• Bulletin of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.585-595
• /
• 2024

We show that a pseudo-Anosov map constructed as a product of the large power of Dehn twists of two filling curves always has a geodesic axis on the curve graph of the surface. We also obtain estimates of the stable translation length of a pseudo-Anosov map, when two filling curves are replaced by multicurves. Three main applications of our theorem are the following: (a) determining which word realizes the minimal translation length on the curve graph within a specific class of words, (b) giving a new class of pseudo-Anosov maps optimizing the ratio of stable translation lengths on the curve graph to that on Teichmüller space, (c) giving a partial answer of how much power is needed for Dehn twists to generate right-angled Artin subgroup of the mapping class group.

• Journal of the Korean Mathematical Society
• /
• v.58 no.1
• /
• pp.109-122
• /
• 2021

In this paper, we consider the problem of finding the hypersurface Mn in the Euclidean (n + 1)-space ℝn+1 that satisfies an equation of mean curvature type, called singular minimal hypersurface equation. Such an equation physically characterizes the surfaces in the upper half-space ℝ+3 (u) with lowest gravity center, for a fixed unit vector u ∈ ℝ3. We first state that a singular minimal cylinder Mn in ℝn+1 is either a hyperplane or a α-catenary cylinder. It is also shown that this result remains true when Mn is a translation hypersurface and u is a horizantal vector. As a further application, we prove that a singular minimal translation graph in ℝ3 of the form z = f(x) + g(y + cx), c ∈ ℝ - {0}, with respect to a certain horizantal vector u is either a plane or a α-catenary cylinder.

• School Mathematics
• /
• v.4 no.2
• /
• pp.161-192
• /
• 2002

This paper investigated the teaching and teaming of contents-related graphing in Korean secondary textbooks and suggested the improved methods of graph instruction through this analysis. reification-the case of function, In Harel, G., Dubinsky(Eds.), The Concept of Function : Aspects of Epistemology and Pedagogy Textbooks are analyzed from the viewpoint of the proportion of graphing contents, their sequencing, the proportion of each domain in graphing activities (interpretation vs. construction, quantitative vs. qualitative aspect, local vs. global aspect) and tasks (prediction, translation, scaling), and the difference in the graphing contents between the sixth and the seventh curriculum. This analysis demonstrates that graphing contents are increasing in textbooks, therefore the high school textbooks appear in almost every content area. The graphing activities concentrate on the construction, the quantitative aspects, and the local aspects, and are gradually focusing on the interpretation and global aspects of high school textbooks. Furthermore, most of graphing tasks favor translation. In contrast, the current seventh curriculum includes a balance of interpretation and construction activities and has more global aspects than the sixth curriculum based textbooks; however, the qualitative approach still rarely appears. For the graphing tasks, translation is still prevalent, but the importances of prediction tasks based on graph have increased in comparison with the sixth curriculum textbooks. Further, the seventh curriculum based textbooks are designed to stimulate more dynamic graphing instruction by introducing new tools such as graphing calculators and computer software. We suggest that the qualitative and global aspects should be emphasized in early graph instruction, a variety of graph activities in realistic contexts should be performed, and educational technology such as graphing calculator and computer can be efficient to implement these ideas.

• International Journal of CAD/CAM
• /
• v.6 no.1
• /
• pp.99-104
• /
• 2006

Engineering graph plays an important role in design and manufacture, such as architecture, machinery, manufacture, military. However, almost no persons consider the security and copyright of two-dimensional engineering graph. A novel method for two-dimensional engineering graph watermark based U system is proposed in this paper. Watermarks generated by this technique can be successfully extracted even after rotation, translation and scaling transform.

• Journal of Korea Multimedia Society
• /
• v.1 no.2
• /
• pp.224-238
• /
• 1998

The EMFG (Extended Mark Flow Graph) is not only a powerful tool for designing the discrete-event system conceptually or specifically but also a good representation tool for implementing the system directly. But it is difficult to design or analyze the system because the impossibility of mathematical analysis results from some complicated representation of the EMFG. In this paper, therefore we redefined EMFG representations to provide the possibility of mathematical analysis, and employed an output inhibit are of a transition, which makes possible the adequate representations for the indescribable parts. We also solved trouble parts in the circuit translations of the EMFG and proposed the circuit translation method by using the mathematical formula. Finally, we compared the conventional EMFG with the redefined EMFG, and we designed a 0101 detecter with the redefined EMFG and translated it to the corresponding circuit.

