• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.441-455
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• 2017

In this article we have determined the spectrum and fine spectrum of the lower triangular matrix B(r, s) on the Hahn sequence space h. We have also determined the approximate point spectrum, the defect spectrum and the compression spectrum of the operator B(r, s) on the sequence space h.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.785-795
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• 2022

In this paper, we introduce a Mann-like three step iteration method and show that it can be used to approximate the fixed point of a weak contraction mapping. Furthermore, we prove that this scheme is equivalent to the Mann iterative scheme. A comparison is made with the other third order iterative methods. Results are presented in a table to support our conclusion.

• ETRI Journal
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• v.38 no.3
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• pp.518-528
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• 2016

The searching of an extensive document database for documents that are locally similar to a given query document, and the subsequent detection of similar regions between such documents, is considered as an essential task in the fields of information retrieval and data management. In this paper, we present a framework for such a task. The proposed framework employs the method of short-read mapping, which is used in bioinformatics to reveal similarities between genomic sequences. In this paper, documents are considered biological objects; consequently, edit operations between locally similar documents are viewed as an evolutionary process. Accordingly, we are able to apply the method of evolution tracing in the detection of similar regions between documents. In addition, we propose heuristic methods to address issues associated with the different stages of the proposed framework, for example, a frequency-based fragment ordering method and a locality-aware interval aggregation method. Extensive experiments covering various scenarios related to the search of an extensive document database for documents that are locally similar to a given query document are considered, and the results indicate that the proposed framework outperforms existing methods.

• Journal of Information Processing Systems
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• v.10 no.1
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• pp.23-35
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• 2014

Recently, novel application areas in digital geometry processing, such as simulation, dynamics, and medical surgery simulations, have necessitated the representation of not only the surface data but also the interior volume data of a given 3D object. In this paper, we present an efficient framework for the shape approximations of spherical solid objects based on trivariate B-splines. To do this, we first constructed a smooth correspondence between a given object and a unit solid cube by computing their harmonic mapping. We set the unit solid cube as a rectilinear parametric domain for trivariate B-splines and utilized the mapping to approximate the given object with B-splines in a coarse-to-fine manner. Specifically, our framework provides user-controllability of shape approximations, based on the control of the boundary condition of the harmonic parameterization and the level of B-spline fitting. Experimental results showed that our method is efficient enough to compute trivariate B-splines for several models, each of whose topology is identical to a solid sphere.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.6D
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• pp.1025-1032
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• 2006

Sensor modeling of high-resolution satellites is a prerequisite procedure for mapping and GIS applications. Sensor models, describing the geometric relationship between scene and object, are divided into two main categories, which are rigorous and approximate sensor models. A rigorous model is based on the actual geometry of the image formation process, involving internal and external characteristics of the implemented sensor. However, approximate models require neither a comprehensive understanding of imaging geometry nor the internal and external characteristics of the imaging sensor, which has gathered a great interest within photogrammetric communities. This paper described a comparison between rigorous and various approximate sensor models that have been used to determine three-dimensional positions, and proposed the appropriate sensor model in terms of the satellite imagery usage. Through the case study of using IKONOS satellite scenes, rigorous and approximate sensor models have been compared and evaluated for the positional accuracy in terms of acquirable number of ground controls. Bias compensated RFM(Rational Function Model) turned out to be the best among compared approximate sensor models, both modified parallel projection and parallel-perspective model were able to be modelled with a small number of controls. Also affine transformation, one of the approximate sensor models, can be used to determine the planimetric position of high-resolution satellites and perform image registration between scenes.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.203-208
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• 2007

Due to the long tectonic history and the very complex geologic formations in Korea, the anisotropic characteristics of subsurface material may often change very greatly and locally. The algorithms for the travel time computation commonly used, however, may not give sufficiently precise results particularly for the complex and strong anisotropic model, since they are based on the two-dimensional (2D) earth and/or weak anisotropy assumptions. This study is intended to develope a three-dimensional (3D) modeling algorithm to precisely calculate the first arrival time in the complex anisotropic media. We assume 3D TTI (tilted transversely isotropy) medium having the arbitrary symmetry axis. The algorithm includes the 2D non-linear interpolation scheme to calculate the traveltimes inside the grid and the 3D traveltime mapping to fill the 3D model with first arrival times. The weak anisotropy assumption, moreover, can be overcome through devising a numerical approach of the steepest descent method in the calculation of minimum traveltime, instead of using approximate solution.

• Journal of Korea Game Society
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• v.14 no.2
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• pp.77-84
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• 2014

Presence of soft shadow effects from an area light makes virtual scenes look more realistic. However, since computation of soft shadow effects takes a long time, acceleration methods are required to apply it to real-time 3D applications. Many researches assumed that area lights are white rectangles. We suggest a new method which renders soft shadows under the area light source having arbitrary shape and color. In order to approximate visibility test, we use a shadow mapping result near a pixel. Complexity of shadow near a pixel is used to determine degree of precision of our visibility estimation. Finally, our method can present more realistic soft shadows for the area light that have more general shape and color in real-time.

• The KIPS Transactions:PartA
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• v.11A no.2
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• pp.189-194
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• 2004

This paper describes method to distribute much high-dimensional facial expression motion data to 2 dimensional space, and method to create facial expression animation by select expressions that want by realtime as animator navigates this space. In this paper composed expression space using about 2400 facial expression frames. The creation of facial space is ended by decision of shortest distance between any two expressions. The expression space as manifold space expresses approximately distance between two points as following. After define expression state vector that express state of each expression using distance matrix which represent distance between any markers, if two expression adjoin, regard this as approximate about shortest distance between two expressions. So, if adjacency distance is decided between adjacency expressions, connect these adjacency distances and yield shortest distance between any two expression states, use Floyd algorithm for this. To materialize expression space that is high-dimensional space, project on 2 dimensions using Sammon's Mapping. Facial animation create by realtime with animators navigating 2 dimensional space using user interface.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1363-1379
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• 2011

Halpern iterative algorithm is one of the most cited in the literature of approximation of fixed points of nonexpansive mappings. Different authors modified this iterative algorithm in Banach spaces to approximate fixed points of nonexpansive mappings. One of which is Hu [8] and Yao et al [21] modification of Halpern iterative algorithm for nonexpansive mappings in Banach spaces. It is the purpose of this paper to thoroughly analyze this modification and its convergence conditions. Unfortunately, Hu [8] and Yao et al [21] control conditions imposed on the modified Halpern iterative algorithm to have strong convergence are found to be not sufficient. In this paper, counterexamples are constructed to prove that the strong convergence conditions of Hu [8] and Yao et al [21] are not sufficient. It is also proved that with some additional conditions on the control parameters, strong convergence of the defined iterative algorithm is obtained in different Banach space settings.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.55-60
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• 1984

In [2], D. Downing and W.A. Kirk obtained a number of fixed point theorems for set-valued maps in matric and Banach spaces. The authors considered maps which are more general than the contractions with nonempty and closed mapping values, and obtain results for maps satisfying certain "inwardness" conditions. A key aspect of their approach is the application of a general fixed point theorem due to Caristi [1]. On the other hand, in [6], the present author obtained a number of equivalent formulations of the well-known result of I. Ekeland [3, 4] on the variational principle for approximate solutions of minimization problems. Some of such formulations include sharpened forms of the Caristi theorem. In this paper, using one of such formulations, we show that Theorems 1-3 and Corollaries 1-5 of [2] are substantially improved by giving geometric estimations of fixed points.ed points.