• 대한수학회논문집
• /
• 제9권4호
• /
• pp.853-855
• /
• 1994

The object of present note is to give a very short proof of Stirling's formula which uses only a formula for the generalized zeta function. There are several proofs for this formula. For example, Dr. E. J. Routh gave an elementary proof using Wallis' theorem in lectures at Cambridge ([5, pp.66-68]). We can find another proof which used the Maclaurin summation formula ([5, pp.116-120]). In [1], they used the Central Limit Theorem or the inversion theorem for characteristic functions. In [2], pp. Diaconis and D. Freeman provided another proof similarly as in [1]. J. M. Patin [7] used the Lebesgue dominated convergence theorem.

• 대한수학교육학회지:학교수학
• /
• 제8권3호
• /
• pp.327-339
• /
• 2006

이 연구에서는 브레트슈나이더 공식의 재발명을 소재로, 중등예비교사용 수학화 교수단원 <사각형의 넓이>를 디자인하고 있다. 예비교사들이 이 교수단원을 통해 얻을 수 있는 것을 제시하면 다음과 같다. 첫째, 예비교사들은 현상을 조직하는 본질을 발명하는 수학화를 경험할 수 있다. 예비교사들은 그들이 정말로 수학을 발명하는 것처럼, 브라마굽타의 공식과 브레트슈나이더 공식을 발명하는 경험을 할 수 있다. 둘째, 예비교사들은 수학 지식 발명의 한 가지 메커니즘을 이해할 수 있다. 예비교사들은 브라마굽타 공식과 브레트슈나이더 공식을 재발명하면서, 새로운 수학 지식이 이미 잘 알고 있는 수학 지식으로부터 유추를 통해 발명되는 메커니즘을 이해할 수 있다. 셋째, 예비교사들은 학교수학과 학문 수학의 연결을 이해할 수 있다 예비교사들은 직사각형, 정사각형, 마름모, 평행사변형, 사다리꼴의 구적 공식과 헤론의 공식과 같은 학교수학이 학문 수학이라 할 수 있는 브라마굽타의 공식과 브레트슈나이더 공식 사이의 관계를 통해, 학교수학과 학문 수학이 어떻게 연결될 수 있는지 알 수 있다.

• 대한지역사회영양학회지
• /
• 제9권3호
• /
• pp.251-262
• /
• 2004

The aim of this study was to assess the nutrient intakes from infant formula and supplemental foods of 246 healthy infants fed infant formula, aged from 5 to 18 months. Subjects were devided into two groups depending on supplemental food type for weaning, Domestic supplemental foods (mainly home-made, n = 129) and Delivery supplemental foods (mainly commercially-delivered, n = 117). Four subgroups were assigned to 5-6 months, 7-8 months, 9-11 months, and 12-18 months by ages, respectively. Dietary assessment was carried out using 24-hour-recall method. Formula intakes in the delivery group tended to decrease accordingly with the ages. However, in the domestic group, formula intakes up to 8 months were similar and decreased after 9 month. Energy, protein, calcium and iron intakes from infant formula and supplemental foods were assessed. Energy intake at 12-18 months were lower than the RDA in both groups. Daily intake of protein and calcium at all ages were much higher than the RDA in both groups. Therefore, protein and calcium overnutrition were elucidated. Especially, protein intake at 5-6 months, calcium intake at all ages from infant formula was higher than the RDA in both groups. Iron intake at 5-6 months from infant formula were higher than the RDA. Consequently, as for infant formula, it was suggested that not only formula intakes but also nutrient content in formula should be reconsidered. On the other hand, nutrient intakes from supplemental foods in the domestic group tended to be higher than that of the delivery group. Especially at 9-11 months, significant differences between the two groups were observed. This may be due to high dependency on commercial powdered baby food in the domestic group. This study revealed that daily nutrient intakes of formula-fed infants are desirable but nutrient intakes from infant formula are too high. Conclusively, this study suggests that as the age of infants increases, formula intakes should be controlled and various supplemental foods besides commercially powdered baby food should be appropriately provided.

• 한국염색가공학회지
• /
• 제18권5호
• /
• pp.72-79
• /
• 2006

There are many discrepancies between visually perceived color-difference and that which is quantified from an instrumental measurement when dark color samples are measured in the textile industry. The samples were prepared to represent these dark shades and the values of the instrumental results from conventional color-difference formulae(CIELAB, CMC, BFD II, CIE94, LCD99 and CIEDE2000). Those of visual assessment were compared. The experimental results show that the CIELAB formula gives the best performance over other formulae, and the CIEDE2000 formula for the color-difference according to chroma presents the worst performance. Therefore, we can say that the problems in color matching of dark shades are caused by imperfect formula, because the results obtained from a color-difference formulae are different and the CMC which is used as a standard color-difference formula in the textile industry is not correct. So, a revised color-difference formula is proposed in this study, to account for these problems.

• 한국환경과학회지
• /
• 제7권5호
• /
• pp.581-590
• /
• 1998

This st at the development of the adequate sediment yield formulas in Wi-Stream basin ; IHP representative basin in Korea. As a result of applying outstanding sediment yield formulas among the existing formulas, it is analyzed that including the Engelund ＆ Hansen formula, Yang formula is proper to the Wi-Stream basin. And as a result of sensitivity analysis to the sediment parameters it is analyzed that Rijn and Actors ＆ White formula is more sensible than any other formulas which has been applied the velocity and depth among the parameters. Also, Engelund ＆ Hansen and Yang formula is less sensible than any other formulas. In Wi-Stream basin, it is analyzed that Yang and Engelund ＆ Hansen formula is the most suitable sediment yield formula in this study. But because the existing formulas had been developed in foreign countries and applied the foreign natural livers and reservoirs, it makes careful use of Korean alluvial river and hoped that it will be developed the most adequate formula in Wi-Stream basin.

