• 호남수학학술지
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• 제27권3호
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• pp.477-485
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• 2005

Let ($M^n$, g) be a compact oriented Riemannian manifold. It has been conjectured that every solution of the equation $z_g=D_gdf-{\Delta}_gfg-fr_g$ is an Einstein metric. In this article, we deal with the 3 dimensional case of the equation. In dimension 3, if the conjecture fails, there should be a stable minimal hypersurface in ($M^3$, g). We study some necessary conditions to guarantee that a stable minimal hypersurface exists in $M^3$.

• 한국안전학회지
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• 제11권1호
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• pp.16-26
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• 1996

A.Satyanarayana와 다른이들은 [1.2.5]에서 domination이론을 사용하여 네트워크의 정확한 신뢰도 계산을 위한 새로운 topologic formel을 발견하였다. 이들은 이식을 통하여 그래프 G로 표현되는 어떤 시스템이나 네트워크의 신뢰도 계산을 위하여 path 또는 k-tree를 사용한 Inclusion-Exclusion식에 나타나는 항들(=2$^{m}$ -1, m은 path나 k-tree의 수)중 서로 소거되지 않는 항들은 그래프 G의 acyclic k-부분그래프(subgraph)와 1대 1로 상응되며, cyclic-과 k-부분그래프들에 상응되는 항들은 소거되어지거나 Inclusion-Exclusion식에 나타나지 않는 -결국 신뢰도계산에 필요없는- 항들임을 밝혔다. 이들은 이성질을 이용하여 그래프 G의 정확한 신뢰도계산을 위한 빠른 알고리즘을 제시하였다. 이 알고리즘은 결국 그래프 G의 path나 k-tree를 기초로 하는 Inclusion-Exclusion식에서 나타나는 항들중 소거되지 않는 항들에 1:1로 대응하는 acyclic k-subgraph만을 찾아 신뢰도계산을 할수있게 하여 준다. 이때 acyclic k-subgraph들은 각각의 domination을 갖으며, 이들은 Inclusion-Exclusion식에서 대응되는 항의 부호들의 합과 같다. 본 논문에서는 첫째로 신뢰도계산을 위하여 주어진 어떤 그래프 G에서 G를 구성하는 선(edge)을 기초로 하는 어떤 임의로 주어진 family M(G) (예: cutset이나 path, 또는 k-tree 등의 family)에 의한 (부분)그래프의 domination에 대한 성질을 관찰하고 몇가지 식을 유도한후, k-tree의 family K(G)를 기초로 한 어떤 그래프의 domination과 Inclusion-Exclusion식과의 관계를 고찰하고, 이식의 강력함과 응용의 가능성을 A. Satyanarayana의 topologic formel의 재증명을 통하여 보인다.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2005년도 춘계종합학술대회
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• pp.771-773
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• 2005

웹 환경에서 사용자들의 정보검색 패턴을 얻어내기 위해 흔히 로그 파일의 정보검색 패턴을 분석하는 기존 연구들이 있어 왔다. 이들에서 흔히 사용하는 방법은 경로 순회 패턴(path traversal patterns)에서 효율적으로 빈번 패턴(frequent patterns)을 찾아내는 알고리즘을 제안하는 것이다. 하지만 이들의 기존 연구의 가장 일반적인 문제점들 중의 하나는 일반적인 패턴 즉, 복잡한 형태 패턴(topological patterns)에 대한 적절한 해답을 찾아주지는 못한다는 것이다. 따라서 본 논문에서는 일반적인 패턴 유형을 정의하고 이들로부터 정보검색 패턴을 알아내는 효율적인 알고리즘을 제안하고자 한다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 26-27 Oct. 1990
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• pp.1150-1155
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• 1990

This paper proposes an optimal redundancy resolution of a kinematically redundant manipulator while considering homotopy classes. The necessary condition derived by minimizing an integral cost criterion results in a second-order differential equation. Also boundary conditions as well as the necessary condition are required to uniquely specify the solution. In the case of a cyclic task, we reformulate the periodic boundary value problem as a two point boundary value problem to find an initial joint velocity as many dimensions as the degrees of redundancy for given initial configuration. Initial conditions which provide desirable solutions are obtained by using the basis of the null projection operator. Finally, we show that the method can be used as a topological lifting method of nonhomotopic extremal solutions and also show the optimal solution with considering the manipulator dynamics.

• Biomaterials and Biomechanics in Bioengineering
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• 제2권1호
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• pp.15-22
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• 2015

Poly(ethylene glycol) end-capped with pentafluorophenyl group(s) in ABA (FP-PEG-FP) and AB (mPEG-FP) types were prepared. Even though they were similar in composition, the lower critical solution temperature (LCST) of FP-PEG-FP was observed at $23^{\circ}C$, whereas that of mPEG-FP was observed at $65^{\circ}C$. To understand the large difference in solution behaviour of the two polymers, UV-VIS spectroscopy, microcalorimetry, 1H-NMR spectroscopy, and dynamic light scattering were used. FP-PEG-FP has two hydrophobic pentafluorophenyl groups at the ends of hydrophilic PEG (1000 Daltons), whereas mPEG-PF has a highly dynamic PEG (550 Daltons) block that are anchored to a hydrophobic pentafluorophenyl group. PF-PEG-PF not only has a smaller conformational degree of freedom than mPEG-PF but also can form extensive intermolecular aggregates, therefore, PF-PEG-PF exhibits a significantly lower LCST than mPEG-PF. This paper suggests that topological control is very important in designing a temperature-sensitive polymer.

