• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.45-54
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• 1994

Throughout this paper, the definitions and properities related to probabilistic normed spaces are followed as in [2]. Let R be the set of all real numbers. A mapping F:R .rarw. [0, 1] is called a distribution function on R if it is nondecreasing and left continuous with inf F = 0 and sup F = 1. We denote by L the set of all distribution functions on R.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.255-275
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• 2022

In this paper, we introduce a new system of set-valued variational inclusion problems in semi-inner product spaces. We use resolvent operator technique to propose an iterative algorithm for computing the approximate solution of the system of set-valued variational inclusion problems. The results presented in this paper generalize, improve and unify many previously known results in the literature.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.461-475
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• 2000

In the present paper, we first give some examples of self-mappings which are asymptoticaly nonexpansive in the intermediate, not strictly hemicontractive, but satisfy the property (H). It is then shown that the modified Mann and Ishikawa iteration processes defined by $x_{n+1}=(1-\alpha_n)x_n+\alpha_nT^nx_n\ and\ x_{n+1}=(1-\alpha_n)x_n+\alpha_nT^n[(1-\beta_n)x_n+\beta_nT^nx_n]$,respectively, converges strongly to the unique fixed point of such a self-mapping in general Banach spaces.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.31 no.5
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• pp.305-313
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• 2019

Number of coastal protection structures have been increased rapidly due to rising sea levels and deteriorated sea conditions. Coastal structures should be designed to meet coastal engineering requirements and ecosystem conditions, while they are not lost or removed. In this study, trapezoidal gabion block was developed for the purpose, and two-dimensional laboratory experiments were conducted to validate applicability of the block. The experiments were carried out with eight types of erosive and accretive wave conditions. As a result, it was confirmed that the gabion blocks have a feature of preventing erosion of beach. The newly designed gabion blocks could be an alternative as a countermeasure method for beach erosion.

• Ocean Systems Engineering
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• v.6 no.1
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• pp.61-97
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• 2016

This is the second of two papers on the 3D numerical modeling of nearshore hydro- and morphodynamics. In Part I, the focus was on surf and swash zone hydrodynamics in the cross-shore and longshore directions. Here, we consider nearshore processes with an emphasis on the effects of oceanic forcing and beach characteristics on sediment transport in the cross- and longshore directions, as well as on foreshore bathymetry changes. The Delft3D and XBeach models were used with four turbulence closures (viz., ${\kappa}-{\varepsilon}$, ${\kappa}-L$, ATM and H-LES) to solve the 3D Navier-Stokes equations for incompressible flow as well as the beach morphology. The sediment transport module simulates both bed load and suspended load transport of non-cohesive sediments. Twenty sets of numerical experiments combining nine control parameters under a range of bed characteristics and incident wave and tidal conditions were simulated. For each case, the general morphological response in shore-normal and shore-parallel directions was presented. Numerical results showed that the ${\kappa}-{\varepsilon}$ and H-LES closure models yield similar results that are in better agreement with existing morphodynamic observations than the results of the other turbulence models. The simulations showed that wave forcing drives a sediment circulation pattern that results in bar and berm formation. However, together with wave forcing, tides modulate the predicted nearshore sediment dynamics. The combination of tides and wave action has a notable effect on longshore suspended sediment transport fluxes, relative to wave action alone. The model's ability to predict sediment transport under propagation of obliquely incident wave conditions underscores its potential for understanding the evolution of beach morphology at field scale. For example, the results of the model confirmed that the wave characteristics have a considerable effect on the cumulative erosion/deposition, cross-shore distribution of longshore sediment transport and transport rate across and along the beach face. In addition, for the same type of oceanic forcing, the beach morphology exhibits different erosive characteristics depending on grain size (e.g., foreshore profile evolution is erosive or accretive on fine or coarse sand beaches, respectively). Decreasing wave height increases the proportion of onshore to offshore fluxes, almost reaching a neutral net balance. The sediment movement increases with wave height, which is the dominant factor controlling the beach face shape.