• 한국학교수학회논문집
• /
• 제14권3호
• /
• pp.261-275
• /
• 2011

최석정의 지수귀문도는 비교적 최근에 재조명되기 시작했고, 그동안 지수귀문도의 해를 구하려는 노력이 있었다. 88~92 그리고 94~98의 마법수에 한정해서 H-교호법을 사용하여 지수귀문도의 해를 구하는 것이 수학적으로 가능하다. 본 연구에서는 $n{\times}n$ 지수귀문도를 정의하고, H-교호법을 사용하여 $n{\times}n$ 지수귀문도에서 분할 $({\upsilon}+1)+{\upsilon}+({\upsilon}+1)$과 그것의 여분할 ${\upsilon}+({\upsilon}+1)+{\upsilon}$에 대해, 분할 $({\upsilon}+1)+({\upsilon}-1)+({\upsilon}+1)$과 그것의 여분할 $({\upsilon}-1)+({\upsilon}+1)+({\upsilon}-1)$에 대해, 분할 $({\upsilon}+1)+({\upsilon}+2)+({\upsilon}+1)$과 그것의 여분할 $({\upsilon}+2)+({\upsilon}+1)+({\upsilon}+2)$에 대해, 분할 $({\upsilon}+1)+({\upsilon}+3)+({\upsilon}+1)$과 그것의 여분할 $({\upsilon}+3)+({\upsilon}+1)+({\upsilon}+3)$에 대해 일반화된 지수귀문도의 해를 항상 구할 수 있다는 것을 보였다. 그리고 일반화된 지수귀문도의 해를 구하는 것을 중등수학교육과 중등 영재수학교육에서 문제해결의 과제로 활용할 것을 제안했다.

• 경영과학
• /
• 제31권3호
• /
• pp.113-130
• /
• 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.

• 한국토양비료학회지
• /
• 제37권5호
• /
• pp.322-328
• /
• 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.

• 한국콘텐츠학회논문지
• /
• 제20권11호
• /
• pp.15-27
• /
• 2020

문제해결이 중심인 디자인 과정에서 일반적으로 디자인 창의성의 저해요소는 2-3개가 동시에 발생하며 연계되어 어려움을 가중시킨다. 디자인 문제는 언제나 특이하고 독특하며 정의하기 힘든 난해한 상황에서 발생하므로 공식을 통한 정답도출은 가능하지 않으며 그 해답은 언제나 복수로 나타난다. 본 연구는 선행연구에서 논의된 디자인 창의성의 대표적인 저해요소에 대한 극복방법을 모색하는 후속연구로서 해결방안 제시와 그 효과성 입증을 목적으로 하고 있다. 이를 위해 선행연구에서 제시된 저해요소의 해결방안 모색과 핵심적인 해결팁(창의성 발전카드)을 고안하는 질적 연구를 수행하였다. 동시에 실험과 통계분석을 활용하는 양적 연구 방법론을 채택하였다. 창의성 발전카드를 활용하여 어떤 대상(원형)의 핵심특성을 파악한 후 핵심특성의 변형, 본질적 문제 재고, 의도적 차별화 등 원형의 환원적 분석을 활용해 창의적 해결방안에 효과적으로 접근할 수 있었다. 결과로써 제시된 해결방안은 디자인 창의성 저해요소의 극복방법으로서뿐만 아니라 창의성 향상에 효과적임을 확인하였다.

• 한국해안해양공학회지
• /
• 제17권4호
• /
• pp.232-242
• /
• 2005

본 연구에서 Penney and Price(1952)의 해석 해를 사용하여 반무한방파제, 양익방파제 등에서 발생하는 파랑의 회절 및 다중반사 현상에 대한 해석 해를 구하였다. 구조물에서의 반사 현상을 양익방파제를 지나는 회절 현상으로 간주하여 방파제에서 발생하는 단일반사 및 다중반사 현상을 규명하였다. 이를 바탕으로 방파제의 위치와 입사파랑의 각도에 따라 다른 경우에도 해석해를 구할 수 있다. 이러한 해석해는 국내의 항만 실무자들에게 회절 및 다중반사 현상에 대한 이해를 도울 수 있을 것이며, 실무의 해안 및 항만 구조물 설계 시에 사용되는 수치프로그램들의 정확도를 판단할 수 있는 비교 대상으로 사용될 수 있으리라 판단된다.

• 한국추진공학회:학술대회논문집
• /
• 한국추진공학회 2008년 영문 학술대회
• /
• pp.226-234
• /
• 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.

• 한국주거학회논문집
• /
• 제16권4호
• /
• pp.73-80
• /
• 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.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2005년도 춘계학술대회논문집
• /
• pp.836-839
• /
• 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
• /
• 제3권2호
• /
• pp.46-58
• /
• 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).

• 한국경영과학회지
• /
• 제22권3호
• /
• pp.37-58
• /
• 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.