• Title/Summary/Keyword: Topological Method

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TOPOLOGICAL METHOD DOES NOT WORK FOR FRANKEL-MCDUFF CONJECTURE

  • Kim, Min Kyu
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.1
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    • pp.31-35
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    • 2007
  • In dealing with transformation group, topological approach is very natural. But, it is not sufficient to investigate geometric properties of transformation group and we need geometric method. Frankel-McDuff Conjecture is very interesting in the point that it shows struggling between topological method and geometric method. In this paper, the author suggest generalized Frankel-McDuff conjecture as a topological version of the conjecture and construct a counterexample for the generalized version, and from this we assert that topological method does not work for Frankel-McDuff Conjecture.

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Topological Geometry Education and its Application to the Analysis of the Map of West Capital Pyongyangbu of Old Korea (위상수학을 활용한 고려 평양부 고지도 분석)

  • Jung, Tacksun;Choi, Q-Heung
    • East Asian mathematical journal
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    • v.34 no.4
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    • pp.487-509
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    • 2018
  • We analyse the map of the west capital Pyongyangbu of Old Korea(AD 920) by topological method and geometrical method and compare it with the map of North Korea Pyongyang. By the analyse of the map we find the real place of the old map. The analysing and finding the real place of the old map is a very good example of geometry education. Many Koreans had learned and recognized that Old Korea(AD 920) was a small country located in the south part of Ablok river. But, after reading this paper they change their old recognitions and they take prides in Great Old Korea.

TOPOLOGICAL APPROACH FOR THE MULTIPLE SOLUTIONS OF THE NONLINEAR PARABOLIC PROBLEM WITH VARIABLE COEFFICIENT JUMPING NONLINEARITY

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.19 no.1
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    • pp.101-109
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    • 2011
  • We get a theorem which shows that there exist at least two or three nontrivial weak solutions for the nonlinear parabolic boundary value problem with the variable coefficient jumping nonlinearity. We prove this theorem by restricting ourselves to the real Hilbert space. We obtain this result by approaching the topological method. We use the Leray-Schauder degree theory on the real Hilbert space.

Shape design for viscoelastic vibration isolators to minimize rotational stiffness (회전강성 최소화를 위한 절연요소의 형상 설계)

  • Oh, Hwan-Youp;Kim, Kwang-Joon
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • pp.343-347
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    • 2008
  • Design of shape for visco-elastic vibration isolation elements, which are very cost-effective and so popular in many applications is frequently based on experiences, intuitions, or trial and errors. Such traditions in shape design make it difficult for drastic changes or new concepts to come out. In this paper, both topological method and shape optimization method are combined together to find out a most desirable isolator shape efficiently by using two commercial engineering programs. ABAQUS and MATLAB. The procedure is divided into two steps. At the first step, a topology optimization method is employed to find an initial shape. where density of either 0 or 1 for finite elements is used for physical realizability. At the second step, based on the initial shape, finer tuning of the shape is done by boundary movement method. An illustration of the procedure will be presented for a mount of an air-conditioner compressor system and the effectiveness will be discussed.

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Shape Design for Viscoelastic Vibration Isolators to Minimize Rotational Stiffness (회전강성 최소화를 위한 절연요소의 형상 설계)

  • Oh, Hwan-Youp;Kim, Kwang-Joon
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.18 no.12
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    • pp.1250-1255
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    • 2008
  • Design of shape fur visco-elastic vibration isolation elements, which are very cost-effective and so popular in many applications is fi?equently based on experiences, intuitions, or trial and errors. Such traditions in shape design make it difficult for drastic changes or new concepts to come out. In this paper, both topological method and shape optimization method are combined together to find out a most desirable isolator shape efficiently by using two commercial engineering programs, ABAQUS and MATLAB. The procedure is divided into two steps. At the first step, a topology optimization method is employed to find an initial shape, where density of either 0 or 1 for finite elements is used fur physical realizability. At the second step, based on the initial shape, finer tuning of the shape is done by boundary movement method. An illustration of the procedure is presented fur a mount of an air-conditioner compressor system and the effectiveness is discussed.

The Main Stream of Mathematical Modeling of a Suspension Bridge (교량건설방식에 따른 수학적 모델링의 변천과정 기술과 현수교 방정식의 수학적 연구의 흐름)

  • Nam, Hye-Won
    • Journal for History of Mathematics
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    • v.20 no.4
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    • pp.93-104
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    • 2007
  • It is well known that a suspension bridge may display certain oscillations under external aerodynamic forces. Under the action of a strong wind, in particular, a narrow and very flexible suspension bridge can undergo dangerous oscillations. The collapse of the Tacoma Narrows suspension bridge caused by a wind blowing at a speed of 42 miles per hour, is one of the most striking examples. In this paper, we study models describing oscillations in suspension bridges and known results.

