• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1033-1046
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• 1999

This paper is devoted to the point wise error estimate up to boundary for the standard finite element solution of Poisson equation with Dirichlet boundary condition. Our new approach used the discrete maximum principle for the discrete harmonic solution. once the mesh in our domain satisfies the $\beta$-condition defined by us, the discrete harmonic solution with dirichlet boundary condition has the discrete maximum principle and the pointwise error should be bounded by L-errors newly obtained.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.377-393
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• 2024

In this paper, we study the positive solutions to a discrete harmonic function for a random walk satisfying finite range and ellipticity conditions, killed at the boundary of an unbounded cylinder in ℤ^d. We first prove the existence and uniqueness of positive solutions, and then establish that all the positive solutions are generated by two special solutions, which are exponential growth at one end and exponential decay at the other. Our method is based on maximum principle and a Harnack type inequality.

• International Journal of Highway Engineering
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• v.18 no.2
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• pp.51-60
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• 2016

PURPOSES : The applicability of the mechanics-based similarity concept (suggested by Feng et al.) for determining scaled variables, including length and load, via laboratory-scale tests and discrete element analysis, was evaluated. METHODS: Several studies on the similarity concept were reviewed. The exact scaling approach, a similarity concept described by Feng, was applied in order to determine an analytical solution of a free-falling ball. This solution can be considered one of the simplest conditions for discrete element analysis. RESULTS : The results revealed that 1) the exact scaling approach can be used to determine the scale of variables in laboratory tests and numerical analysis, 2) applying only a scale factor, via the exact scaling approach, is inadequate for the error-free replacement of small particles by large ones during discrete element analysis, 3) the level of continuity of flowable materials such as SCC and cement mortar seems to be an important criterion for evaluating the applicability of the similarity concept, and 4) additional conditions, such as the kinetics of particle, contact model, and geometry, must be taken into consideration to achieve the maximum radius of replacement particles during discrete element analysis. CONCLUSIONS : The concept of similarity is a convenient tool to evaluate the correspondence of scaled laboratory test or numerical analysis to physical condition. However, to achieve excellent correspondence, additional factors, such as the kinetics of particles, contact model, and geometry, must be taken into consideration.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.151-160
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• 2004

Genetic algorithm is the theory of grafting the principle of survival of the fittest in genetics on to the computer algorithm and it is used to solve the optimization problems, especially the shape and size optimization of the structure in Architectural problems. In the size optimization problem discrete variables are used, but series variables have to be used in the shape optimization problem because of the incongruenty. The purpose of this study is to obtain the optimum shape of cable domes by using the real coding genetic algorithm. Generally, the structural performance of the cable domes is influenced very sensitively by pre-stress, geometry and length of the mast because of its flexible characteristic. So, it is very important to decide the optimum shape to get maximum stiffness of cable domes. We use the model to verify the usefulness of this algorithm for shape optimization and analyze the roof system of Seoul Olympic Gymnastic Arena as analytical model of a practical structures. It is confirmed lastly that the optimum shape domes have more stiffness than initial shape ones.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.10 no.16
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• pp.113-119
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• 1987

A Multistage production-inventory model is developed for deteriorating items. The model is developed deterministic but time-varing demand pattern and instantaneous delivery. Deterioration rates are assumed to vary from period to period. Discrete version of Pontryagin's maximum principle is used to present the efficient alogrithm to solve this model easily. A numerical example is given to illustrate the derived results.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.7
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• pp.883-889
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• 2013

The distribution of a response usually depends on the distribution of a variable. When the distribution of a variable has two different modes, the response also follows a distribution with two different modes. In most reliability analysis methods, the number of modes is irrelevant, but not the type of distribution. However, in actual problems, because information is often provided with two or more modes, it is important to estimate the distributions with two or more modes. Recently, some reliability analysis methods have been suggested for bimodal distributions. In this paper, we review some methods such as the Akaike information criterion (AIC) and maximum entropy principle (MEP) and compare them with the Monte Carlo simulation (MCS) using mathematical examples with two different modes.

• Composites Research
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• v.13 no.2
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• pp.40-50
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• 2000

In an effort to construct a structure under the design principle of minimal use of materials for maximum performances, a discrete gradient structure has been introduced in laminate composite systems. Using a sequential linear programming method, the gradient structure of composites to maximize the buckling load was optimized in terms of fiber volume fraction and thickness of each layer. The buckling load showed maximum value with the outmost [$0^{\circ}$] layer concentrated by almost all the fibers when the ratio of length to width(aspect ratio) was less than 1.0. But when the aspect ratio was 2.0, the optimum was determined in a structure where the thickness and fiber volume fraction were well-balanced in each layer. From the optimization of gradient structure, the optimal fiber volume fraction and thickness of each layer were proposed. Gradient structures have also shown an advantage in the weight reduction of composites compared with the conventional homogeneous structures.

• Proceedings of the Korean Society For Composite Materials Conference
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• 1999.11a
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• pp.68-72
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• 1999

In an effort to construct a structure under the design principle of minimal use of materials for maximum performances, a discrete gradient structure has been introduced in laminate composite systems. Using a sequential linear programming method, the gradient structure of composites to maximize the buckling load was optimized in terms of fiber volume fraction and thickness of each layer. Theoretical optimization results were then verified with experimental ones. The buckling load of laminate composite showed maximum value with the outmost [$0^{\circ}$] layer concentrated by almost all the fibers when the ratio of length to width(aspect ratio) was less than 1.0. But when the aspect ratio was 2.0, the optimum was determined in a structure where the thickness and fiber volume fraction were well balanced in each layer. From the optimization of gradient structure, the optimal fiber volume fraction and thickness of each layer were proposed. Experimental results agreed well with the theoretical ones. Gradient structures have also shown an advantage in the weight reduction of composites compared with the conventional homogeneous structures.

• Journal of Communications and Networks
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• v.15 no.1
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• pp.77-86
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• 2013

Cognitive radio (CR) has emerged as one of effective methods to enhance the utilization of existing radio spectrum. Main principle of CR is that secondary users (SUs) are allowed to use the spectrum unused by primary users (PUs) without interfering PU's transmissions. In this paper, PUs operate on a slot-by-slot basis and SUs try to exploit the slots unused by PUs. We propose OSA protocols in the single channel and we propose an opportunistic spectrum access (OSA) protocols in the multi-channel cognitive radio networks with one control channel and several licensed channels where a slot is divided into contention phase and transmission phase. A slot is divided into reporting phase, contention phase and transmission phase. The reporting phase plays a role of finding idle channels unused by PUs and the contention phase plays a role of selecting a SU who will send packets in the data transmission phase. One SU is selected by carrier sense multiple access / collision avoidance (CSMA/CA) with request to send / clear to send (RTS/CTS) mechanism on control channel and the SU is allowed to occupy all remaining part of all idle channels during the current slot. For mathematical analysis, first we deal with the single-channel case and we model the proposed OSA media access control (MAC) protocol by three-dimensional discrete time Markov chain (DTMC) whose one-step transition probability matrix has a special structure so as to apply the censored Markov chain method to obtain the steady state distribution.We obtain the throughput and the distribution of access delay. Next we deal with the multi-channel case and obtain the throughput and the distribution of access delay by using results of single-channel case. In numerical results, our mathematical analysis is verified by simulations and we give numerical results on throughput and access delay of the proposed MAC protocol. Finally, we find the maximum allowable number of SUs satisfying the requirements on throughput and access delay.