• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.531-540
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• 2008

We discuss the decomposition problems on circuit graphs and triangular graphs, and show how they can be applied to obtain results on spanning trees or hamiltonian cycles. We also prove that every circuit graph containing no separating 3-cycles can be extended by adding new edges to a triangular graph containing no separating 3-cycles.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.05a
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• pp.44-47
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• 2004

This paper proposes an approach for composite surface reconstruction from 2D serial cross-sections, where the number of contours varies from section to section. In a triangular surface-based approach taken in most reconstruction methods, a triangular $G^{1}$ surface is constructed by stitching triangular patches over a triangular net generated from the compiled contours. In the proposed approach, the resulting surface is a composite $G^{1}$ surface consisting of three kinds of surfaces: skinned, surface is first represented by a B-spline surface approximating the serial contours of the skinned region and then serial contours of the skinned region and then transformed into a mesh of rectangular Bezier patches. On branched and capped regions, triangular $G^{1}$ surfaces are constructed so that the connections between the triangular surfaces and their neighboring surfaces are $G^{1}$ continuous. Since each skinned region is represented by an approximated rectangular $G^{2}$ surface instead of an interpolated triangular $G^{1}$ surface, the proposed approach can provide more visually pleasing surfaces and realize more efficient data reduction than the triangular surface-based approach. Some experimental results demonstrate its usefulness and quality.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.9
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• pp.148-157
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• 2007

A new method which uses distance fields scheme and marching cube algorithm is proposed in order to get an accurate offset model of arbitrary shapes composed of triangular net. In the method, the space bounding the triangular net is divided into smaller cells. For the efficient calculation of distance fields, valid cells which will generate a portion of offset model are selected previously by the suggested detection algorithm. These valid cells are divided again into much smaller voxels which assure required accuracy. At each voxel distance fields are created by calculating the minimum distances between corner points of voxels and triangular net. After generating the whole distance fields, the offset surface were constructed by using the conventional marching cube algorithm together with mesh smoothing scheme. The effectiveness and validity of this new offset method was demonstrated by performing numerical experiments for the various types of triangular net.

• Journal of The Korea Institute of Healthcare Architecture
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• v.12 no.2
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• pp.59-67
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• 2006

The purpose of this study is to present the research data to improve the quality of triangular ward in general hospital in Korea. Drawing documents analysis were used to examine the condition of ward. This study in focused on patient room and atrium according to connection type of triangular ward, allocation of NS, module and direction of patient room. The results of this study is as follows; Triangular ward has two joint pattern(conner and conner, side and side). Conner and conner joint pattern is good at planning of lighting than side and side joint pattern. Triangular ward can has different module system in each side. Allocation of NS is important factor which is focused on patient relationship or ward control.

• Korean Journal of Computational Design and Engineering
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• v.9 no.1
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• pp.1-10
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• 2004

In the process of finite element analysis, mesh generation is tedious job which consumes tremendous time. Therefore, the automation of well shaped mesh generation from the minimal boundary input data is desirable to improve reliability and accuracy of the analysis and also to reduce the process time of the entire design process. The automation of triangular mesh generation has been relatively well treated due to its robustness and ease of handling when compared to rectangular element mesh generation. In this study, the offset method developed previously for generating plane rectangular element mesh has been corrected and modified to generate triangular element mesh on the B-spline surface having arbitrary holes. The result shows that the generated triangular mesh has the average aspect ratio over 0.9. The designed arbitrary surface shape has been interactively constructed by non-uniform B-spline theory for triangular mesh generation.

