• Journal of Korean Society of Steel Construction
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• v.19 no.1
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• pp.29-41
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• 2007

Structural design, like other complex decision problems, involves many trade-offs among competing criteria. Although mathematical programming models are becoming increasingly realistic, they often have design limitations, that is, there are often relevant issues that cannot be easily captured. From the understanding of these limitations, a decision-support system is developed that can generate some useful alternatives as well as a single optimum value in the optimization of steel frame structures. The alternatives produced using this system are "good" with respect to modeled objectives, and yet are "different," and are often better, with respect to interesting objectives not present in the model. In this study, we created a decision-support system for designing the most cost-effective moment-resisting steel frame structures for resisting lateral loads without compromising overall stability. The proposed approach considers the cost of steel products and the cost of connections within the design process. This system makes use of an optimization formulation, which was modified to generate alternatives of optimum value, which is the result of the trade-off between the number of moment connections and total cost. This trade-off was achieved by reducing the number of moment connections and rearranging them, using the combination of analysis based on the LRFD code and optimization scheme based on genetic algorithms. To evaluate the usefulness of this system, the alternatives were examined with respect to various design aspects.

• Journal of Korean Association for Spatial Structures
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• v.6 no.3 s.21
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• pp.103-110
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• 2006

This study presents a technique to control quantitatively lateral drift of RC tall frameworks subject to lateral loads. To this end, lateral drift constraints are established by introducing approximation concept that preserves the generality of the mathematical programming and can efficiently solve large scale problems. Also the relationships of sectional properties are established to reduce the number of design variables and resizing technique of member is developed under the 'constant-shape' assumption. Specifically, the methodology of dynamic displacement sensitivity analysis is developed to formulate the approximated lateral displacement constraints. Three types of 10 and 50 story RC framework models are considered to illustrate the features of dynamic stiffness-based optimal design technique proposed in this study.

• Progress in Medical Physics
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• v.15 no.2
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• pp.84-93
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• 2004

Stereotactic radiosurgery (SRS) is a technique that delivers a high dose to a target legion and a low dose to a critical organ through only one or a few irradiations. For this purpose, many mathematical methods for optimization have been proposed. There are some limitations to using these methods: the long calculation time and difficulty in finding a unique solution due to different tumor shapes. In this study, many clinical target shapes were examined to find a typical pattern of tumor shapes from which some possible ideal geometrical shapes, such as spheres, cylinders, cones or a combination, are assumed to approximate real tumor shapes. Using the arrangement of multiple isocenters, optimum variables, such as isocenter positions or collimator size, were determined. A database was formed from these results. The optimization procedure consisted of the following steps: Any shape of tumor was first assumed to an ideal model through a geometry comparison algorithm, then optimum variables for ideal geometry chosen from the predetermined database, followed by a final adjustment of the optimum parameters using the real tumor shape. Although the result of applying the database to other patients was not superior to the result of optimization in each case, it can be acceptable as a plan starling point.

• The Mathematical Education
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• v.63 no.2
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• pp.165-186
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• 2024

Despite the growing attention on artificial intelligence-based automated scoring technology as a support method for the introduction of descriptive items in school environments and large-scale assessments, there is a noticeable lack of foundational research in mathematics compared to other subjects. This study developed an automated scoring model for two descriptive items in first-year middle school mathematics using the Random Forest algorithm, evaluated its performance, and explored ways to enhance this performance. The accuracy of the final models for the two items was found to be between 0.95 to 1.00 and 0.73 to 0.89, respectively, which is relatively high compared to automated scoring models in other subjects. We discovered that the strategic selection of the number of evaluation categories, taking into account the amount of data, is crucial for the effective development and performance of automated scoring models. Additionally, text preprocessing by mathematics education experts proved effective in improving both the performance and interpretability of the automated scoring model. Selecting a vectorization method that matches the characteristics of the items and data was identified as one way to enhance model performance. Furthermore, we confirmed that oversampling is a useful method to supplement performance in situations where practical limitations hinder balanced data collection. To enhance educational utility, further research is needed on how to utilize feature importance derived from the Random Forest-based automated scoring model to generate useful information for teaching and learning, such as feedback. This study is significant as foundational research in the field of mathematics descriptive automatic scoring, and there is a need for various subsequent studies through close collaboration between AI experts and math education experts.

• Communications of Mathematical Education
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• v.21 no.4
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• pp.621-646
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• 2007

In our new learning environment, we were asked to change our teaching method in our Linear Algebra class. In mathematics class, we could use several math-softwares such as MATHEMATICA, MATLAB, MAPLE, Drive etc.. MATLAB was quite well fit with our Linear Algebra class. In this paper we introduce an efficient way of delivery on important concepts in linear algebra by using well-known MATLAB/ATLAST M-files which we downloded from http://www.umassd.edu/specialprograms/atlast/.

• Journal of the Korean School Mathematics Society
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• v.13 no.2
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• pp.225-241
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• 2010

Even though geometry is an important part basic to mathematics, studies on the program designs and teaching strategies of geometry are insufficient. The aims of this study are to propose the model of program design for autonomous learners taking their characteristics of the mathematically gifted into consideration. The core of teaching materials are analytic geometry and projective geometry. And the new teaching strategy will introduce three steps ; a draft strategies step(problem presentation, problem solving), a supportive strategies step(abstraction of a mathematical concept, mathematical induction, and extension), a transference strategies step to teaching strategy suitable for mathematically gifted. As a result, this study will suggest the effective methods of geometry teaching for the mathematically gifted.

