• Communications of the Korean Mathematical Society
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• v.3 no.1
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• pp.99-107
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• 1988

• Kyungpook Mathematical Journal
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• v.3 no.1
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• pp.7-12
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• 1960

• The KIPS Transactions:PartD
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• v.13D no.3 s.106
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• pp.337-346
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• 2006

In order to analyze the behavior of moving objects, a measure for determining the similarity of trajectories needs to be defined. Although research has been conducted that retrieved similar trajectories of moving objects in Euclidean space, very little research has been conducted on moving objects in the space defined by road networks. In terms of real applications, most moving objects are located in road network space rather than in Euclidean space. In similarity measure between trajectories, however, previous methods were based on Euclidean distance and only considered spatial similarity. In this paper, we define similarity measure based on POI and TOI in road network space. With this definition, we present methods to retrieve similar trajectories using spatio-temporal similarity between trajectories. We show clustering results for similar trajectories. Experimental results show that similar trajectories searched by each method and consistency rate between each method for the searched trajectories.

• Korean Journal of Child Studies
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• v.12 no.2
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• pp.51-66
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• 1991

The purpose of study I was to investigate developmental processes and sex differences in the acquisition of topological seriation and Euclidean horizontal/vertical concepts. The purpose of Study II was to investigate the effects of basic geometric activity on the acquisition of space concepts. The subjects of Study I were 164 five- and six-year-old children. The children were grouped by age in 6 month units. The subjects of Study II were 45 children who showed immature space concepts. The data were analyzed by two-way ANOVA, $Scheff{\acute{e}}^{\prime}s$ posthoc test, and paired comparison t-test. On Study I, significant differences were found among the age groups in each of the dependent variables. Sex differences were found on all tasks except cued Euclidean tasks. In Study II, basic geometric activity of 3 weeks duration was found to be effective in the acquisition of the horizontal/vertical concepts in children whose space concept had been immature.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.1-19
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• 2020

Using the complex parabolic rotations of holomorphic null curves in ℂ⁴ we transform minimal surfaces in Euclidean space ℝ³ to a family of degenerate minimal surfaces in Euclidean space ℝ⁴. Applying our deformation to holomorphic null curves in ℂ³ induced by helicoids in ℝ³, we discover new minimal surfaces in ℝ⁴ foliated by hyperbolas or straight lines. Applying our deformation to holomorphic null curves in ℂ³ induced by catenoids in ℝ³, we rediscover the Hoffman-Osserman catenoids in ℝ⁴ foliated by ellipses or circles.

• Spatial Information Research
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• v.16 no.3
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• pp.291-301
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• 2008

While most GIS are based on Euclidean space, cellular space can be used as an alternative type of space for a large number of GIS applications. In order to analyze the pattern of moving objects in cellular space, we need new definitions of similarity between their trajectories since the trajectory in cellular space significantly differs from those in Euclidean space. In this paper, we study the properties of moving objects in cellular space. Based on these observations, we propose several similarity measures between trajectories in cellular space. We analyze the difference of the proposed measures by experiments.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.403-404
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• 2014

• Communications for Statistical Applications and Methods
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• v.31 no.3
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• pp.349-363
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• 2024

Compositional data refers to data where the sum of the values of the components is a constant, hence the sample space is defined as a simplex making it impossible to apply statistical methods developed in the usual Euclidean vector space. A natural approach to overcome this restriction is to consider an appropriate transformation which moves the sample space onto the Euclidean space, and log-ratio typed transformations, such as the additive log-ratio (ALR), the centered log-ratio (CLR) and the isometric log-ratio (ILR) transformations, have been mostly conducted. However, in scenarios with sparsity, where certain components take on exact zero values, these log-ratio type transformations may not be effective. In this work, we mainly suggest an alternative transformation, that is the square-root transformation which moves the original sample space onto the directional space. We compare the square-root transformation with the log-ratio typed transformation by the simulation study and the real data example. In the real data example, we applied both types of transformations to the USG% data obtained from NBA, and used a density based clustering method, DBSCAN (density-based spatial clustering of applications with noise), to show the result.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.225-236
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• 2021

In this paper, we determine position vector of a line of curvature of a regular surface which is relatively normal-slant helix, with respect to Darboux frame. Then, a vector differential equation is established by means Darboux formulas, in the case of the geodesic torsion is vanishes. In terms of solution, we determine the parametric representation of a line of curvature which is relatively normal-slant helix, with respect to standard frame in Euclidean 3-space. Thereafter, we apply this result to find the position vector of a line of curvature which is isophote curve.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1099-1108
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• 2013

We define the Mannheim curve in a 3-dimensional Riemannian manifold, which is a generalization of the Mannheim curve in Euclidean space. In particular, we study the Mannheim curves and their partner curves in 3-dimensional space forms.