• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.521-535
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• 2023

In this work, some various types of Dissipativity in random dynamical systems are introduced and studied: point, compact, local, bounded and weak. Moreover, the notion of random Levinson center for compactly dissipative random dynamical systems presented and prove some essential results related with this notion.

• Journal of the Korean earth science society
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• v.31 no.6
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• pp.555-562
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• 2010

Three-dimensional laser scanner was used to accurately measure any possible strain on a slope under pertaining stress with the time difference of 7 months. The laser scanner has the ability to measure the 3-D coordinate of a target point by calculating the travel time of laser beam between the laser device and the target point, and has been proved to be effective for analysis of the displacement of slopes or large construction. The scanning data measured with time difference were analyzed to find any strain by approaches of plane angle change, curvature variation, twist of frame, displacement of merging point, etc. From the analysis, some weak points showing heavily distorted shape were detected, which was used to design the reinforcement.

• Proceedings of the Korean Geotechical Society Conference
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• 2003.03a
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• pp.359-364
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• 2003

For safety evaluation of a rock-fill dim, it is often necessary to investigate spatial distribution of weak zones such as fracture. Both DC-resistivity survey and seismic(SASW) method are usually used for the purpose. Recently, Multichannel analysis of surface waves(MASW) method which makes up for the weak point of SASW method is developed and the site examination which is simple came to be possible comparatively. In order to obtain 2-D shear-wave velocity(Vs) profile along the dam axis that can be associated with dynamic properties of filled materials, MASW method was adapted. Then, DC-resistivity survey and drilling survey were performed to compare with each results. We confirmed that the MASW method and DC-resistivity survey show complementary result that corresspond with drilling result. Therefore, MASW method is an efficient method for dynamic characterization of dam-filling materials and also the combination of related methods such as DC-resistivity can lead to an effective safety evaluation of rock-fill dam.

• Journal of the Korean Geotechnical Society
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• v.22 no.8
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• pp.63-72
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• 2006

In the ASTM and ISRM, an uniaxial compressive strength(${\sigma}_{c}$) has been estimated to be 23(ASTM) or $20{\sim}25$(ISRM) times of point load strength index using a diametral test regardless of the rock rating or geological conditions. This paper presents a relationship between $I_{s}$ and ${\sigma}_{c}$ of a weak sedimentary rocks on Ulsan of the Kyung-Sang Basin in Korea. In the results of 291 for ${\sigma}_{c}$ test and 2310 for $I_{s}$ test from 77 spots, the predicted errors of ${\sigma}_{c}$ determined by strength ratio of ${\sigma}_{c}/I_{s}$ have been relatively less than those determined by linear regression analysis. And in case of weak sedimentary rocks such as mudstones, shales and sandstones, ${\sigma}_{c}$ should be lower than those suggested by ISRM and ASTM.

• Journal of the Korean Institute of Navigation
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• v.7 no.2
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• pp.47-63
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• 1983

In this paper, we have investigated the tidal characteristics of the Nakdongpo estuary. We have carried out the analysis of harmonic constant with the use of the recorded data on tidal level at the Gadeong Do tide station and analyzed the flow velocity data obtained by ourselves at two points in the Nakdongpo estuary. In addition, we have analyzed the variation of the mean-sea level. Typical items of the characteristics we have found are; (1) The principal harmonic constants and non-harmonic constants are shown in table 2. (2) Tide in this area shows the semidiurnal inequality. (3) The mean-sea level is shown to be depressed at the rate of about 1cm to the rise of 1 mbar of the atmospheric pressure. (4) (i) At $K_2$ point, The E-W component of the velocty reveals the nature of progressive waves. The N-S component reveals the nature of stationary waves. (ii) At $K_3$ point, The E-W component shows the characteristics of progressive waves to some degree. The N-S component shows a weak hint of stationary waves. (5) At $K_2$ point, S-component is predominant due to the flow of river. At $K_3$ point, E-component is predominant due to the Tsushima current.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.341-348
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• 2004

This paper presents a modeling technique of cracks by combined extended and superposed finite element method (XSFEM) which is a combination of the extended finite element method (XFEM) and the mesh superposition method (sversion FEM). In the proposed method, the near-tip field is modeled by a superimposed patch consisting of quarter point elements and the rest of the discontinuity is treated by the XFEM. The actual crack opening in this method is measured by the sum of the crack openings of XFEM and SFEM in transition region. This method retains the strong point of the XFEM so it can avoid remeshing in crack evolution and trace the crack growth by translation or rotation of the overlaid mesh and the update of the nodes to be enriched by step functions. Moreover, the quadrature of the Galerkin weak form becomes simpler. Numerical experiments are provided to demonstrate the effectiveness and robustness of the proposed method.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.87-98
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• 2010

The purpose of this paper is to prove a weak convergence theorem for a common fixed points of finite family of nonspreading mappings and nonexpansive mappings in Hilbert spaces. The results presented in this paper extend and improve the results of Mondafi [A. Moudafi, Krasnoselski-Mann iteration for hierarchical fixed-point problems, Inverse Problems 23 (2007) 1635-1640], and Iemoto and Takahashi [So Iemoto, W.Takahashi, Approximating common fixed points of nonexpansive mappings and nonspreading mappings in a Hilbert space, Nonlinear Analysis (2009), doi:10.1016/j.na.2009.03.064].

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.995-1009
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• 2021

Many iterative algorithms like that Picard, Mann, Ishikawa and S-iteration are very useful to elucidate the fixed point problems of a nonlinear operators in various topological spaces. The recent trend for elucidate the fixed point via inertial iterative algorithm, in which next iterative depends on more than one previous terms. The purpose of the paper is to establish convergence theorems of new inertial Picard normal S-iteration algorithm for nonexpansive mapping in Hilbert spaces. The comparison of convergence of InerNSP and InerPNSP is done with InerSP (introduced by Phon-on et al. [25]) and MSP (introduced by Suparatulatorn et al. [27]) via numerical example.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.449-469
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• 2022

This paper deals with the new iterative algorithm for approximating the fixed point of generalized 𝛼-nonexpansive mappings in a hyperbolic space. We show that the proposed iterative algorithm is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur and Piri iteration processes for contractive mappings in a Banach space. We also establish some weak and strong convergence theorems for generalized 𝛼-nonexpansive mappings in hyperbolic space. The examples and numerical results are provided in this paper for supporting our main results.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.179-195
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• 2024

In this article, we study the Picard-Ishikawa iterative method for approximating the fixed point of generalized α-Reich-Suzuki nonexpanisive mappings. The weak and strong convergence theorems of the considered method are established with mild assumptions. Numerical example is provided to illustrate the computational efficiency of the studied method. We apply our results to the solution of a nonlinear delay integral equation. The results in this article are improvements of well-known results.