• Proceedings of the Korean Vacuum Society Conference
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• 1999.07a
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• pp.37-37
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• 1999

KSTAR(Korea Superconducting Tokamak Advanced Research) 핵융합 토카막 실험 장치의 플라즈마 가열을 위한 수소 중성입자빔 수송라인 내에 설치되는 collimator에 가해지는 열속 및 플라즈마에 전달되는 빔의 통과율을 해석하였다. 43cm$\times$12cm 크기의 이온원으로부터 방출되는 이온빔의 공간적 분산은 기본적으로는 Gaussian 분산(수직바향으로 1.2$^{\circ}$, 수평방향으로 0.5$^{\circ}$)의 형태를 가지지만 이온 가속 전장의 공간적 불균일로 인해 Gaussian 분산에서 다소 벗어나는 형태를 띠게 되는데, 이의 영향을 고려할 수 있는 수학적 모델을 정립하였다. 해석에 고려된 요소들은 다음과 같다. 이온원을 수많은 점원의 집합으로 가정하여 각각의 점원으로부터 주어진 공간적 분산을 가지는 이온들이 방출되는 것으로 가정하였으며, 방출된 이온은 중성화 과정을 거쳐 40%의 이온만이 중성입자화되며, 중성화되지 않은 60%의 이온들은 bending magnet에서 ion dump로 유도되어 사라지며, 나머지 중성입자들은 직진 운동을 하게 된다. 빔 진행 도중 빔 중앙에서 크게 벗어나는 일부 중성입자들은 여러 겹으로 존재하는 빔 collimator에 의해 단계적으로 제거되며, 일부 중성입자들은 잔류 수소기체에 의한 재이온화 과정을 거치기도 한다. 여기서는 정립된 수학적 모델을 이용하여 이들 collimator에서 제거되는 양 및 재이온화 손실들을 고려하여 최종적으로 플라즈마에 입사되는 중성입자 빔을 계산하였다. 한편, 빔 수송라인 설치시에 발생할 수 있는 설치 오차를 이온원 설치시의 오차와 빔 collimator 설치상의 오차로 구분하여 이들의 의한 영향도 계산하였다. Gaussian 분산을 가정하였을 경우, 이온원에 가장 근접하여 설치되는 collimator에 가해지는 수직성분의 열속은 9.7kW/cm2로 계산되었다. 이 열속을 제어 가능한 수준으로 낮추기 위해서 collimator는 빔 라인과 거의 나란하게 설치될 것이다. 빔의 통과율은 약 33%로서 하나의 이온원에서 방출된 7.8MW 중 2.5 MW만이 플라즈마에 전달되는 것을 알 수 있었다. Non-Gaussian 분산의 경우, 최대 열속은 9.1kW/cm2로 다소 낮아졌으나, 빔통과율은 28%정도로 더욱 낮아졌다. 설치상의 오차에 의한 영향을 살펴보면, 이온원이 1$^{\circ}$ 정도 기울어지게 설치된다면 collimaor에 가해지는 최대 열속 및 빔통과율은 약 15kW/cm2, 16.6% 정도로 나타나 매우 심각한 결과를 초래함을 알 수 있었다. 이에 비해 collimator 설치상의 오차의 영향은 이보다 훨씬 작아 5mm 오차가 발생했을 경우에도 최대 열속은 12kW/cm2까지 증가했으나, 빔 통과율의 변화는 거의 없었다.

• 전기의세계
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• v.30 no.3
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• pp.167-171
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• 1981

In this paper, the mathematical model of influenza derived by the state space method induced a new model by using normal distribution curve of incubation period and researched the effect of vaccination. The important results are as follows. (1) A new model represents accurate spread curve. (2) The standard deviation period in Korea is about 1.5 degree. (3) The number of carries of influenza since put in practice to the vaccination 20% is reduced by average 9.8% degree, the period of spread increase 4 days degree. (4) The vaccination at early put in operation was far surperior and the period of spread grow longer more or less. (5) In the first stage of an attack of disease a case increase since reducing. (6) The number of carries at night is reduced by average 5.468% than in the daytime.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.12
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• pp.597-603
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• 2001

In the mathematical model for the transmission dynamics of HIV infection described in previous papers, the population under consideration is assumed to be homogeneous community of homosexual males for which the parameter x represents the constant rate at which individual members of the population acquire new sexual partners. This is a gross oversimplification since it is well known that individuals vary widely in their levels of sexual activity and in this papers the heterogeneous model is modified to allow for this variation. The pattern on the epidemic character of HIV, the causative agent of AIDS, was analysed by heterogeneous-mixing model. The computer simulation was performed using real date.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.699-702
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• 1998

This study investigates the population model of the spread of HIV/AIDS which the infection is generated by an infectious in dividual in a population of susceptibles. A mathematical model is presented for the transmission dynamics of HIV infection within the communities of homosexual males. The pattern on the epidemic character of HIV, the causative agent of AIDS, was analysed by the mathematical model of AIDS system which is derived according to the ecological relationship between five epidemilogic states of individuals. The computer simulation was performed using real data.