• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.207-220
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• 2004

Necessary and sufficient conditions are given for the regularity of block triangular fuzzy matrices. This leads to characterization of idem-potency of a class of triangular Toeplitz matrices. As an application, the existence of group inverse of a block triangular fuzzy matrix is discussed. Equivalent conditions for a regular block triangular fuzzy matrix to be expressed as a sum of regular block fuzzy matrices is derived. Further, fuzzy relational equations consistency is studied.

• Korean Journal of Computational Design and Engineering
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• v.9 no.3
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• pp.203-211
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• 2004

In this paper, we present a method of extracting a regular 2-manifold triangular net from a triangular net including degenerate and self-intersected triangles. This method can be applied to obtaining an offset model without degenerate and self-intersected triangles. Then this offset model can be used to generate CL curves and extract machining features for CAPP The robust and efficient algorithm to detect valid triangles by growing regions from an initial valid triangle is presented. The main advantage of the algorithm is that detection of valid triangles is performed only in valid regions and their adjacent selfintersections, and omitted in the rest regions (invalid regions). This advantage increases robustness of the algorithm. As well as a k-d tree bucketing method is used to detect self-intersections efficiently.

• Journal of Korean Association for Spatial Structures
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• v.15 no.2
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• pp.87-94
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• 2015

This paper aimed at modeling a fine triangular grid for network dome by using Harmony Search (HS) algorithm. For this purpose, an optimization process to find a fine regular triangular mesh on the curved surface was proposed and the analysis program was developed. An objective function was consist of areas and edge's length of each triangular and its standard deviations, and design variables were subject to the upper and lower boundary which was calculated on the nodal connectivity. Triangular network dome model, which was initially consist of randomly irregular triangular mesh, was selected for the target example and the numerical result was analyzed in accordance with the HS parameters. From the analysis results of adopted model, the fitness function has been converged and the optimized triangular grid could be obtained from the initially distorted network dome example.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1713-1726
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• 2018

We study the one-sided regularity of matrices in upper triangular matrix rings in relation with the structure of diagonal entries. We next consider a ring theoretic condition that ab being regular implies ba being also regular for elements a, b in a given ring. Rings with such a condition are said to be commutative at regular product (simply, CRP rings). CRP rings are shown to be contained in the class of directly finite rings, and we prove that if R is a directly finite ring that satisfies the descending chain condition for principal right ideals or principal left ideals, then R is CRP. We obtain in particular that the upper triangular matrix rings over commutative rings are CRP.

• Korean Journal of Computational Design and Engineering
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• v.10 no.3
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• pp.168-178
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• 2005

The Delaunay triangular net is primarily characterized by a balance of the whole by improving divided triangular patches into a regular triangle, which closely resembles an equiangular triangle. A triangular net occurring in certain, point-clustered, data is unique and can always create the same triangular net. Due to such unique characteristics, Delaunay triangulation is used in various fields., such as shape reconstruction, solid modeling and volume rendering. There are many algorithms available for Delaunay triangulation but, efficient sequential algorithms are rare. When these grids involve a set of points whose distribution are not well proportioned, the execution speed becomes slower than in a well-proportioned grid. In order to make up for this weakness, the ids are divided into sub-grids when the sets are integrated inside the grid. A method for finding a mate in an incremental construction algorithm is to first search the area with a higher possibility of forming a regular triangular net, while the existing method is to find a set of points inside the grid that includes the circumscribed sphere, increasing the radius of the circumscribed sphere to a certain extent. Therefore, due to its more efficient searching performance, it takes a shorer time to form a triangular net than general incremental algorithms.

• Korean Journal of Computational Design and Engineering
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• v.20 no.1
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• pp.44-54
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• 2015

Solving partial differential equations (PDEs) on a manifold setting is frequently faced problem in CAD, CAM and CAE. However, unlikely to a regular grid, solutions for those problems on a triangular mesh are not available in general, as there are no well-established intrinsic differential operators. Considering that a triangular mesh is a powerful tool for representing a highly-complicated geometry, this problem must be tackled for improving the capabilities of many geometry processing algorithms. In this paper, we introduce mathematically well-defined differential operators on a triangular mesh setup, and show some examples of their applications. Through this, it is expected that many CAD/CAM/CAE application will be benefited, as it provides a mathematically rigorous solution for a PDE problem which was not available before.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.11 no.2
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• pp.176-184
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• 1999

