• The Korean Journal of Applied Statistics
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• v.24 no.2
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• pp.279-292
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• 2011

Credibility theory is one of the most important theories of actuarial science to calculate the proper insurance premium. In this paper, the rule of relative exposure volume, the square root rule, the B$\"{u}$hlmann credibility and B$\"{u}$hlmann-Straub credibility with the basic concept of credibility have been introduced, Also, we estimate new premiums based on these methods for real data. As a result, the rule of relative exposure volume provides the highest accuracy.

• Communications for Statistical Applications and Methods
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• v.17 no.5
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• pp.713-724
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• 2010

Calculating or estimating the proper insurance premium is very important decision making process for both the policyholder and the insurance company. The credibility theory is one of the most important theories in actuarial science to get the proper premium. In this research, we introduce the rule of relative exposure volume, the square root rule and the B$\ddot{u}$hlmann credibility, and estimate the new premiums based on these methods. By real data analysis, the accuracy of these credibility methods are compared.

• The Korean Journal of Applied Statistics
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• v.26 no.2
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• pp.321-333
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• 2013

Credibility theory is one of important theories in actuarial science to produce proper insurance premium. In this paper, new partial credibilities are proposed and introduced with widely accepted credibility theories such as rule of relative exposure volume, square root rule, B$\ddot{u}$hlmann credibility and B$\ddot{u}$hlmann-Straub credibility. Also, with credibilities estimated by current and newly suggested, the performance of the accuracy for estimating the risk is compared through real data analysis and we show that the newly suggested methods are improving the performance by reducing the error.

• School Mathematics
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• v.13 no.4
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• pp.581-598
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• 2011

Given the growing agreement that algebra should be taught in the early stage of the curriculum, considerable studies have been conducted with regard to early algebra in the elementary school. However, there has been lack of research on how to organize mathematic lessons to develop of algebraic reasoning ability of the elementary school students. This research attempted to gain specific and practical information on effective algebraic teaching and learning in the elementary school. An exploratory qualitative case study was conducted to the fourth graders. This paper focused on the associative law of the multiplication. This paper showed what kinds of activities a teacher may organize following three steps: (a) focus on the properties of numbers and operations in specific situations, (b) discovery of the properties of numbers and operations with many examples, and (c) generalization of the properties of numbers and operations in arbitrary situations. Given the steps, this paper included an analysis on how the students developed their algebraic reasoning. This study provides implications on the important factors that lead to the development of algebraic reasoning ability for elementary students.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.1
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• pp.143-168
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• 2019

Along with the significance of algebraic thinking in elementary school, it has been recently emphasized that the properties of number and operations need to be explored in a meaningful way rather than in an implicit way. Given this, the purpose of this study was to analyze how third graders could understand the properties of operations in multiplication after they were taught such properties through a reconstructed unit of multiplication. For this purpose, the students from three classes participated in this study and they completed pre-test and post-test of the properties of operations in multiplication. The results of this study showed that in the post-test most students were able to employ the associative property, commutative property, and distributive property of multiplication in (two digits) × (one digit) and were successful in applying such properties in (two digits) × (two digits). Some students also refined their explanation by generalizing computational properties. This paper closes with some implications on how to teach computational properties in elementary mathematics.

• The Journal of Natural Sciences
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• v.13 no.1
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• pp.1-6
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• 2003

Strong laws of large numbers are established for the weighted sums of i.i.d. random variables which have higher order moment condition. One of the results of Sung(2001) is extended.

• Journal of Korean Society for Geospatial Information Science
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• v.20 no.2
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• pp.15-22
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• 2012

The variation in the wind speed with height above ground is called the wind shear profile. In the field of wind resource assessment, analysts typically use one of two mathematical relations to characterize the measured wind shear profile: the logarithmic profile (log law) and the power law profile (power law). The logarithmic law uses the surface roughness as a parameter, and the power law uses the power law exponent as a parameter. The shape of the wind shear profile typically depends on several factors, most notably the roughness of the surrounding terrain and the stability of the atmosphere. Since the atmospheric stability changes with season, time of day, and meteorological conditions, the surface roughness and the power law exponent also tends to change in time. For this study, Using the observed data from Met-mast, located in Pyeongdae, Handong in Jeju. we used the matlab and windograper to calculate roughness length and the law exponents. These calculations are similar to reference the data, but they have different ranges. In the ocean case, each reference data and calculated data was the same, but the crop area is higher than the earlier studies. In addition, the agricultural village is lower than the earlier studies.

