• Journal of the Korean School Mathematics Society
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• v.14 no.3
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• pp.261-275
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• 2011

Seok-Jung Choi's Jisuguimundo mentioned as a brilliant legacy in the history of Korean mathematics had been cloaked in mystery for 300 years. In the meantime there has been some efforts to find solutions, and some particular answers were found, but no one achieved full success mathematically. By the way, H-alternating method showed that to find solutions of Jisuguimundo is possible, even though that method restricted magic number to 88~92 and 94~98. In this paper, $n{\times}n$ Jisuguimundo is defined, and it is showed that finding solutions of it is always possible in case of partition $({\upsilon}+1)+{\upsilon}+({\upsilon}+1)$ & co-partition ${\upsilon}+({\upsilon}+1)+{\upsilon}$, partition $({\upsilon}+1)+({\upsilon}-1)+({\upsilon}+1)$ & co-partition $({\upsilon}-1)+({\upsilon}+1)+({\upsilon}-1)$, partition $({\upsilon}+1)+({\upsilon}+2)+({\upsilon}+1)$ & co-partition $({\upsilon}+2)+({\upsilon}+1)+({\upsilon}+2)$, and partition $({\upsilon}+1)+({\upsilon}+3)+({\upsilon}+1)$ & co-partition $({\upsilon}+3)+({\upsilon}+1)+({\upsilon}+3)$. And It is suggested to find solutions of $n{\times}n$ Jisuguimundo could be used as a task for problem solving.

• Korean Management Science Review
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• v.31 no.3
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• pp.113-130
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• 2014

Cooperative coevolutionary algorithm (CCEA) has proven to be a very powerful means of solving optimization problems through problem decomposition. CCEA implies the use of several populations, each population having the aim of finding a partial solution for a component of the considered problem. Populations evolve separately and they interact only when individuals are evaluated. Interactions are made to obtain complete solutions by combining partial solutions, or collaborators, from each of the populations. In this respect, we can think of various interaction modes. The goal of this research is to develop a CCEA for a supply chain network design (SCND) problem and identify which interaction mode gives the best performance for this problem. We present general design principle of CCEA for the SCND problem, which require several co-evolving populations. We classify these populations into two groups and classify the collaborator selection scheme into two types, the random-based one and the best fitness-based one. By combining both two groups of population and two types of collaborator selection schemes, we consider four possible interaction modes. We also consider two modes of updating populations, the sequential mode and the parallel mode. Therefore, by combining both four possible interaction modes and two modes of updating populations, we investigate seven possible solution algorithms. Experiments for each of these solution algorithms are conducted on a few test problems. The results show that the mode of the best fitness-based collaborator applied to both groups of populations combined with the sequential update mode outperforms the other modes for all the test problems.

• Korean Journal of Soil Science and Fertilizer
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• v.37 no.5
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• pp.322-328
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• 2004

Available nutrients in soil solution play key roles on the growth of plants, but the equilibria in soil solution can be disturbed by acid precipitation. In this study, we investigated the relationships between element concentrations in the needles of Pinus thunbergii and chemical properties of forest soil solutions in the industrial complexes as an effort to find the possible limiting factor(s) causing the forest decline. The Ca/Al molar ratios in needles of Pinus thunbergii collected from the control sites were 18. However, at Onsan and Ulsan industrial complexes, those were decreased to the ranges from 10 to 11 for the one-year old needles and from 9 to 10 for the two-year old needles. The Mg/Al molar ratios showed similar tendencies with the Ca/Al molar ratios of the needles of Pinus thunbergii. In the A horizon, there existed a significant correlation between Mg concentrations in the needles of Pinus thunbergii and Ca/Al molar ratio of forest soil solution. Calcium concentrations in the needles of Pinus thunbergii in the B horizon were also significantly correlated with Ca/Al molar ratios of forest soil solutions. The uptakes of Ca and Mg by Pinus thunbergii were mainly limited by Al in the soil solutions of the A horizon and by Mn and Al in the soil solutions of the B horizon.

