• Bulletin of the Korean Mathematical Society
• /
• v.60 no.3
• /
• pp.785-827
• /
• 2023

In this paper, under some new appropriate conditions imposed on the parameter and mappings involved in the resolvent operator associated with a P-accretive mapping, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. This paper is also concerned with the construction of a new iterative algorithm using the resolvent operator technique and Nadler's technique for solving a new system of generalized multi-valued resolvent equations in a Banach space setting. The convergence analysis of the sequences generated by our proposed iterative algorithm under some appropriate conditions is studied. The final section deals with the investigation and analysis of the notion of H(·, ·)-co-accretive mapping which has been recently introduced and studied in the literature. We verify that under the conditions considered in the literature, every H(·, ·)-co-accretive mapping is actually P-accretive and is not a new one. In the meanwhile, some important comments on H(·, ·)-co-accretive mappings and the results related to them appeared in the literature are pointed out.

• Journal of Korean Tunnelling and Underground Space Association
• /
• v.14 no.4
• /
• pp.357-374
• /
• 2012

Considerable uncertainties are included in ground properties used for tunnel designs due to the limited investigation and tests. In this study, a back analysis was performed to find optimal ground properties based on artificial neural network using both face mapping data and convergence measurement data. First of all, the rock class of a study tunnel is determined from face mapping data. Then the possible ranges of ground properties were selected for each rock class through a literature review on the previous studies and utilized to establish more precise learning data. To find an optimal training model, a sensitivity analysis was also conducted by varying the number of hidden layers and the number of nodes more minutely than the previous study. As a result of this study, more accurate ground properties could be obtained. Therefore it was confirmed that the accuracy of the results could be increased by making use of not only convergence measurement data but also face mapping data in tunnel back analyses using artificial neural network. In future, it is expected that the methodology suggested in this study can be used to estimate ground properties more precisely.

• Proceedings of the KIEE Conference
• /
• 1997.07c
• /
• pp.864-866
• /
• 1997

This paper presents fault recognition and interpretation in power transformers using dissolved gas analysis embedded Kohonen feature mapping. The imprecision of gas ratio analysis in dissolved gas analysis are managed by mapping in accordance with learning of Kohonen neural network. To verify the effectiveness of the proposed system, it has been tested by the historical gas records to power transformers of Korea Electric Power Corporation. More appropriate fault types can support the maintenance personnels to increase the disgnostic performance for fault of power transformers.

• Applied Microscopy
• /
• v.46 no.4
• /
• pp.179-183
• /
• 2016

Mapping brain structural and functional connections through the whole brain is essential for understanding brain mechanisms and the physiological bases of brain diseases. Although region specific structural or functional deficits cause brain diseases, the changes of interregional connections could also be important factors of brain diseases. This review will introduce common neuroimaging modalities, including structural magnetic resonance imaging (MRI), functional MRI (fMRI), diffusion tensor imaging, and other recent neuroimaging analyses methods, such as voxel-based morphometry, cortical thickness analysis, local gyrification index, and shape analysis for structural imaging. Tract-Based Spatial Statistics, TRActs Constrained by UnderLying Anatomy for diffusion MRI, and independent component analysis for fMRI also will also be introduced.

• Structural Engineering and Mechanics
• /
• v.9 no.3
• /
• pp.215-226
• /
• 2000

Computational procedure within the framework of return mapping technique has been presented to integrate the constitutive behavior of a concrete model. Developed by Ohtani and Chen, this concrete model is based on multiple hardening concept, and is rate-independent and associative. Consistent tangent operator suitable for finite element analysis is derived to preserve the rate of convergence. Accuracy of the integration technique is verified and compared with available experimental data. Computational efficiency is demonstrated by comparing with results based on elasto-plastic tangent.

• Korean Journal of Mathematics
• /
• v.24 no.2
• /
• pp.181-198
• /
• 2016

In this work, we suggest a new system of generalized nonlinear regularized nonconvex variational inequalities in a real Hilbert space and establish an equivalence relation between this system and fixed point problems. By using the equivalence relation we suggest a new perturbed projection iterative algorithms with mixed errors for finding a solution set of system of generalized nonlinear regularized nonconvex variational inequalities.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.3
• /
• pp.601-610
• /
• 2021

A convergence theorem for a generalized 𝜑-weakly contractive mapping is proved which satisfy a generalized contraction condition on a complete metrically convex metric space. The result in this paper generalizes the relevant results due to Rhoades [18], Alber and Guerre-Delabriere [1], Khan and Imdad [14], Xue [20] and others. An illustrative example is also furnished in support of our main result.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.5
• /
• pp.1105-1114
• /
• 2021

In this paper, we prove a fixed point theorem for G-contractive type non-self mapping in cone metric space endowed with a graph. Our result generalizes many results in the literature and provide a new pavement for solving nonlinear functional equations.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.4
• /
• pp.731-742
• /
• 2022

In this paper, we present a new mixed type iterative process for approximating the common fixed points of single-valued nonexpansive mapping and multi-valued nonexpansive mapping in a CAT(0) space. We demonstrate strong and weak convergence theorems for the new iterative process in CAT(0) spaces, as well as numerical results to support our theorem.

• Bulletin of the Korean Chemical Society
• /
• v.33 no.7
• /
• pp.2338-2340
• /
• 2012

The spin exchange parameters of $VOSb_2O_4$ were evaluated by performing energy-mapping analysis based on density functional calculations. The spin exchange interaction between the nearest-neighbor $V^{4+}$ ions is strongly antiferromagnetic while other interactions are negligible. Thus, the magnetic structure of $VOSb_2O_4$ is best described by a spin-1/2 Heisenberg antiferromagnetic chain with no spin frustration.