• Journal for History of Mathematics
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• v.17 no.1
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• pp.87-96
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• 2004

This article dealt with two approaches, algebraic and geometric approaches in terms of Pythagoreans theorem. As mathematics evolves, many theorems had been developed beginning with geometric approaches. However, the algebraic techniques that survive these days are so powerful and generalized in school curriculum. So, if students have more chances to see mathematical properties in geometrical ways, they can experience how beautiful and meaningful they are through the process of the advent of them. Also, it was to try to develop an insight into their applications to other problems.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1473-1479
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• 2009

We introduce the resistant length and examine its properties. We also consider the geometric applications of resistant length to the boundary behavior of analytic functions, conformal mappings and derive the theorem in connection with the fundamental sequences, purely geometric problems. The method of resistant length leads a simple proofs of theorems. So it shows us the usefulness of the method of resistant length.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.867-883
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• 2019

The canal surfaces foliated by pseudo spheres $\mathbb{S}_1^2$ along a space curve in Minkowski 3-space are studied. The geometric properties of such surfaces are shown by classifying the linear Weingarten canal surfaces, the developable, minimal and umbilical canal surfaces are discussed at the same time.

• Korean Journal of Mathematics
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• v.31 no.3
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• pp.295-303
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• 2023

This paper introduces a novel method for obtaining umbrella matrices, which are defined as orthogonal matrices with row sums of one, using skew-symmetric matrices and Cayley's Formula. This method is presented for the first time in this paper. We also investigate the kinematic properties and applications of umbrella matrices, demonstrating their usefulness as a tool in geometry and kinematics. Our findings provide new insights into the connections between matrix theory and geometric applications.

• Journal of Ocean Engineering and Technology
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• v.27 no.2
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• pp.1-7
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• 2013

This paper aims at contributing to the field of ship design by introducing new systematic variation methods for ship hull forms. Hull form design is generally carried out in two stages. The first is the global variation considering the sectional area curve. Because the geometric properties of a sectional area curve have a decisive effect on the global hydrodynamic properties of ships, the design of a sectional area curve that satisfies various global design conditions, e.g., the displacement, longitudinal center of buoyancy, etc., is important in the initial hull form design stage. The second stage involves the local design of section forms. Section forms affect the local hydrodynamic properties, e.g., the local pressure in the fore- and aftbody. This paper deals with a new method for the systematic variation of sectional area curves. The longitudinal volume distribution of a ship depends on the sectional area curve, which can geometrically be controlled using parametric variation and a variation that uses the modification function. Based on these methods, we suggest a more generalized method in connection with the derivation of the lines for a new design compared to those for similar ships. This is the so-called the volumetric balanced variation (VOB) method for ship forms using a B-spline modification function and an optimization technique. In this paper the global geometric properties of hull forms are totally controlled by the form parameters. We describe the new method and some application examples in detail.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2002.10a
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• pp.292-295
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• 2002

In this paper, an analytical model for the prediction of the elastic properties of multi-axial warp knit fabric (MWK) composites is proposed. The geometric limitation, effect of stitching fibers and design parameters of MWK composites are considered in the model. The elastic behavior of MWK composites was conducted by using an averaging method. The predicted elastic properties are in reasonably good agreement with experimental values. Finally the effect of stitching in the MWK composites are discussed.

• Journal of Advanced Marine Engineering and Technology
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• v.20 no.1
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• pp.44-48
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• 1996

In manufacturing of exact products, the offsetting is required to transfer the design data of shape to manufacturing data. In offsetting the degeneracies are occurred, and these problems are mere difficult in freeform shapr manufacuring. This paper is using the geometric properties of B-spline curves to solve the degeneracy of offsetting and to generating of enhanced offsetting. The offsetting of B-spline control polygon spans generates exact control polygon of original shapes. This method is faster in generating offset curve than the normal offsetting, and the resulted offset curves are exact. The additional property of this method is using to control offset shape as B-spline curves. We believe that this method is as effective solution for modifying of offset curves.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.27 no.1
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• pp.723-733
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• 2009

This study proposes a sequence of procedures to extract building boundaries and planar patches through segmentation of rasterized lidar data. Although previous approaches to building extraction have been shown satisfactory, there still exist needs to increase the degree of automation. The methodologies proposed in this study are as follows: Firstly, lidar data are rasterized into grid form in order to exploit its rapid access to neighboring elevations and image operations. Secondly, propagation of errors in raw data is taken into account for in assessing the quality of gradients-driven properties and further in choosing suitable parameters. Thirdly, extraction of planar patches is conducted through a sequence of processes: histogram analysis, least squares fitting, and region merging. Experimental results show that the geometric components of building models could be extracted by the proposed approach in a streamlined way.

• Journal of Korean Society for Quality Management
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• v.31 no.3
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• pp.185-192
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• 2003

In this paper, the properties on the optimal replacement policies for the general failure model are developed. In the general failure model, two types of system failures may occur : one is Type I failure (minor failure) which can be removed by a minimal repair and the other, Type II failure (catastrophic failure) which can be removed only by complete repair. It is assumed that, when the unit fails, Type I failure occurs with probability 1-p and Type II failure occurs with probability p, $0\leqp\leq1$. Under the model, the system is minimally repaired for each Type I failure, and it is repaired completely at the time of the Type II failure or at its age T, whichever occurs first. We further assume that the repair times are non-negligible. It is assumed that the minimal repair times in a renewal cycle consist of a strictly increasing geometric process. Under this model, we study the properties on the optimal replacement policy minimizing the long-run average cost per unit time.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.1410-1415
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• 2007

Recently introduced WBK(Wire-wounded Bulk Kagome) shows relatively superior mechanical properties compared to other types of PCM. WBK is fabricated by assembling helical wires in 6 directions. Wire being a helix, the wire's geometric properties like pitch and helical radius shows certain geometric characteristics which can play some critical role in setting up an automatic fabrication process. In this study, geometry of WBK is modeled by various transformations of a piece of helical wire and the characteristics of the geometry of an element of WBK truss are discussed. In addition, the roles of pitch and helical radius of wire in optimizing the assembling process are described and the derivation of criteria is attempted to decide proper helical radius which would maintain minimal interference between wires at the crossings.