• International Journal of CAD/CAM
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• 제7권1호
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• pp.41-49
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• 2007

In density-based topology optimization, 0/1 solutions are sought. Discrete topological problems are often relaxed with continuous design variables so that they can be solved using continuous mathematical programming. Although the relaxed methods are practical, grey areas appear in the optimum topologies. SIMP (Solid Isotropic Microstructures with Penalization) employs penalty schemes to suppress the intermediate densities. SRV (the Sum of the Reciprocal Variables) drives the solution to a 0/1 layout with the SRV constraint. However, both methods cannot effectively remove all the grey areas. SRV has some numerical aspects. In this work, a new scheme SIMP-SRV is proposed by combining SIMP and SRV approaches, where SIMP is employed to generate an intermediate solution to initialize the design variables and SRV is then adopted to produce the final design. The new method turned out to be very effective in conjunction with the method of moving asymptotes (MMA) when using for the stiffness topology optimization of continuum structures for minimum compliance. The numerical examples show that the hybrid technique can effectively remove all grey areas and generate stiffer optimal designs characterized with a sharper boundary in contrast to SIMP and SRV.

• 산업경영시스템학회지
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• 제42권1호
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• pp.87-94
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• 2019

A wireless sensor network is emerging technology and intelligent wireless communication paradigm that is dynamically aware of its surrounding environment. It is also able to respond to it in order to achieve reliable and efficient communication. The dynamical cognition capability and environmental adaptability rely on organizing dynamical networks effectively. However, optimally clustering the cognitive wireless sensor networks is an NP-complete problem. The objective of this paper is to develop an optimal sensor network design for maximizing the performance. This proposed Ranking Artificial Bee Colony (RABC) is developed based on Artificial Bee Colony (ABC) with ranking strategy. The ranking strategy can make the much better solutions by combining the best solutions so far and add these solutions in the solution population when applying ABC. RABC is designed to adapt to topological changes to any network graph in a time. We can minimize the total energy dissipation of sensors to prolong the lifetime of a network to balance the energy consumption of all nodes with robust optimal solution. Simulation results show that the performance of our proposed RABC is better than those of previous methods (LEACH, LEACH-C, and etc.) in wireless sensor networks. Our proposed method is the best for the 100 node-network example when the Sink node is centrally located.

• 대한수학회보
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• 제59권1호
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• pp.241-263
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• 2022

We consider a nonlinear Schrödinger equation with critical frequency, (P_𝜀) : 𝜀²∆v(x) - V(x)v(x) + |v(x)|^p-1v(x) = 0, x ∈ ℝ^N, and v(x) → 0 as |x| → +∞, for the infinite case as described by Byeon and Wang. Critical means that 0 ≤ V ∈ C(ℝ^N) verifies Ƶ = {V = 0} ≠ ∅. Infinite means that Ƶ = {x₀} and that, grossly speaking, the potential V decays at an exponential rate as x → x₀. For the semiclassical limit, 𝜀 → 0, the infinite case has a characteristic limit problem, (P_inf) : ∆u(x)-P(x)u(x) + |u(x)|^p-1u(x) = 0, x ∈ Ω, with u(x) = 0 as x ∈ Ω, where Ω ⊆ ℝ^N is a smooth bounded strictly star-shaped region related to the potential V. We prove the existence of an infinite number of solutions for both the original and the limit problem via a Ljusternik-Schnirelman scheme for even functionals. Fixed a topological level k we show that v_k,𝜀, a solution of (P_𝜀), subconverges, up to a scaling, to a corresponding solution of (P_inf ), and that v_k,𝜀 exponentially decays out of Ω. Finally, uniform estimates on ∂Ω for scaled solutions of (P_𝜀) are obtained.

• 정보처리학회논문지C
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• 제10C권3호
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• pp.367-376
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• 2003

본 연구는 로컬 네트워크의 토폴로지를 설계하거나 루트 노드로부터 여러 개의 통신 경로를 구하는 데 사용될 수 있는 DCMST(Delay constrained Capacitated Minimum Spanning Tree) 문제를 다룬다. 기존의 CMST 문제는 루트 노드의 한 포트가 담당하는 트래픽의 용량에만 제한이 있는 데 비해 DCMST 문제에는 네트워크 평균 지연 시간의 제약 조건이 추가된다. 이 문제는 종단 노드의 트래픽 요구량과 네트워크의 평균 지연 시간을 만족시키는 스패닝 트리의 집합을 구하는 것으로 목적 함수는 전체 링크 비용을 최소로 하는 것이다. 본 연구에서는 트레이드-오프에 기준한 노드 교환 알고리즘과 노드 이동 알고리즘 그리고 평균 지연 알고리즘으로 구성되는 2 단계 휴리스틱을 제시한다. 실제 계산 경험과 성능 분석을 통해 제안한 알고리즘이 평균 지연을 고려한 기존의 CMST 알고리즘보다 비용 측면에 있어 더 우수한 해를 생성할 수 있음을 보였다.

• Structural Engineering and Mechanics
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• 제40권3호
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• pp.335-346
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• 2011

This paper deals with the bifurcations of non-semi-simple eigenvalues at critical point of Hopf bifurcation to understand the dynamic behavior of the system. By using the Puiseux expansion, the expression of the bifurcation of non-semi-simple eigenvalues and the corresponding topological structure in the parameter space are obtained. The zero-order approximate solutions in the vicinity of the critical points at which the multiple Hopf bifurcation may occur are developed. A numerical example, the flutter problem of an airfoil in simplified model, is given to illustrate the application of the proposed method.