• East Asian mathematical journal
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• v.25 no.2
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• pp.141-146
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• 2009

In this paper, we introduce a new generalized nonlinear quasivariational inequality and establish its equivalence with a xed point problem by using the resolvent operator technique. Utilizing this equivalence, we suggest two iterative schemes, prove two existence theorems of solutions for the generalized nonlinear quasivariational inequality involving generalized cocoercive mapping and establish some convergence results of the sequences generated by the algorithms. Our results include several previously known results as special cases.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.251-261
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• 2003

The purpose of this paper is to establish the necessary and sufficient conditions which ensure the strong convergence of the Ishikawa iterative schemes with errors to the unique fixed point of a $\Phi$-hemicontractive mapping defined on a nonempty convex subset of a normed linear space. The results of this paper extend substantially most of the recent results.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1323-1339
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• 2008

In this paper, a new class of $(h,{\eta})$-proximal for proper functionals in Hilbert spaces is introduced. The existence and Lip-schitz continuity of the $(h,{\eta})$-proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonlinear quasi-variational-like inclusion is suggested. The existence and uniqueness theorems of solution for the generalized nonlinear quasi-variational-like inclusion are established. The convergence and stability results of iterative sequence generated by the perturbed three-step iterative algorithm with errors are discussed.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.3
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• pp.451-457
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• 2009

Most of objects in computer graphics may be represented by a form of mesh. The exact computation of vertex normal vectors is essential for user to apply a variety of geometric operations to the mesh and get more realistic rendering results. Most of the previous algorithms used a weight which resembles a local geometric property of a vertex of a mesh such as the interior angle, the area, and so on. In this paper, we propose an efficient algorithm for computing the normal vector of a vertex in meshes. Our method uses the conformal mapping which resembles synthetically the local geometric properties, and the mean value coordinates which may smoothly represent a relationship with the adjacent vertices. It may be confirmed by experiment that the normal vector of our algorithm is more exact than that of the previous methods.

• Advances in nano research
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• v.10 no.3
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• pp.253-261
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• 2021

Polydimethylsiloxane (PDMS) is one of the most widely adopted silicon-based organic polymeric elastomers. Elastomeric nanostructures are normally required to accomplish an explicit mechanical role and correspondingly their mechanical properties are crucial to affect device and material performance. Despite its wide application, the mechanical properties of PDMS are yet fully understood. In particular, the time dependent mechanical response of PDMS has not been fully elucidated. Here, utilizing state-of-the-art PeakForce Quantitative Nanomechanical Mapping (PFQNM) together with Force Volume (FV) and Fast Force Volume (FFV), the elastic moduli of PDMS samples were assessed in a time-dependent fashion. Specifically, the acquisition frequency was discretely changed four orders of magnitude from 0.1 Hz up to 2 kHz. Careful calibrations were done. Force data were fitted with a linearized DMT contact mechanics model considering surface adhesion force. Increased Young's modulus was discovered with increasing acquisition frequency. It was measured 878 ± 274 kPa at 0.1 Hz and increased to 4586 ± 758 kPa at 2 kHz. The robust local probing of mechanical measurement as well as unprecedented high-resolution topography imaging open new avenues for quantitative nanomechanical mapping of soft polymers, and can be extended to soft biological systems.

• Journal of KIISE:Computer Systems and Theory
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• v.30 no.11
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• pp.663-674
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• 2003

Bump mapping is a technique that represents the detailed parts of the object surface, such as a perturberance of the skin of a peanut, using the geometry mapping without complex modeling. However, the hardware implementation for bump mapping is considerable, because a large amount of per pixel computation, including the normal vector shading, is required. In this paper, we propose a new bump mapping algorithm using the polar coordinate system and its hardware architecture. Compared with other existing architectures, our approach performs bump mapping effectively by using a new vector rotation method for transformation into the reference space and minimizing illumination calculation. Consequently, our proposed architecture reduces a large amount of computation and hardware requirements.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.3 s.180
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• pp.187-194
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• 2006

Unexpected postoperative changes, such as growth in rib hump and shoulder unbalance, have been occasionally reported after corrective surgery for scoliosis. However there has been neither experimental data fer explanation of these changes, nor the suggestion of optimal correction method. Therefore, the numerical study was designed to investigate the post-operative changes of vertebral rotation and rib cage deformation after the corrective surgery of scoliosis. A mathematical finite element model of normal spine including rib cage, sternum, both clavicles, and pelvis was developed with anatomical details. In this study, we also developed a special program which could convert a normal spine model to a desired scoliotic spine model automatically. A personalized skeletal deformity of scoliosis model was reconstructed with X-ray images of a scoliosis patient from the normal spine structures and rib cage model. The geometric mapping was performed by translating and rotating the spinal column with an amount analyzed from the digitized 12 built-in coordinate axes in each vertebral image. By utilizing this program, problems generated in mapping procedure such as facet joint overlapping, vertebral body deformity could be automatically resolved.

