• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.677-690
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• 2020

In this article, we study a reaction-diffusion system with homogeneous Dirichlet boundary conditions, which describing a three-species food chain model. Under some conditions, the predator-prey subsystem (u₁ ≡ 0) has a unique positive solution (${\bar{u_2}}$, ${\bar{u_3}}$). By using the birth rate of the prey r1 as a bifurcation parameter, a connected set of positive solutions of our system bifurcating from semi-trivial solution set (r₁, (0, ${\bar{u_2}}$, ${\bar{u_3}}$)) is obtained. Results are obtained by the use of degree theory in cones and sub and super solution techniques.

• Journal of the Korean Society for Precision Engineering
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• v.9 no.4
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• pp.36-43
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• 1992

This paper presents a hierarchical real-time operation control and monitoring scheme of the FMS/CIM center which has been implemented at the Automation and Systems Research Institute of Seoul National University. The hierarchical structure of the whole scheme consists of three lavers. The upper layer is in charge of on-line scheduling, computer network control, shop-floor monitoring and command generation for AGV dispatching, machining, assembly, inspection, set-up, etc. The middle layer has six modules, which are installed in the FMS host computer with the upper layer and run on the multi-tasking basis. Each module is connected to one of six cell controllers distributed in the FMS model plant and transfers operation command down to each cell controller through the Ethernet/TCP-IP local area network. The lower layer is comprised of six cell control software modules for machining cell, assembly cell, inspection cell, set-up stations. AS/RS and AGV. Each cell controller reports the status of the manufacturing facilites to the middle layer as well as ecxecuting the appropriate sequence control of the manufacturing processes.

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1976-1979
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• 2002

A new and efficient layout object extraction technique is presented in this paper, which is to be used in technology migration or hard-U reuse. The technique models the original polygon layout represented by a set of edges as a set of connected or overlapped rectangles. The rectangle model provides easy and efficient recognition, extraction, resizing, and compaction of layout objects such as transistors, contacts, and wires. Experiments on several designs from simple standard cells to more complex designs using standard and/or custom cells demonstrate the effectiveness of our technique.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.855-861
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• 2019

The geodesics on the round 2-sphere $S^2$ are all simple closed curves of equal length. In 1903 Otto Zoll introduced other Riemannian surfaces with the same property. After that, his name is attached to the Riemannian manifolds whose geodesics are all simple closed curves of the same length. The question that "whether or not the set of Zoll metrics on 2-sphere $S^2$ is connected?" is still an outstanding open problem in the theory of Zoll manifolds. In the present paper, continuing the work of D. Jane for the case of the Ricci flow, we show that a naive application of some famous geometric flows does not work to answer this problem. In fact, we identify an attribute of Zoll manifolds and prove that along the geometric flows this quantity no longer reflects a Zoll metric. At the end, we will establish an alternative proof of this fact.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.857-867
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• 2019

Suppose that G = (V, E) is a connected locally finite graph with the vertex set V and the edge set E. Let ${\Omega}{\subset}V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph G $$\{-{\Delta}_{pu}={\lambda}K(x){\mid}u{\mid}^{p-2}u+f(x,u),\;x{\in}{\Omega}^{\circ},\\u=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}^{\circ}$ and ${\partial}{\Omega}$ denote the interior and the boundary of ${\Omega}$, respectively, ${\Delta}_p$ is the discrete p-Laplacian, K(x) is a given function which may change sign, ${\lambda}$ is the eigenvalue parameter and f(x, u) has exponential growth. We prove the existence and monotonicity of the principal eigenvalue of the corresponding eigenvalue problem. Furthermore, we also obtain the existence of a positive solution by using variational methods.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.645-651
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• 2020