• Proceedings of the Korea Multimedia Society Conference
• /
• 1998.04a
• /
• pp.423-431
• /
• 1998

이진값을 가지는 이진 시스템을 모델화하고 설계하여 구현할 수 있도록 Petri Net의 한 부류인 박스의 마크수가 최대 1인 안전(safe)한 확장된 마크흐름선도(EMFG : Extended Mark Flow Graph)를 재구성하였다. 레벨박스와 펄스박스 및 게이트박스를 하나의 박스로 통일하였으며, 보존아크를 제거하고 서로 상반되는 개념을 가지는 일반아크와 역아크만을 사용하였고, 특히 트랜지션의 출력아크로 새로이 역아크를 도입함으로써 EMFG의 표현을 명확하게 하였다. 또한 EMFG에서 자기루프를 정의하였다. 그리고 이진 시스템을 모델링한 EMFG를 실제회로로 구현하는 방법이 새로이 제시되었다.

• Journal of KIISE:Software and Applications
• /
• v.31 no.3
• /
• pp.267-275
• /
• 2004

Directed graph and Lindenmayer system (L-system) are two major encoding methods of representation to develop creatures in application field of artificial life. It is difficult to define real morphology structurally using the L-systems which are a grammatical rewriting system because L-systems represent genotype as loops, procedure calls, variables, and parameters. This paper defines a class of representations called structured directed graph, which is identified by its ability to define structures of the genotype in the translation to the phenotype, and presents an example of creating 3D flowers using a directed graph which is proper method to represent real morphology, and interactive genetic algorithm which decodes the problem with human's emotional evaluation. The experimental results show that natural flower morphology can be generated by the proposed method.

• East Asian mathematical journal
• /
• v.30 no.4
• /
• pp.451-474
• /
• 2014

The purpose of this study is to analyze error patterns third-year middle school students make on quadratic function graph problems and to examine about the possible correct them by providing supplementary tutoring. To exam the error patterns that occur during problem solving processes, to 82 students, We provided 25 quadratic function graph problems in the preliminary-test. The 5 types of errors was conceptual errors, false intuition errors, incorrect use of conditions in problems, technical errors, and errors from slips or carelessness. Statistical analysis of the preliminary-test and post-test shows that achievement level was higher in the post-test, after supplementary tutoring, and the t-test proves this to be meaningful data. According to the per subject analyses, the achievement level in the interest of symmetry, parallel translation, and general graph, respectively, were all higher in the post-test than the preliminary-test and this is meaningful data as well. However, no meaningful relation could be found between the preliminary-test and the post-test on other subjects such as graph remodeling and relations positions of the parabola. For the correction of errors, try the appropriate feedback and various teaching and learning methods.

• Korean Journal of Computational Design and Engineering
• /
• v.15 no.2
• /
• pp.85-93
• /
• 2010

This paper proposes a CAE data translation and visualization technique that can verify time-varying continuous analysis simulation in a virtual reality (VR) environment. In previous research, the use of CAE analysis data has been problematic because of the lack of any interactive simulation controls for visualizing continuous simulation data. Moreover, the research on post-processing methods for real-time verification of CAE analysis data has not been sufficient. We therefore propose a scene graph based visualization method and a post-processing method for supporting interoperability of continuous CAE analysis data. These methods can continuously visualize static analysis data independently of any timeline; it can also continuously visualize dynamic analysis data that varies in relation to the timeline. The visualization system for continuous simulation data, which includes a CAE middleware that interfaces with various formats of CAE analysis data as well as functions for visualizing continuous simulation data and operational functions, enables users to verify simulation results with more realistic scenes. We also use the system to do a performance evaluation with regard to the visualization of continuous simulation data.

• Journal of the Korean School Mathematics Society
• /
• v.16 no.1
• /
• pp.141-155
• /
• 2013

Process to translate into other forms in the form of expression for function is important in the development of functional thinking. Also it should be emphasized on the teaching of the function. This study will identify the translation ability of functional expressions and errors in the process to translate. The purpose of this study is to suggest important implications for the teaching and learning of function. To do this, we lead high school students perform the task to examine the translation ability. Then we compute a percentage of correct answers for each question and analyze the types of errors and their causes.