• Proceedings of the Korea Water Resources Association Conference
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• 2011.05a
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• pp.185-185
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• 2011

Mapping of artificial levee lines, one of major tasks in river zone mapping, is critical to prevention of river flood, protection of environments and eco systems in river zones. Thus, mapping of artificial levee lines is essential for management and development of river zones. Coastal mapping including river zone mapping has been historically carried out using surveying technologies. Photogrammetry, one of the surveying technologies, is recently used technology for national river zone mapping in Korea. Airborne laser scanning has been used in most advanced countries for coastal mapping due to its ability to penetrate shallow water and its high vertical accuracy. Due to these advantages, use of LiDAR data in coastal mapping is efficient for monitoring and predicting significant topographic change in river zones. This paper introduces a method for construction of a 3D artificial levee line using a set of LiDAR points that uses normal vectors. Multiple steps are involved in this method. First, a 2.5-dimensional Delaunay triangle mesh is generated based on three nearest-neighbor points in the LiDAR data. Second, a median filtering is applied to minimize noise. Third, edge selection algorithms are applied to extract break edges from a Delaunay triangle mesh using two normal vectors. In this research, two methods for edge selection algorithms using hypothesis testing are used to extract break edges. Fourth, intersection edges which are extracted using both methods at the same range are selected as the intersection edge group. Fifth, among intersection edge group, some linear feature edges which are not suitable to compose a levee line are removed as much as possible considering vertical distance, slope and connectivity of an edge. Sixth, with all line segments which are suitable to constitute a levee line, one river levee line segment is connected to another river levee line segment with the end points of both river levee line segments located nearest horizontally and vertically to each other. After linkage of all the river levee line segments, the initial river levee line is generated. Since the initial river levee line consists of the LiDAR points, the pattern of the initial river levee line is being zigzag along the river levee. Thus, for the last step, a algorithm for smoothing the initial river levee line is applied to fit the initial river levee line into the reference line, and the final 3D river levee line is constructed. After the algorithm is completed, the proposed algorithm is applied to construct the 3D river levee line in Zng-San levee nearby Ham-Ahn Bo in Nak-Dong river. Statistical results show that the constructed river levee line generated using a proposed method has high accuracy in comparison to the ground truth. This paper shows that use of LiDAR data for construction of the 3D river levee line for river zone mapping is useful and efficient; and, as a result, it can be replaced with ground surveying method for construction of the 3D river levee line.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.38 no.5
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• pp.425-433
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• 2020

Three-dimensional data has been used for different applications such as robotics, building reconstruction, and so on. 3D data can be generated from an optical camera or a laser scanner. Especially, a wearable multi-sensor system including the above-mentioned sensors is an optimized structure that can overcome the drawbacks of each sensor. After finding the geometric relationships between sensors, georeferencing of the datasets acquired from the moving system, should be carried out. Especially, in an indoor environment, error propagation always causes problem in the georeferencing process. To improve the accuracy of this process, other sources of data were used to combine with LiDAR (Light Detection and Ranging) data, and various registration methods were also tested to find the most suitable way. More specifically, this paper proposed a new process of NDT (Normal Distribution Transform) to register the LiDAR point cloud, with additional information from other sensors. For real experiment, a wearable mapping system was used to acquire datasets in an indoor environment. The results showed that applying the new process of NDT and combining LiDAR data with IMU (Inertial Measurement Unit) information achieved the best result with the RMSE 0.063 m.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.329-341
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• 2005

In this paper, we introduce new random iterative sequences with errors approximating a unique random common fixed point for three random set-valued strongly pseudo-contractive mappings and show the convergence of the random iterative sequences with errors by using an approximation method in real uniformly smooth separable Banach spaces. As applications, we study the existence of random solutions for some kind of random nonlinear operator equations group in separable Hilbert spaces.