of operators. After collecting detailed data from 16 collective energy operators between 2016 and 2019, the production efficiency of operators was estimated using the panel stochastic frontier model. As a result of the estimation, combined steam power operators showed the highest production efficiency and reverse CHP operators showed the lowest efficiency. Furthermore, as a result of examining the factors influencing profitability, it was confirmed that production efficiency has a positive effect on overall profitability. However, businesses with a high proportion of heat production, such as small district electricity operators, profitability was lower. This phenomenon is due to the structural limitations of the current heat sales market. Hence, the adjustment of the heat sales unit price is necessary to improve profitability of collective energy operators.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.149-167
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• 2019

In this work, we study the existence, uniqueness and stability in the ${\alpha}$-norm of solutions for some stochastic partial functional integrodifferential equations. We suppose that the linear part has an analytic resolvent operator in the sense given in Grimmer [8] and the nonlinear part satisfies a $H{\ddot{o}}lder$ type condition with respect to the ${\alpha}$-norm associated to the linear part. Firstly, we study the existence of the mild solutions. Secondly, we study the exponential stability in pth moment (p > 2). Our results are illustrated by an example. This work extends many previous results on stochastic partial functional differential equations.