• International Journal of CAD/CAM
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• v.5 no.1
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• pp.51-58
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• 2005

Interpreting a natural line drawing as a solid object requires simplifying assumptions in order to make the problem more tractable. Unfortunately, some of the assumptions made in the past have overly simplified the problem. Restricting the valency of vertices, and in particular allowing only trihedral vertices, distorts the problem, since algorithms which are satisfactory for the simplified problem are not satisfactory in the general case. This paper presents a test set of drawings of objects with higher-valency vertices. The intention in creating this test set is that it may be used to determine how effective various algorithms are in dealing with general (i.e. unrestricted) valency vertices.

• Communications of the Korean Mathematical Society
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• v.30 no.1
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• pp.45-64
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• 2015

In this article, we consider a proper total coloring distinguishes adjacent vertices by sums, if every two adjacent vertices have different total sum of colors of the edges incident to the vertex and the color of the vertex. Pilsniak and Wozniak [15] first introduced this coloring and made a conjecture that the minimal number of colors need to have a proper total coloring distinguishes adjacent vertices by sums is less than or equal to the maximum degree plus 3. We study proper total colorings distinguishing adjacent vertices by sums of some graphs and their products. We prove that these graphs satisfy the conjecture.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.633-642
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• 1998

The isomorphism classes of association schemes with 18 and 19 vertices are classified. We obtain 95 isomorphism classes of association schemes with 18 vertices and denote the representatives of the isomorphism classes as subschemes of 7 association schemes. We obtain 7 isomorphism classes of association schemes with 19 vertices and six of them are cyclotomic schemes.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.18 no.1
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• pp.19-29
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• 2020

This paper gives two graph-based algorithms for radioactive decay computation. The first algorithm identifies the connected components of the graph induced from the given radioactive decay dynamics to reduce the size of the problem. The solutions are derived over the precalculated connected components, respectively and independently. The second algorithm utilizes acyclic structure of radioactive decay dynamics. The algorithm evaluates the reachable vertices of the induced system graph from the initially activated vertices and finds the minimal set of starting vertices populating the entire reachable vertices. Then, the decay calculations are performed over the reachable vertices from the identified minimal starting vertices, respectively, with the partitioned initial value over the reachable vertices. Formal arguments are given to show that the proposed graph inspired divide and conquer calculation methods perform the intended radioactive decay calculation. Empirical efforts comparing the proposed radioactive decay calculation algorithms are presented.

• 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.

• East Asian mathematical journal
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• v.30 no.3
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• pp.303-310
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• 2014

We study the existence of regular polygons and regular solids whose vertices have integer coordinates in the three dimensional space and study side lengths of such squares, cubes and tetrahedra. We show that except for equilateral triangles, squares and regular hexagons there is no regular polygon whose vertices have integer coordinates. By using this, we show that there is no regular icosahedron and no regular dodecahedron whose vertices have integer coordinates. We characterize side lengths of such squares and cubes. In addition to these results, we prove Ionascu's result [4, Theorem2.2] that every equilateral triangle of side length $\sqrt{2}m$ for a positive integer m whose vertices have integer coordinate can be a face of a regular tetrahedron with vertices having integer coordinates in a different way.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1197-1211
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• 2007

In this article, we characterize the quasi-isomorphism classes of bracket groups in terms of vertices using vertex-switches. In particular, if two bracket groups are quasi-isomorphic, then there is a sequence of vertex-switches transforming a collection of vertices of a group to a collection of vertices of the other group.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.695-704
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• 2023

Area problems for triangles and polygons whose vertices have Fibonacci numbers on a plane were presented by A. Shriki, O. Liba, and S. Edwards et al. In 2017, V. P. Johnson and C. K. Cook addressed problems of the areas of triangles and polygons whose vertices have various sequences. This paper examines the conditions of triangles and polygons whose vertices have Lucas sequences and presents a formula for their areas.

• Journal of Integrative Natural Science
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• v.10 no.1
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• pp.27-32
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• 2017

In this paper we consider the two tangent lines of isogonal and isotomic conjugates of the line at both vertices of a given triangle. We find the necessary and sufficient condition for the two tangent lines of isogonal or isotomic conjugates of the line at both vertices and the median line to be concurrent. We also prove that every line whose isogonal conjugate tangent lines at both vertices are concurrent with the median line intersects at a unique point. Moreover, we show that the three intersection points correspond to the vertices of triangle are collinear.

• Journal of Information Processing Systems
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• v.13 no.1
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• pp.104-113
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• 2017

In this paper, we present an approach to transmit data from the source to the destination through a minimal path (least-cost path) in a computer network of n nodes. The motivation behind our approach is to address the problem of finding a minimal path between the source and destination. From the work we have studied, we found that a Steiner tree with bounded Steiner vertices offers a good solution. A novel algorithm to construct a Steiner tree with vertices and bounded Steiner vertices is proposed in this paper. The algorithm finds a path from each source to each destination at a minimum cost and minimum number of Steiner vertices. We propose both the sequential and parallel versions. We also conducted a comparative study of sequential and parallel versions based on time complexity, which proved that parallel implementation is more efficient than sequential.