• Journal for History of Mathematics
• /
• v.25 no.4
• /
• pp.53-67
• /
• 2012

Today, it is necessary to calculate orbits with high accuracy in space flight. The key words of Poincar$\acute{e}$ in celestial mechanics are periodic solutions, invariant integrals, asymptotic solutions, characteristic exponents and the non existence of new single-valued integrals. Poincar$\acute{e}$ define an invariant integral of the system as the form which maintains a constant value at all time $t$, where the integration is taken over the arc of a curve and $Y_i$ are some functions of $x$, and extend 2 dimension and 3 dimension. Eigenvalues are classified as the form of trajectories, as corresponding to nodes, foci, saddle points and center. In periodic solutions, the stability of periodic solutions is dependent on the properties of their characteristic exponents. Poincar$\acute{e}$ called bifurcation that is the possibility of existence of chaotic orbit in planetary motion. Existence of near exceptional trajectories as Hadamard's accounts, says that there are probabilistic orbits. In this context we study the eigenvalue problem in early 20th century in three body problem by analyzing the works of Darwin, Bruns, Gyld$\acute{e}$n, Sundman, Hill, Lyapunov, Birkhoff, Painlev$\acute{e}$ and Hadamard.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1993.10a
• /
• pp.127-127
• /
• 1993

Separating Hyperplane의 기하학적인 성질을 이용하여, 일반적인 Closed Convex Set들의 교집합에 속하는 점을 찾아가는 방법을 제안하고, 교집합에 속하는 점을 찾아가는 과정에서 그 교집합의 공집합 여부를 판정할 수 있는 방법을 제안하였다. 이 기법은 기존의 방법들이 가정하는 수렴조건보다 더 일반적인 조건 하에서도 수렴성을 갖는 것을 증명할 수 있었으며, 그 교집합의 공집합 여부를 선형부동식 해의 존재 유무로 판정할 수 있는 방법을 제시하였다. 몇가지 특수한 경우의 Convex Set들의 경우에 대한 기법의 적용 결과도 알아 보기로 한다.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2008.04a
• /
• pp.23-25
• /
• 2008

In this paper, we study the existence and uniqueness of solutions for the fuzzy differential equations in ${(E_N)^n}$ using by Banach fixed point theorem. ${(E_N)^n}$ is n-dimension fuzzy vector space.

• Communications of the Korean Mathematical Society
• /
• v.15 no.2
• /
• pp.197-231
• /
• 2000

평형문제들에서의 기본적인 정리들이 일반화 볼록공간에서 어떻게 확장되는가를 보인다. KKM 이론의 중요한 정리들 대부분이 위상벡터공간에서의 선형성을 가정하지 않아도 위상적인 성질만으로 성립한다. 이같은 정리들의 예로는 KKM정리, von Neumann의 최소최대정리와 교차정리, Nash의 평형정리, 여러 가지 부동점정리, 극대원정리, Ky Fan의 최소최대부등식, 변분부등식들, 최량근사정리, 일반화 의사평형문제들의 해의 존재정리들이 있다.

• East Asian mathematical journal
• /
• v.36 no.2
• /
• pp.131-146
• /
• 2020

The isoperimetric problem is a well-known optimization problem from ancient Greek. Among plane figures with the same perimeter, which is the largest area surrounded? The answer to the question is circle. Zenodorus and Steiner's pure geometric proofs, which left a lot of achievements in this matter, looked beautiful with ideas at that time. But there was a fatal flaw in the proof. The weakness is related to the existence of the solution. In this paper, from a view of the existence of the solution, we investigate proofs of Zenodorus and Steiner and get educational implications.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2001.12a
• /
• pp.353-356
• /
• 2001

In this paper, we study the existence of fuzzy solution for the following differential system with fuzzy coefficient using the different two methods: (equation omitted), where a, b is the fuzzy natural number generated by fuzzy number l . The a-level set of the fuzzy number (equation omitted). The -level set of a is (equation omitted) and -level set of b is (equation omitted).

• Journal of the Korean Society of Hazard Mitigation
• /
• v.10 no.1
• /
• pp.73-80
• /
• 2010

The optimal design of water distribution system have started with the least cost design of single objective function using fixed hydraulic variables, eg. fixed water demand and pipe roughness. However, more adequate design is accomplished with considering uncertainties laid on water distribution system such as uncertain future water demands, resulting in successful estimation of real network's behaviors. So, many researchers have suggested a variety of approaches to consider uncertainties in water distribution system using uncertainties quantification methods and the optimal design of multi-objective function is also studied. This paper suggests the new approach of a multi-objective optimization seeking the minimum cost and maximum robustness of the network based on two uncertain variables, nodal demands and pipe roughness uncertainties. Total design procedure consists of two folds: least cost design and final optimal design under uncertainties. The uncertainties of demands and roughness are considered with Latin Hypercube sampling technique with beta probability density functions and multi-objective genetic algorithms (MOGA) is used for the optimization process. The suggested approach is tested in a case study of real network named the New York Tunnels and the applicability of new approach is checked. As the computation time passes, we can check that initial populations, one solution of solutions of multi-objective genetic algorithm, spread to lower right section on the solution space and yield Pareto Optimum solutions building Pareto Front.

• Tribology and Lubricants
• /
• v.6 no.1
• /
• pp.89-98
• /
• 1990

시일의 접촉면이 경사지고, 정현파형이 존재하며 코닝이 있는 경우에 대한 해석을 하였다. 또한 시일링 간극에 존재하는 유체는 비압축성 점성유체이다. 이러한 요소들을 고려한 레이놀즈 방정식의 일반해를 구하기 위하여 멱급수 근사이론을 이용하여 압력분포를 구하였고, 이 결과를 이용하여 시일의 누설 유동량 및 마찰 토오크를 해석하였다. 계산 결과에 의하면 시일 접촉면의 표면파형이나 코닝에 비하여 경사정도가 시일의 성능에 커다란 영향을 주고 있음을 보여주고 있다.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2003.05a
• /
• pp.1-4
• /
• 2003

This paper we study the existence of a global solution for the nonlinear fuzzy differential equations in E$_{N}$$^{n}$ by using the concept of fuzzy number of dimension n whose values are normal, convex, upper semicontinuous and compactly supported surface in R$^{n}$ . .

• Proceedings of the Korean Society for Rock Mechanics Conference
• /
• 2003.03a
• /
• pp.1-12
• /
• 2003

지반조사 결과에 의거하여 돌리네와 공동이 존재하는 지역을 구분하여 지역에 적합한 카르스트 형식을 적용, 예측하였다. 특히, 터널이 돌리네 발달 가능성이 적은 백운산 지역을 통과하는 경우에 소규모의 KT-1 ∼ KT-5가 존재하는 것으로 예측되었다. 그러나 설계시 지반조사의 한계성을 인식하고 시공 중에 필요하다고 판단되는 구간에는 막장 전방의 지질상태를 파악할 수 있는 조사를 선 시행하여, 그 결과를 토대로 최종 등급을 결정하여 안전한 시공에 대처할 수 있도록 해야 한다.