• Bulletin of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1131-1138
• /
• 2010

In the present paper, we evaluate an analytic formula as a solution of Susceptible Infective (SI) model problem for communicable disease in which the daily contact rate (C(N)) is supposed to be varied linearly with population size N(t) that is large so that it is considered as a continuous variable of time t. Again, we introduce some Lie group of operators to make an extension of above analytic formula of the determin-istic epidemics model problem. Finally, we discuss some of its particular cases.

• Journal of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1197-1222
• /
• 2010

There is a well-known classical reduction formula by Griffiths and Harris for Littlewood-Richardson coefficients, which reduces one part from each partition. In this article, we consider an extension of the reduction formula reducing two parts from each partition. This extension is a special case of the factorization theorem of Littlewood-Richardson coefficients by King, Tollu, and Toumazet (the KTT theorem). This case of the KTT factorization theorem is of particular interest, because, in this case, the KTT theorem is simply a reduction formula reducing two parts from each partition. A bijective proof using tableaux of this reduction formula is given in this paper while the KTT theorem is proved using hives.

• Communications of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.619-630
• /
• 2018

In this paper, we obtain a (p, q)-extension of the Whittaker function $M_{k,{\mu}}(z)$ together with its integral representations, by using the extended confluent hypergeometric function of the first kind ${\Phi}_{p,q}(b;c;z)$ [recently extended by J. Choi]. Also, we give some of its main properties, namely the summation formula, a transformation formula, a Mellin transform, a differential formula and inequalities. In addition, our extension on Whittaker function finds interesting connection with the Laguerre polynomials.

• Communications of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.705-714
• /
• 2021

The Whittaker function and its diverse extensions have been actively investigated. Here we aim to introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function 𝚽_p,v and investigate some of its formulas such as integral representations, a transformation formula, Mellin transform, and a differential formula. Some special cases of our results are also considered.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.289-294
• /
• 1996

The double Gamma function had been defined and studied by Barnes [4], [5], [6] and others in about 1900, not appearing in the tables of the most well-known special functions, cited in the exercise by Whittaker and Waston [25, pp. 264]. Recently this function has been revived according to the study of determinants of Laplacians [8], [11], [15], [16], [19], [20], [22] and [24]. Shintani [21] also uses this function to prove the classical Kronecker limit formula. Its p-adic analytic extension appeared in a formula of Casson Nogues [7] for the p-adic L-functions at the point 0.

• Journal of Agricultural Extension & Community Development
• /
• v.2 no.1
• /
• pp.1-21
• /
• 1995

This study examines the socioeconomic returns to agricultural research and extension services in Korea, using multivariate time series technique and Akino-Hyami formula. Results find that the socioeconomic returns are quite competitive in case of agricultural research with 44.82% internal rate of return and very high in case of extension services with 207.82% internal rate of return. Agricultural production responds to the agricultural research shock about four years after the shock. The magnitudes of the impacts increase until a peak is reached nine years after the initial expenditures and the impacts declines to a zero level after about twenty years. This lag lengths are consistent to the usual literature on research, which finds lags of seven to thirty years. Agricultural production responds to an agricultural extension shock immediately and declines to a zero level after about four years. Thus, the lag lengths are much shorter than those by research shock.

• Journal of Korea Water Resources Association
• /
• v.49 no.12
• /
• pp.1007-1014
• /
• 2016

The FORGEX (Focused Rainfall Growth Extension) method was developed to estimate rainfall quantiles in the United Kingdom. This method does not need any regional grouping and can estimate rainfall quantiles with relatively long return period. The spatial dependence formula (ln $N_e$) was derived to consider the distance from growth curve of proper population to the distributed network maximum (netmax) data using the UK rainfall data. For this reason, there is an inaccurate problem in rainfall quantiles when this formula is applied in Korea. In this study, the new formula was derived in order to improve such shortcomings using rainfall data of 64 sites from the Korea Meteorological Administration (KMA). A 42-year period (1973~2014) was taken as the reference period from rainfall data, then the formula was derived using three parameters such as rainfall duration, number of site, area of network. Then the new formula was applied to the FORGEX method for regional rainfall frequency analysis. In addition, rainfall quantiles were compared with those from the UK formula. As a result, the new formula shows more accurate results than the UK formula, in which the FORGEX method by the UK formula underestimates rainfall quantiles. Finally, the new improved formula may estimate accurate rainfall quantiles for long return period.

• Food Science and Biotechnology
• /
• v.16 no.4
• /
• pp.590-593
• /
• 2007

The textural properties of doughs mixed with L-ascorbic acid (AA), trypsin hydrolyzed gluten peptide (THGP), and a mixture of AA-THGP were investigated using texture analyzer under the fermentation of the full formula and the freezing process. The full formula dough (FFD) required a shorter mixing time than the flour and water formula dough (FWD). The maximum resistance (Rmax) values of both the unfrozen and frozen doughs were lower for the FFD. The effects of AA and THGP additions were not significant (p<0.01) in FFD, however, they were significant in FWD. The freezing effect was significant (p<0.0001) for FFD, indicating that yeast fermented dough was much more sensitive to damage from freezing, which subsequently affected dough strength. Additions of AA (p=0.0026) and THGP (p=0.0097) had a significant effect on the extensibility (E-value) of unfrozen FWD, where THGP increased and AA decreased the E-value. However, freezing did not significantly effect the extensibilities of FWD (p=0.64) or FFD (p=0.21). The area of FFD was lower than the area of FWD for both the unfrozen and frozen doughs. However, the frozen dough mixed with THGP alone had the largest area overall. The addition of additives did not result in significantly different (p<0.01) areas under the curve, except in the frozen FFD. Freezing caused a statistically significant difference in the area of FWD (p=0.0045).

• Journal of Electrical Engineering and Technology
• /
• v.13 no.6
• /
• pp.2561-2567
• /
• 2018

The extension of DC battery backup time in the DC power supply system of nuclear power plants (NPPs) remains a challenge. The lead-acid battery is the most popular at present. And it is generally the most popular energy storage device. However, extension of backup time requires too much space. The lithium-ion battery has high energy density and advanced gravimetric and volumetric properties. The aim of this paper is development of the sizing formula of stationary lithium-ion batteries. The ongoing research activities and related industrial standards for stationary lithium-ion batteries are reviewed. Then, the lithium-ion battery sizing calculation formular is proposed for the establishment of industrial design standard which is essential for the design of stationary batteries of nuclear power plants. An example of calculating the lithium-ion battery capacity for a medium voltage UPS is presented.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.20 no.3
• /
• pp.277-290
• /
• 2008

In order to apply UTM coordinates conversion in zones larger than $14^{\circ}$ wide, a new conversion formula, based on the 12th expansion of Taylor series, is derived which is shown to be an extension of Thomas' formula(1952). Some examples of coordinate conversion between WGS84 and UTM are presented and convergences of computational results are also tested according to the order of formula. The present conversion formula can be used to make rectangular coordinate grid systems for numerical models to compute long wave propagation such as tide or tsunami around Korea.