• Honam Mathematical Journal
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• v.27 no.3
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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 $M^3$.

• Journal of the Korean Society of Safety
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• v.11 no.1
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• pp.16-26
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• 1996

In a series of original papers, [1-17] efficient methods and algorithms have been presented, for the exact solution of many reliability problems represented by binary networks. A starting point of these methods was the concept of domination, firstly introduced in ,elation with reliability problems in [2]. It's application to directed networks resulted in the development of a topological formula for the classical problem of the two terminal reliability. This result was extended later to the all-terminal and the k-terminal reliability problems. All papers mentioned above use a path oriented representation for the network topology. In practical applications, however, it is common and often advantageous to work with cut sets. This article considers the Domination theory for reliability problem of a network. Some topological formula are derived and the power and the application of this formula are shown through the alternative proof of topological formula of A. Satyanarayana [2].

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• v.9 no.1
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• pp.771-773
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• 2005

There have been researches about analyzing the information retrieval patterns of log file to efficiently obtain the users' information research patters in web environment. The methods frequently used in their researches is to suggest the algorithms by which the frequent one is derived from the path traversal patterns in efficient way. But one of their general problems is not to provide the proper solution in case of complex, that is, general topological patterns. Therefore this paper tries to suggest a efficient algorithm after defining the general information retrieval pattern.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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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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• v.2 no.1
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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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• v.7 no.1
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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.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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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.

• The KIPS Transactions:PartC
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• v.10C no.3
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• pp.367-376
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• 2003

This study deals with the DCMST (Delay constrained Capacitated Minimum Spanning Tree) problem applied in the topological design of local networks or finding several communication paths from root node. While the traditional CMST problem has only the traffic capacity constraint served by a port of root node, the DCMST problem has the additional mean delay constraint of network. The DCMST problem consists of finding a set of spanning trees to link end-nodes to the root node satisfying the traffic requirements at end-nodes and the required mean delay of network. The objective function of problem is to minimize the total link cost. This paper presents two-phased heuristic algorithm, which consists of node exchange, and node shift algorithm based on the trade-off criterions, and mean delay algorithm. Actual computational experience and performance analysis show that the proposed algorithm can produce better solution than the existing algorithm for the CMST problem to consider the mean delay constraint in terms of cost.

• Structural Engineering and Mechanics
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• v.40 no.3
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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.