• 한국지반환경공학회 논문집
• /
• 제17권7호
• /
• pp.27-33
• /
• 2016

This study expanded Terzaghi arching formula, which assumed a vertical surface as a sliding surface, to consider an arbitrarily inclined surface as a sliding surface and examined the effect of a sliding surface. This study firstly developed a formula to expand the existing Terzaghi arching formula to consider an inclined surface as well as a vertical surface as a sliding surface under the downward movement of a trap door. Using the expanded formula, the effect of excavation, ground, and surcharge conditions on a vertical stress was examined and the results were compared with them from Terzaghi arching formula. The comparison indicated that the induced vertical stress was highly affected by the angle of an inclined sliding surface and the degree of influence depended on the excavation, ground, and surcharge conditions. It is expected that the results from this study would provide a better understanding of various arching phenomenon in the future.

• 한국식품과학회지
• /
• 제38권1호
• /
• pp.75-81
• /
• 2006

한약재 및 천연 propolis를 직접 음식으로 이용하여 재료과학화 및 저장성 향상을 통하여 돼지고기용 기능성 한방양념소스 개발을 위한 기초 자료로서 품질특성을 규명 하고자 하였다. 한약재 추출조건 및 특성에 따라 기존 양념소스(formula A), 표준화된 양념소스로 propolis를 첨가한 것(formula B), propolis를 첨가하지 않는 것(formula C)으로 제조하였으며, 저장조건은 20일 동안 $4{\pm}1^{\circ}C$에서 실시하였다. 저장기간이 증가함에 따라 한방양념 돼지고기의 pH의 변화는 대체로 비슷한 경향으로 증가하였으나 formula B가 약간 우수하였으며 각 formula 간의 큰 변화는 보이지 않았다. 저장기간별 품질을 평가하는데 pH 보다는 총균수 및 대장균군수 변화가 보다 예민한 지표로서 작용하였다. 육제품의 신선도를 평가하는데 지표가 되고 있는 POV와 TBA가는 저장기간이 증가할수록 증가하는 경향을 보여 propolis를 첨가한 formula B에서 다른 formula 보다 현저하게 감소하여 지질산화 효과를 나타냈다. VBN값도 formula B가 formula A와 C 보다 낮은 수준으로 증가하여 propolis의 단백질 분해억제 효과를 나타냈다. 관능적 특성을 조사한 결과 각 formula별로 유의성은 없었으나 formula B군에서 특유의 향이 어우러져 부드러운 질감과 독특한 향취가 느껴졌다는 의견이 관능평가표 참고란을 통해 알 수 있었다. 이상의 결괴를 종합해 보면, 한방양념돼지고기의 품질특성은 전체적으로 formula B > formula C > formula A순으로 나타났다. 그러므로 한약재 및 propolis 첨가가 저장기간을 연장하고 식품의 보존제로서의 가치를 부여해 줄 수 있는 가능성을 보여주었다.

• 대한수학회지
• /
• 제38권6호
• /
• pp.1235-1243
• /
• 2001

We obtain bounds relating to Eulers formula for the case of a function with higher-order convexity properties. These are used to derive estimates of the error involved in the use of the trapezoidal formula for integrating such a function.

• Kyungpook Mathematical Journal
• /
• 제47권4호
• /
• pp.529-548
• /
• 2007

The purpose of this article is to find a relation between the finite difference method and the boundary element method, and propose a new approach deriving a discrete approximation formula as like that of the finite difference method for harmonic functions. We develop a discrete approximation formula on a uniform grid based on the boundary integral formulations. We consider three different boundary integral formulations and derive one discrete approximation formula on the uniform grid for the harmonic function. We show that the proposed discrete approximation formula has the same computational molecules with that of the finite difference formula for the Laplace operator ${\nabla}^2$.

• 한국농공학회지
• /
• 제38권2호
• /
• pp.108-122
• /
• 1996

This study was to introduced estimation model for optimum probabilistic rainfall intensity on hydrological area. Originally, probabilistic rainfall intensity formula have been characterized different coefficient of formula and model following watersheds. But recently in korea rainfall intensity formula does not use unionize applyment standard between administration and district. And mingle use planning formula with not assumption model. Following the number of year hydrological duration adjust areal index. But, with adjusting formula applyment was without systematic conduct. This study perceive the point as following : 1) Use method of excess probability of Iwai to calculate survey rainfall intensity value. 2) And, use method of least squares to calculate areal coefficient for a unit of 157 rain gauge station. And, use areal coefficient was introduced new probabilistic rainfall intensity formula for each rain gauge station. 3) And, use new probabilistic rainfall intensity formula to adjust a unit of fourteen duration-a unit of fifteen year probabilistic rainfall intensity. 4) The above survey value compared with adjustment value. And use three theory of error(absolute mean error, squares mean error, relative error ratio) to choice optimum probabilistic rainfall intensity formula for a unit of 157 rain gauge station.