• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.185-191
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• 2004

Given a connected graph G, we say that a set EC\;{\subseteq}\;V(G)$ is convex in G if, for every pair of vertices x, $y\;{\in}\;C$, the vertex set of every x - y geodesic in G is contained in C. The convexity number of G is the cardinality of a maximal proper convex set in G. In this paper, we show that every pair k, n of integers with $2\;{\leq}k\;{\leq}\;n\;-\;1$ is realizable as the convexity number and order, respectively, of some connected triangle-free graph, and give a lower bound for the convexity number of k-regular graphs of order n with n > k+1.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.503-509
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• 2014

For a connected graph G, there are orientations of G have different hull numbers, geodetic numbers, and convexity numbers. The lower orientable hull number $h^-(G)$ is defined as the minimum hull number among all the orientations of G and the upper orientable hull number $h^+(G)$ as the maximum hull number among all the orientations of G. The lower and upper orientable geodetic numbers $g^-(G)$ and $g^+(G)$ are defined similarily. In this paper, We investigate characterizations of the orientable numbers and the conditions that the relation $h^-(G){\leq}g^-(G)$ < $h^+(G){\leq}g^+(G)$ holds.

• Journal of the Ergonomics Society of Korea
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• v.22 no.3
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• pp.27-44
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• 2003

An experiment was carried out to compare the suitability in visual tasks between flat and conventional (convex) cathode-ray tube (CRT) displays. The subjects performed visual search tasks during 2-h for detecting target words among distracters presented on the screen. The subjects' visual performance was evaluated with average time and number of errors made to complete the tasks. Visual fatigue after the search tasks was also evaluated in terms of degradations in accommodative power and subjective ratings. Difference was not found in task time between the two displays, but flat CRT showed a lower number of errors than conventional CRT. The difference in number of errors was statistically significant at 0=0.05. Although there was no difference between the displays in degradations of accommodative power, results from the subjective ratings showed that flat CRT yields less fatigue than conventional CRT. The results partially support the hypothesis that panel convexity of CRT displays has a significant effect on the performance and fatigue during visual tasks and thus flat CRT is the better display than conventional one.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.3
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• pp.289-297
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• 2014

This article surveys the control theoretic study on time delay systems. Since time delay systems are infinite dimensional, there are not analytic but numerical solutions on almost analysis and synthesis problems, which implies that there are a tremendous number of approximated solutions. To show how to find such solutions, several results are summarized in terms of two different axes: 1) theoretic tools like integral inequality associated with the derivative of delay terms, Jensen inequality, lower bound lemma for reciprocal convexity, and Wirtinger-based inequality and 2) various candidates for Laypunov-Krasovskii functionals.

• The Journal of Korea Robotics Society
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• v.6 no.2
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• pp.189-196
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• 2011

This paper presents a method of topological modeling using only low-cost sonar sensors. The proposed method constructs a topological model by extracting sub-regions from the local grid map. The extracted sub-regions are considered as nodes in the topological model, and the corresponding edges are generated according to the connectivity between two sub-regions. A grid confidence for each occupied grid is evaluated to obtain reliable regions in the local grid map by filtering out noisy data. Moreover, a convexity measure is used to extract sub-regions automatically. Through these processes, the topological model is constructed without predefining the number of sub-regions in advance and the proposed method guarantees the convexity of extracted sub-regions. Unlike previous topological modeling methods which are appropriate to the corridor-like environment, the proposed method can give a reliable topological modeling in a home environment even under the noisy sonar data. The performance of the proposed method is verified by experimental results in a real home environment.

• International Journal of Contents
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• v.5 no.4
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• pp.55-61
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• 2009

In this paper, we propose a hierarchical method for segmenting a given 3D mesh, which hierarchically clusters sharp vertices of the mesh using the metric of geodesic distance among them. Sharp vertices are extracted from the mesh by analyzing convexity that reflects global geometry. As well as speeding up the computing time, the sharp vertices of this kind avoid the problem of local optima that may occur when feature points are extracted by analyzing the convexity that reflects local geometry. For obtaining more effective results, the sharp vertices are categorized according to the priority from the viewpoint of cognitive science, and the reasonable number of clusters is automatically determined by analyzing the geometric features of the mesh.

• International Journal of Control, Automation, and Systems
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• v.1 no.1
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• pp.156-161
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• 2003

An overview of our approach to autonomous navigation is presented showing how motion information can be integrated into existing navigation schemes. Particular attention is given to our short range motion estimation scheme which utilises a number of unique assumptions regarding the nature of the visual environment allowing a direct fusion of visual and range information. Graduated non-convexity is used to solve the resulting non-convex minimisation problem. Experimental results show the advantages of our fusion technique.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.627-639
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• 2021

Numerical techniques are used to determine the radius of convexity of the starlike functions related to cardioid shaped bounded domain. In addition, radius constants of certain starlikeness associated with right half plane of various starlike functions are computed.

• Journal of Korean Society for Geospatial Information Science
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• v.3 no.1 s.5
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• pp.91-104
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• 1995

The spatial aggregation of data, in transportation and other planning processes, is an important theoretical consideration because the results of any analysis are not entirely independent of the delineation of zones. Moreover, using a different spatial aggregation may lead to different, and sometimes contradictory conclusions. Two criteria have been considered as important in designing zone systems. They are scale and aggregation. The scale problem arises because of uncertainty about the number of zones needed for a study and the aggregation problem arises because of uncertainty about how the data are to be aggregated to from a given scale problem. In a transportation study, especially in the design of traffic analysis zone(TAZ), the scale problem is directly related to the number dof zones and the aggregation problem involves spatial clustering, meeting the general requirements of forming the zones system such as equal traffic generation, convexity, and the consistency with the political boundary. In this study, first, the comparative study of delineating spatial units has been given. Second, a FORTRAN-based heuristic algorithm for designing TAZ based on socio-economic data has been developed and applied to the Korean peninsula containing 132 micro parcels. The vector type ARC/INFO GIS topological data mosel has been used to provise the adjacency information between parcels. The results, however, leave some to be desired in order to overcome such problems as non-convexity of the agglomerated TAZ system and/or uneven traffic phenomenon for each TAZ.

• Korean Journal of Computational Design and Engineering
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• v.5 no.2
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• pp.196-205
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• 2000

This paper proposes a topology-based algorithm for recognizing the passage features using a concept of multi-face hole loop. The Multi-face hole loop is a concetpual hole loop that is formed over several connected faces. A passage feature is recognized in the proposed approach by two multi-face hole loops that constitute its enterance and exit. The algorithm proposed in this paper checks the connectivity of the two multi-face hole loops to recognize passage features. The total number of passage features in a part is calculated from Euler equation and is compared with the number of found passage features to decide when to terminate. To find all multi-face hole loops in a part, this paper proposes an algorithm for finding all combinations of connected faces. The edge convexity is used to judge the validity of multi-face hole loops. By using the algorithm proposed in this paper, the passage features could be recognized effectively. The approach proposed in this paper is illustrated with several example parts.