Numerical and experimental studies were performed to examine the characteristics of heat and mass transfer processes for a Micro Heat Pipe(MHP) with a triangular cross-section. Solutions on mass flow rate, pressure variation, and radius of meniscus were obtained using the mathematical model developed by Faghri and Khrustalev. To obtain an increase in capillary limitation, a triangular tube with curved walls was designed and fabricated. The measurement by microscope showed that the radius at corners of the tube was ranging between 0.03-0.05mm. Performance test for MHPs using the triangular tube with curved walls proved a substantial increasement in heat transport limitation, with 4.5W and 2.0W in case of using water and ethanol as a working fluid, respectively. In the previous study by Faghri a limitation of 0.5W was reported for a water MHP with a regular triangular tube.

• Journal of the Korean Dietetic Association
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• v.29 no.2
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• pp.73-85
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• 2023

This study examined the nutritional information using the nutrition labels of gimbap sold at convenience stores and evaluated nutritional adequacy compared to dietary reference intakes for Korean adolescents. Thirty gimbaps (triangular gimbaps and regular gimbaps according to the main ingredients of vegetables, fish, and meat) were purchased at five convenience stores of different brands with many stores in Korea. The food and nutrition labels of the gimbaps were investigated, and nine minerals were analyzed using inductively coupled plasma-mass spectrometry (ICP-MS). The average price of gimbap was 1,906.7 won, and average energy was 292.0 kcal, and the protein content was 15.5% of the recommended intake for Korean male adolescents aged 15~18 years. The mineral content ranged from 6.9% for zinc to 39.0% for selenium. Except for sodium and selenium, the energy, protein, and mineral content did not meet 1/3 of dietary reference intakes for adolescents. For the index of nutritional quality (INQ), calcium and zinc were the lowest in the triangular and regular gimbap, respectively. The INQ of potassium was significantly higher in triangular gimbap with vegetables. The content and INQ of selenium were in regular gimbap with fish, and the zinc INQ was in regular gimbap with meat. Overall, gimbap sold in convenience stores has a high sodium content, and the contents of energy, protein, and minerals, except selenium, are insufficient for a single meal.

• Journal of the Korean Society for Precision Engineering
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• v.26 no.2
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• pp.133-140
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• 2009

Presented in this paper is a method to generate round-endmill toolpaths for sculptured surfaces represented as a triangular mesh model. The proposed method is applicable in toolpath generation for ball-endmills and flat-endmills because the round-endmill is a generalized tool in three-axis NC (numerical control) milling. The method uses a wireframe model as the offset model that represents a cutter location surface. Since wireframe models are relatively simple and fast to calculate, the proposed method can process large models and keep high precision. Intersection points with the wireframe offset model and a tool guide plane are calculated, and intersection curves are constructed by tracing the intersection points. The final step of the method is extracting regular curves from the intersection curves including degenerate and self-intersected segments. The proposed method is implemented and tested, and a practical example is presented.

• Structural Engineering and Mechanics
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• v.74 no.3
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• pp.407-423
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• 2020

The pre-peak cyclic shear mechanism of two-order asperity degradation of rock joints in the direct shear tests with static constant normal loads (CNL) are investigated using experimental and numerical methods. The laboratory testing rock specimens contains the idealized and regular two-order triangular-shaped asperities, which represent the specific geometrical conditions of natural and irregular waviness and unevenness of rock joint surfaces, in the pre-peak cyclic shear tests. Three different shear failure patterns of two-order triangular-shaped rock joints can be found in the experiments at constant horizontal shear velocity and various static constant normal loads in the direct and pre-peak cyclic shear tests. The discrete element method is adopted to simulate the pre-peak shear failure behaviors of rock joints with two-order triangular-shaped asperities. The rock joint interfaces are simulated using a modified smooth joint model, where microscopic scale slip surfaces are applied at contacts between discrete particles in the upper and lower rock blocks. Comparing the discrete numerical results with the experimental results, the microscopic bond particle model parameters are calibrated. Effects of cyclic shear loading amplitude, static constant normal loads and initial waviness asperity angles on the pre-peak cyclic shear failure behaviors of triangular-shaped rock joints are also numerically investigated.