• Korean Journal of Computational Design and Engineering
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• v.22 no.1
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• pp.28-36
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• 2017

Sharing of CAD data plays a key role in the PLM and a lightweight model is widely used for visualizing and sharing a large data. The lightweight model is mainly composed of triangular elements to minimize file size. There is no problem at all to visually confirm the shape based on these triangular elements but there is a limit to numerically calculate the exact position on the curve or surface. In this paper, a boundary curve generation method using triangular elements is proposed to increase the utilization of lightweight models. After matching connectivity of triangular elements, boundary element edges are extracted. Boundary curves are generated by connecting of these boundary element edges. This proposed method has been tested on several models to demonstrate the feasibility.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.11C
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• pp.885-888
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• 2010

It is known that triangular QAM with triangular signal constellations gets better SER gain than square QAM with rectangular signal constellations. In the paper, we propose an exact and general closed-form expression of the probability of symbol error for generalized TQAM, which has been currently researched. We verify that the simulation is consistent with the derived equation of generalized TQAM. And, we also suggest the optimal signal constellation schemes for generalized TQAM at given SNR values.

• Journal of Korean Institute of Industrial Engineers
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• v.21 no.4
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• pp.529-540
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• 1995

The paper deals with a procedure for constructing a composite surface interpolating a polygonal curve mesh defined from 3D scattered points. The procedure consists of a poly-angulation, construction of a curve net, and interpolation of the curve net. The poly-angulation contains a stage that changes a triangular edge net obtained from a triangulation into a poly-angular edge net. A curve net is constructed by replacing edges on the edge net with cubic Bezier curves. Finally, inside of an n-sided polygon is interpolated by n subdivided triangular subpatches. The method interpolates given point data with relatively few triangular subpatches. For an n-sided polygon, our method constructs an interpolant with n subdivided triangular subpatches while the existing triangular surface modeling needs 3(n-2) subpatches. The obtained surface is composed of quartic triangular patches which are $G^1$-continuous to adjacent patches.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.931-957
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• 2023

For an arbitrary integer x, an integer of the form $$T(x)={\frac{x^2+x}{2}}$$ is called a triangular number. Let α₁, ... , α_k be positive integers. A sum ${\Delta}_{{\alpha}_1,{\ldots},{\alpha}_k}(x_1,\,{\ldots},\,x_k)=\{\alpha}_1T(x_1)+\,{\cdots}\,+{\alpha}_kT(x_k)$ of triangular numbers is said to be almost universal with one exception if the Diophantine equation ${\Delta}_{{\alpha}_1,{\ldots},{\alpha}_k}(x_1,\,{\ldots},\,x_k)=n$ has an integer solution (x₁, ... , x_k) ∊ ℤ^k for any nonnegative integer n except a single one. In this article, we classify all almost universal sums of triangular numbers with one exception. Furthermore, we provide an effective criterion on almost universality with one exception of an arbitrary sum of triangular numbers, which is a generalization of "15-theorem" of Conway, Miller, and Schneeberger.

• Archives of Reconstructive Microsurgery
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• v.1 no.1
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• pp.51-55
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• 1992

Problems of composite tissue transfer commonly arise when a single indispensable recipient vessel receives the graft vssel, and the graft vessel must be sutured in end-to-side fashion so as not todisturb the vascularity of the recipient vessel. The triangular flap in the recipient vessel wall gives an intact endothelial surface when the flow of blood stream is presented and may reduce the chance of anastomosis. We selected mature Wistar rats weighing over 450 grams to compare the conventional longitudinal slit from the triangular flap in the recipient carotid artery over bloood pressure and blood flow when the donor carotid artery was anastomosed in end-to-side fashion. In 30 minutes after anastomosis, maximum blood pressure measured in the donor carotid arterial side when the recipient arterial wall was fasioned with the longitudinal slit was recorded 114 mmHg and with the triangular flap 100mmHg. Minimum blood pressure with the longitudinal slit was 98mmHg and with the triangular flap 88mmHg. The amount of blood collected for 30 seconds in the conventional longitudinal slit was 1.18mg and in the triangular flap 0.78mg. Histology study in 30 minutes, the conventional longitudinal slit demonstrated the more hemorrhagic features around the suture material compared to that of the triangular. flap and, in the 7th day, the conventional longitudinal slit demonstrated the more prominent granulomatous reactions and vascular proliferations around the suture material compared to that of the triangular flap.