• Communications of Mathematical Education
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• v.25 no.2
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• pp.473-495
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• 2011

Across the secondary school, students deal with the algebraic conditions like as identity, inverse, commutative law, associative law and distributive law. The algebraic structures, group, ring and field, are determined by these algebraic conditions. But the conditioning of these algebraic structures are not mentioned at all, as well as the meaning of the algebraic structures. Thus, students is likely to be considered the algebraic conditions as productions from the number sets. In this study, we systematize didactically the meanings of algebraic conditions and algebraic structures, considering connections between the number systems and the solutions of the equation. Didactically systematizing is to construct the model for student's natural mental activity, that is, to construct the stream of experience through which students are considered mathematical concepts as productions from necessities and high probability. For this purpose, we develop the program for the gifted, which its objective is to teach the meanings of the number system and to grasp the algebraic structure conceptually that is guaranteed to solve equations. And we verify the effectiveness of this developed program using didactical experiment. Moreover, the program can be used in ordinary students by replacement the term 'algebraic structure' with the term such as identity, inverse, commutative law, associative law and distributive law, to teach their meaning.

• Proceedings of the Korea Water Resources Association Conference
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• 2015.05a
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• pp.82-82
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• 2015

해안 대수층은 해수와 담수가 공존하는 지역으로 상대적으로 밀도가 큰 해수가 대수층의 담수 아래에 쐐기형태로 존재하게 된다. 이러한 쐐기형태의 해수와 담수의 경계면은 압력경도의 평형에 의해 경계면이 유지되며, 해수면 또는 지하수위가 변동할 경우 해수-담수 경계면의 균형이 무너짐과 더불어 압력경도의 평행이 이루어질 때 까지 해수-담수 경계면의 이동이 계속 진행된다. 수위 변화의 주요 원인으로는 지구온난화 및 기후변화로 인한 지속적인 해수면 상승과 도서지역의 인구증가 및 산업화로 인한 무분별한 지하수의 사용 등에 의한 지하수위 저하 등을 꼽을 수 있다. 이와 같은 원인으로 해안 및 도서지역에서는 해안 대수층의 해수침투거리가 증가하여 지하수 이용에 큰 어려움을 겪고 있다. 이에 해안 대수층의 해수침투 범위 및 거리를 추정하기 위한 많은 연구들이 다양한 분야에서 지속해서 이루어지고 있지만, 서로 밀도가 다른 해수와 담수가 공존하는 해안 대수층 내의 수리특성을 명확히 파악하기에는 아직까지 미흡한 점들이 많다. 과거에는 Darcy의 법칙 및 Ghyben-Herzberg 식에 근거한 이론적인 연구들이 주로 이루어졌고, 근래에 현장관측이나 수리모형실험이 국내 외적으로 수행되고 있으나, 모든 영역의 지하수의 특성을 조사하는 것이 사실상 불가능하다. 이에 최근에는 컴퓨터 성능의 비약적인 발전과 더불어 다양한 수치해석방법에 의한 수치모델들이 개발되어 시뮬레이션에 적용되고 있다. 하지만 거의 대부분의 수치모델은 해안 대수층 수리특성을 투수계수에 의존하고 있을 뿐, 대수층 내부의 해수-담수에 의한 밀도류의 유동특성을 전혀 고려하지 못한 채 정수압에 근거한 해수-담수 경계면에 대해 모의하고 있는 정도이다. 따라서 본 연구에서는 해안 대수층 내부의 유동현상을 투수계수에 의존하는 방법에서 탈피하여 대수층 매체의 입경, 공극, 형상 등을 고려할 수 있을 뿐만 아니라, 염분 및 온도차에 의한 밀도류를 해석할 수 있는 강비선형 수치모델을 개발하여 해수침투 현상을 직접 모의한다. 나아가 대부분의 이전 연구들에서 간과하고 있는 해안지역의 대표적 물리력인 파랑과 조석의 영향이 해안 대수층의 해수침투에 미치는 영향, 해안 대수층의 지하수위 및 해수면의 수위차에 의한 해수침투 특성 그리고 이를 제어 할 수 있는 새로운 대응기술을 제안하는 것을 목적으로 한다.

• Journal of Aerospace System Engineering
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• v.11 no.6
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• pp.50-55
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• 2017

The objective of this study was to use the Lanchester equation to predict the outcome of our engagement between our unmanned aerial vehicle (UAV) (Blue Group) and enemy UAV (Red Group). Lanchester's law states that the power of corps is proportional to the number of combatants. A second law states that the power of corps is proportional to the square of the number of combatants. The first law is a suitable law for guerrilla warfare while the second law is known as the law suitable for all-out war. Therefore, the second law is commonly used. The second law of Lanchester's was used in this study to predict engagement results. We estimated the battle loss rate value to win the battle as well as the required power number. We also predicted power number to make the damage of our group less than one. The battle loss rate to reliably receive victory when the enemy's UAV and the ally's UAV are equal in number of combat units must be 1: 1.5 or more.