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The Method of realizable Generation of Trees and Co-Trees (수목과 보목의 위상수학적 생성법)

  • 이장우
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.11 no.1
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    • pp.47-51
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    • 1974
  • In this paper, we have tried to study topological method for generating trees and Co-trees of a given circuit which is required in the first step of analysis of networks, and also illustrative examples that compare with other available methods in aspect of the efficiency are given. It is believed that the proposed method is more efficient than other methods already available and that it will play a fundamental role in the topological analysis of electrical networks.

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A Study on Geometrical Glue Operation between Non-manifold Models (비다양체 모델간의 기하학적 접합 연산에 관한 연구)

  • Park, Sang-Ho
    • Journal of the Korea Computer Graphics Society
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    • v.4 no.1
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    • pp.11-19
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    • 1998
  • Non-manifold topological operations such as Euler and Boolean operations provide a versatile environment for modeling domains. The implementation of these operations raises geometrical issues that need to be addressed to ensure the topological validity of the underlying model, and they uses the glue operation which provides a basic method to modify the topology of non-manifold models when vertices, edges and faces are contacting each other. Topological information such as adjacency relationships should be inferred when gluing non-manifold models. Two methods of reasoning can be employed to find the topological information : topological reasoning and geometrical reasoning. The topological method can infer the adjacency relationships by using stored topological information. On the other hand, the geometrical method can find topological ambiguities by considering the geometrical shape at the local area of gluing when the topological relations were not stored. This paper describes the geometrical reasoning method.

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Control Performance Comparison of Model-referenced and Map-based Control Method for Vehicle Lateral Stability Enhancement (차량 횡방향 안정성 향상을 위한 모델 참조 제어와 맵기반 제어 방법의 제어 성능 비교)

  • Yoon, Moonyoon;Baek, Seunghwan;Choi, Jungkwang;Boo, Kwangsuck;Kim, Heungseob
    • Journal of the Korean Society for Precision Engineering
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    • v.31 no.3
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    • pp.253-259
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    • 2014
  • This study proposes a map-based control method to improve a vehicle's lateral stability, and the performance of the proposed method is compared with that of the conventional model-referenced control method. Model-referenced control uses the sliding mode method to determine the compensated yaw moment; in contrast, the proposed map-based control uses the compensated yaw moment map acquired by vehicle stability analysis. The vehicle stability region is calculated by a topological method based on the trajectory reversal method. The performances of model-referenced control and map-based control are compared under various road conditions and driving inputs. Model-referenced control uses a control input to satisfy the linear reference model, and it generates unnecessary tire lateral forces that may lead to worse performance than an uncontrolled vehicle with step steering input on a road with low friction coefficient. The simulation results show that map-based control provides better stability than model-referenced control.

4D-QSAR Study of p56Ick Protein Tyrosine Kinase Inhibitory Activity of Flavonoid Derivatives Using MCET Method

  • Yilmaz, Hayriye;Guzel, Yahya;Onal, Zulbiye;Altiparmak, Gokce;Kocakaya, Safak Ozhan
    • Bulletin of the Korean Chemical Society
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    • v.32 no.12
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    • pp.4352-4360
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    • 2011
  • A four dimensional quantitative structure activity relationship analysis was applied to a series of 50 flavonoid inhibitors of $p56^{lck}$ protein tyrosine kinase by the molecular comparative electron topological method. It was found that the -log (IC50) values of the compounds were highly dependent on the topology, size and electrostatic character of the substituents at seven positions of the flavonoid scaffold in this study. Depending on the negative or positive charge of the groups correctly embedded in these substituents, three-dimensional bio-structure to increase or decrease -log (IC50) values in the training set of 39 compounds was predicted. The test set of 11 compounds was used to evaluate the predictivity of the model. To generate 4D-QSAR model, the defined function groups and pharmacophore used as topological descriptors in the calculation of activity were of sufficient statistical quality ($R^2$ = 0.72 and $Q^2$ = 0.69). Ligand docking approach by using Dock 6.0. These compounds include many flavonoid analogs, They were docked onto human families of p56lck PTKs retrieved from the Protein Data Bank, 1lkl.pdb.