• Honam Mathematical Journal
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• v.45 no.3
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• pp.410-417
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• 2023

Suppose that there are 8 abelian varieties defined over a number field K which satisfy a commutative diagram. We show that if we know that three out of four short exact sequences satisfy the rate formula of Tate-Shafarevich groups, then the unknown short exact sequence satisfies the rate formula of Tate-Shafarevich groups, too.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.10
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• pp.148-155
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• 2003

In this paper, based on the concept of solid particles' hovering problem the working formula for the channel design of a Decanter-type centrifuge were derived. The Shields' diagram and its curve-fitting formula were used in determining the criterion of particle size for the sediment. By using these formula the designer can determine the sectional configuration of the channel, such as the liquid depth, the normal pitch of the screw-blade arrangement and the bowl diameter.

• Journal of Korean Society of Water and Wastewater
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• v.19 no.5
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• pp.613-618
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• 2005

In analysis of pipelines or pipe network we calculated the friction loss using Hazen-Williams or Manning formula approximately, or found one by friction coefficient from Moody diagram graphically. The friction coefficient is determined as a function of relative roughness and Reynolds number. But the calculated friction coefficient by Hazen-Williams or Manning formula considered roughness of pipe or velocity of flow. The friction coefficient in Darcy-Weisbach equation was obtained from the Moody diagram. This method is manual and is not exact from reading. This paper is presented numerical solution of Colebrook-White formula including variables of relative roughness and Reynolds number. The suggested subroutine program by an efficient linear iteration scheme can be applied to any pipe network system.

• Journal of the Korean Ceramic Society
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• v.53 no.5
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• pp.535-540
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• 2016

Effects of compositions and sintering conditions on glaze properties are shown in the diagram constructed by using the unity molecular formula (UMF) method in this study. Glossy characteristics of glaze were clearly differentiated by compositional area in the diagram and sintering process. As alumina and silica contents were increased, texture of the glaze became rough and opaque, akin to having been devitrified or underfired. The correlation between glossiness and surface roughness was found to be non-linear and inversely proportionate. Crystalline phases formed in the glaze were also influenced by the compositional area. Due to the high concentration of CaO, anorthite and wollastonite were formed depending on the compositions. Hardness was increased with an increase of alumina and silica concentrations in the glaze.

• Nuclear Engineering and Technology
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• v.53 no.3
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• pp.833-841
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• 2021

During the postulated severe accident of nuclear reactor, eutectic reaction leads to low-temperature melting of fuel cladding and early failure of core structure. In order to model eutectic melting with the moving particle semi-implicit (MPS) method, the eutectic reaction model is developed to simulate the eutectic reaction phenomenon. The coupling of mass diffusion and phase diagram is applied to calculate the eutectic reaction with the uniform temperature. A heat transfer formula is proposed based on the phase diagram to handle the heat release or absorption during the process of eutectic reaction, and it can combine with mass diffusion and phase diagram to describe the eutectic reaction with temperature variation. The heat transfer formula is verified by the one-dimensional melting simulations and the predicted interface position agrees well with the theoretical solution. In order to verify the eutectic reaction models, the eutectic reaction of uranium and iron in two semi-infinite domains is simulated, and the profile of solid thickness decrease over time follows the parabolic law. The modified MPS method is applied to calculate Transient Reactor Test Facility (TREAT) experiment, the penetration rate in the simulations are agreeable with the experiment results. In addition, a hypothetical case based on the TREAT experiment is also conducted to validate the eutectic reaction with temperature variation, the results present continuity with the simulations of TREAT experiment. Thus the improved method is proved to be capable of simulating the eutectic reaction in the severe accident.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.963-974
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• 1995

We formulate central limit theorems for non-linear functionals of stationary Gaussian vector processes with long-range dependence.