The distinguishing number (index) D(G) (D'(G)) of a graph G is the least integer d such that G has an vertex labeling (edge labeling) with d labels that is preserved only by a trivial automorphism. The strong product G ☒ H of two graphs G and H is the graph with vertex set V (G) × V (H) and edge set {{(x1, x2),(y1, y2)}|xiyi ∈ E(Gi) or xi = yi for each 1 ≤ i ≤ 2.}. In this paper we study the distinguishing number and the distinguishing index of strong product of two graphs. We prove that for every k ≥ 2, the k-th strong power of a connected S-thin graph G has distinguishing index equal two.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.13-24
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• 2021

For a finite commutative ring R with identity 1 ≠ 0, the zero divisor graph ��(R) is a simple connected graph having vertex set as the set of nonzero zero divisors of R, where two vertices x and y are adjacent if and only if xy = 0. We find the signless Laplacian spectrum of the zero divisor graphs ��(ℤn) for various values of n. Also, we find signless Laplacian spectrum of ��(ℤn) for n = pz, z ≥ 2, in terms of signless Laplacian spectrum of its components and zeros of the characteristic polynomial of an auxiliary matrix. Further, we characterise n for which zero divisor graph ��(ℤn) are signless Laplacian integral.

• Laser Solutions
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• v.7 no.2
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• pp.1-10
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• 2004

This work was attempted to join SCP sheet and STS304 sheet by using Nd:YAC laser beam. SCP sheet has good formability and low cost, while STS304 has excellent corrosion resistance and mechanical properties in high temp. In this experiment, butt joint type was used to develop the tailored blank welding for dissimilar steel. Sheets which have different thermal properties. Computer simulation was conducted to obtain the off-set position for efficient welding by considering laser power, scanning speed, focal length and basic properties. The result showed that the optimum thermal distribution was obtained when the laser beam was irradiated at $0.05{\sim}0.1$ mm off-set toward the SCP sheet side. The experiment was conducted based on the result of computer simulation to show the same optimum conditions. Optimum conditions were 3KW in laser beam power, 6m/min in scanning speed, -0.5mm in focal position, 0.1mm off-set toward SCP. Microhardness test, tensile test, bulge test, optical microscopy, EDS, and XRD were performed to observe the microstructure around fusion zone and to evaluate the mechanical properties of optimum conditions, The weld zone had high microhardness values by the formation of the martensitic structure. Tensile test measured the strength of welded region by vertical to strain direction and the elongation of welded region by parallel to strain direction. Bulge test showed $52\%$ formability of the original materials. Bead shape, grain size, and martensitic structure were observed by the optical microscopy in the weld zone. Detailed results of EDS, XRD confirmed that the welded region was connected of martensitic structure.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.11 no.12
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• pp.2413-2418
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• 2007

IN wireless sensor networks (WSNs), one challenging issue is to In wireless sensor networks (WSNs), one challenging issue is to construct a virtual backbone in a distributed and localized way while considering energy limitation. Dominating set has been used extensively as core or virtual backbone in WSNs for the purposes like routing and message broadcast. To ensure network performance, a good dominating set construction protocols should be simple and avoid introducing extra message. In addition, the resulting dominating set should be small, connected, and take into account the energy level at each node. This paper studies efficient and simple virtual backbone construction protocol using defer time in IEEE 802.15.4- based WSNs (e.g. Zigbee). The efficiency of our proposed protocol is confirmed through simulation results.

• Industrial Engineering and Management Systems
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• v.3 no.2
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• pp.92-99
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• 2004

We consider the ATM switching node location problem (ANLP). In this problem, there are two kinds of facilities, hub facilities and remote facilities, with different capacities and installation costs. We are given a set of customers with each demand requirements, a set of candidate installation sites of facilities, and connection costs between facilities. We need to determine the locations to place facilities, the number of facilities for each selected location, the set of customers who are connected to each installed hub via installed remote facilities with minimum cost, while satisfying demand requirements of each customer. We formulate this problem as a general integer programming problem and solve it to optimality. In this paper, we present a preprocessing procedure to tighten the formulation and develop a branch-and-price algorithm. In the algorithm, we consider the integer knapsack problem as the column generation problem. Computational experiments show that the algorithm gives optimal solutions in a reasonable time.