• The Journal of the Korea Contents Association
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• v.20 no.11
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• pp.15-27
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• 2020

In the design process that focuses on problem solving, in general, two or three barriers to design creativity appear at the same time and are linked to increase difficulty. Because the design problem always arises in unusual, unique, weird, and difficult to define, it is not possible to extract the correct answer through the formula and the answer is always plural. This study aims to present solutions and prove their effectiveness as a follow-up study that seeks to overcome the representative obstacles to design creativity discussed in the previous study. To this end, a qualitative study was conducted to find solutions to the obstacles suggested in the previous study and to devise key solutions(creativity development cards). At the same time, a quantitative research methodology using experiments and statistical analysis was adopted. After grasping the core characteristics of an object using the creativity development card, it was able to approach the creative solution by utilizing the reductive analysis of the original such as transformation of the core characteristics, reconsideration of essential problems and intentional differentiation. As a result, it was confirmed that the proposed solutions were effective not only as a method of overcoming the barriers to design creativity, but also in improving creativity.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.17 no.4
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• pp.232-242
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• 2005

In this study, we get an analytical solution for the diffraction and multi-reflection around a semi-infinite breakwater and breakwaters with a gap by using the solution of Penney and Price (1952). We find analytical solutions for single- and multi-reflections around the breakwaters by assuming that the reflected waves are regarded to be those diffracting through a breakwater gap. On the basis of these solutions, it is possible to understand the wave diffraction with different cases of incident wave direction and breakwater layout. These solutions may help harbor engineers to understand the phenomena of diffraction and multi-reflections around the breakwaters. These solutions may also be used to evaluate the applicability of wave transformation models which are used in designing coastal structures.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2008.03a
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• pp.226-234
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• 2008

Grain design has always been a vital and integral part of Solid Rocket Motor(SRM) design. Basing on the design objectives set by the system designer, the SRM designer has many options available for selecting the Grain configuration. Many of the available configurations may fulfill the required parameters of volumetric loading fraction, web fraction & Length to diameter ratios and produce internal ballistic results that may be in accordance to the design objectives. However, for any given set of design objectives, it is deemed necessary that best possible configuration be selected, designed and optimized. Hence optimal results of all applicable configurations are vital to be attained in order to compare and finalize the design that will produce most efficient performance. Generally the engineers pay attention and have skills on a specific grain configuration. The designing methodologies and computer codes available usually focus on single grain configuration may it be Star, Wagon Wheel or slotted tube. Hardly one can find a software or a design methodology where all such configurations can be worked on jointly and not only adequate designs be found but optimal solutions reached by applying an optimization method to find final design best suited for any design objective. In the present work design requirements have been set, grain configurations have been selected and their designing has been conducted. The internal ballistic parameters have been calculated and after finding the preliminary design solutions, the optimal solutions have been found. In doing so, software has been developed comprising of computer programs for designing the 2D grains including Star, Wagon Wheel and Slotted Tube configurations. The optimization toolbox of Matlab Fmincon has been used for getting optimal solutions. The affects of all the independent geometric design variables on the optimized solutions have been analyzed. Based on results attained from Optimization Method, an in depth comparison of Grain Configurations and analysis of performance prediction outputs have been conducted to come to conclusion as to which grain configuration is ideal for the current design requirement under study.