• Proceedings of the Korea Water Resources Association Conference
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• 1993.07a
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• pp.467-474
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• 1993

• Nuclear Engineering and Technology
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• v.49 no.4
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• pp.692-699
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• 2017

The determination of the shape and rising velocity of gas bubbles in a liquid pool is of great importance in analyzing the radioactive aerosol emissions from nuclear power plant accidents in terms of the fission product release rate and the pool scrubbing efficiency of radioactive aerosols. This article suggests a simple parameterization for the gas bubble rising velocity as a function of the volume-equivalent bubble diameter; this parameterization does not require prior knowledge of bubble shape. This is more convenient than previously suggested parameterizations because it is given as a single explicit formula. It is also shown that a bubble shape diagram, which is very similar to the Grace's diagram, can be easily generated using the parameterization suggested in this article. Furthermore, the boundaries among the three bubble shape regimes in the $E_o-R_e$ plane and the condition for the bypass of the spheroidal regime can be delineated directly from the parameterization formula. Therefore, the parameterization suggested in this article appears to be useful not only in easily determining the bubble rising velocity (e.g., in postulated severe accident analysis codes) but also in understanding the trend of bubble shape change due to bubble growth.

• Current Research on Agriculture and Life Sciences
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• v.5
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• pp.158-167
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• 1987

The purpose of this study is to inquire and analyse the relation between traveltime (Tc) and watetshed physical characteristics surveyed such as river length (L), Lea, river main slope (s), base length of time area diagram, and storage constant (k). The results obtained in this study are as follows. The average widths of watersheds were with the range from 4.6 kilometers to 16.7 kilometers. The shape factors of main stream ranged from 0.08 to 0.37. The average slopes to main 8tream were within the range of 1.7-5.5 meter per kilometer. The relation between the base length and traveltime from S. C. S. method, Rational method, and RZIHA+KRAVEN method were derived $Tc=0.524{\times}1.35^c$ (r=0.98), $Tc=0.628{\times}1.339^c$, (r=0.98), $Tc=0.667{\times}1.342^c$ (r=0.97). The base length of the time-area diagram (c) for the IUH was derived as $c=0.9(\frac{L.L_{ca}}{\sqrt{s}})^{0.35}$ and correlation coefficient was 0.98 which defined a high significance. The storage constant K, derived in this study was $K=8.32+0.0213{\frac{L}{\sqrt{s}}}$ with correlation coefficient (0.96). The relation between storage Constant and conventional formula were figured out $Tc=0.0003{\times}3.323^k$ (r=0.97). $Tc=0.00045{\times}3.268^k$ (r=0.99) and $Tc=0.0004{\times}3.26^k$ (r=0.963). The base length (c) and storage constant (k) of time-Area Diagram were very important parts that determined traveltime for flood events. In the estimate of travel time for predicting flood volume, the formula of $Tc=0.524{\times}1.35^c$ that would be available to apply the Nak - Dong river watershed area and homogeneous watershed characteristics was found.

• Journal of the Korean Institute of Navigation
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• v.7 no.1
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• pp.33-62
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• 1983

A navigator on bridge needs to know every kinds of motion characteristics of his vessel at sea. Generally when a vessel is completely built, the shipyard makes turning circle diagrams from the results of turing circle tests made during the sea trials for the reference of the vessel's owner. But referring only the data of a turning circle diagram, an officer on bridge can not figure out his vessel's maneuvering characteristics sufficiently, So nowadays the shipyard often adds Z test to turning circle test for more detail references. In this paper the author made Z and turning circle tests at the rudder angles of 15 and and 35 degress separately and in each of the case made a turrning circle diagram from the results of the turning circle test and the esults numerically calculated from mathematical formula made on the base of the maneuvering indices got from the Z test and compared them each other for the purpose of finding the correlations between them. Followings are concluded from the results. An actual turning circle diagram and a calculated one from the results of the Z test at same rudder angle coincides each other well when the center of the calculated circle is transferred by 1.7B toward the direction of the initial turning perpendicularly to the original course and 0.5L toward the direction in parallel with original course in case of the rudder angle of 35 degrees and 1.2B and 0.3L toward each of the above mentioned directions in case of rudder angle of 15 degrees.