• Journal of the Korean housing association
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• v.16 no.4
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• pp.73-80
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• 2005

A high-rise residential building experienced stack effect problems during the winter such as difficulties in opening residential entrance doors and whistling noise from elevator doors generated by airflow. Field measurements were carried out on the building and the problems were verified by the analysis of the measurement results from three points of view: the total stack pressure difference, pressure distribution on each floor, and the location of the neutral pressure level. Based on the analysis of the three key parameters, possible solutions were proposed, such as zoning vertical shafts, lessening the airflow from the entrance doors on basement floors and lobby floor by installing vestibules, improving the airtightness of exterior walls, and installing separation doors where the problems occur. Simulations of proposed solutions were conducted and the effects of reducing the pressure difference were evaluated. Stack effect problems in a high-rise residential building were verified through field measurements and could be mitigated by the solutions which were drawn from the analysis of the field measurements and the simulation results.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.836-839
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• 2005

The in-plane vibration response of a clamped circular plate should be predicted in many applications. Up to now, papers on the in-plane vibration of rectangular plate are published. However, analytical derivation on the in-plane vibration of the clamped circular plate is not carried out. Therefore, the in-plane vibration of the clamped circular plate is the concern of this paper. In order to derive the equations of motion for the clamped circular plate in the cylindrical coordinate, the kinetic energy and potential energy for the in-plane behavior are obtained by us ing the stress-strain-displacement expressions. Application of Hamilton's principle leads to two sets of differential equations. These displacement equations were highly coupled. It is possible to obtain a simpler set of equations by introducing Helmholtz decomposition. Substituting them into the coupled differential equations, we obtain the uncoupled equations of motion. In order to solve them, we assume that the solutions are harmonic. Then, they lead to the wave equations. Using the separation of variable, we obtain the general solutions for the equations. Based on the solutions, the displacements for r and $\theta$ direction are assumed. Finally we obtain the frequency equation for the clamped circular plate by the application of boundary conditions. The derived equation is compared with the finite element analysis for validation by using the some numerical examples.

• International Journal of Aeronautical and Space Sciences
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• v.3 no.2
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• pp.46-58
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• 2002

An inverse method is introduced to construct benchmark problems for the numerical solution of initial value problems. Benchmark problems constructed through this method have a known exact solution, even though analytical solutions are generally not obtainable. The solution is constructed such that it lies near a given approximate numerical solution, and therefore the special case solution can be generated in a versatile and physically meaningful fashion and can serve as a benchmark problem to validate approximate solution methods. A smooth interpolation of the approximate solution is forced to exactly satisfy the differential equation by analytically deriving a small forcing function to absorb all of the errors in the interpolated approximate solution. A multi-variable orthogonal function expansion method and computer symbol manipulation are successfully used for this process. Using this special case exact solution, it is possible to directly investigate the relationship between global errors of a candidate numerical solution process and the associated tuning parameters for a given code and a given problem. Under the assumption that the original differential equation is well-posed with respect to the small perturbations, we thereby obtain valuable information about the optimal choice of the tuning parameters and the achievable accuracy of the numerical solution. Illustrative examples show the utility of this method not only for the ordinary differential equations (ODEs) but for the partial differential equations (PDEs).

• Journal of the Korean Operations Research and Management Science Society
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• v.22 no.3
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• pp.37-58
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• 1997

An AI approach with tabu search is designed to solve multi-level knapsack problems. The approach performs intelligent actions with memories of historic data and learning effect. These action are developed ont only by observing the attributes of the optimal solution, the solution space, and its corresponding path to the optimal, but also by applying human intelligence, experience, and intuition with respect to the search strategies. The approach intensifies, or diversifies the search process appropriately in time and space. In order to create a good neighborhood structure, this approach uses two powerful choice rules that emphasize the impact of candidate variables on the current solution with respect to their profit contribution. "Pseudo moves", similar to "aspirations", support these choice rules during the evaluation process. For the purpose of visiting as many relevant points as possible, strategic oscillation between feasible and infeasible solutions around the boundary is applied. To avoid redundant moves, short-term (tabu-lists), intemediate-term (cycle-detection), and long-term (recording frequency and significant solutions for diversfication) memories are used. Test results show that among the 45 generated problems (these problems pose significant or insurmountable challenges to exact methods) the approach produces the optimal solutions in 39 cases.lutions in 39 cases.