• Title/Summary/Keyword: summation formula

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Theoretical Prediction of Vertical Motion of Planing Monohull in Regular Head Waves - Improvement of Zarnick's Nonlinear Strip Method (선수 규칙파 중 단동 활주선의 연직면 거동 추정 - Zarnick 비선형 스트립 방법의 개선)

  • Zhang, Yang;Yum, Deuk-Joon;Kim, Dong-Jin
    • Journal of Ocean Engineering and Technology
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    • v.29 no.3
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    • pp.217-223
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    • 2015
  • In order to predict the motions of a planing hull in waves, it is necessary to accurately estimate the force components acting on the hull such as the hydrodynamic force, buoyancy, and friction, as well as the wave exciting force. In particular, based on strip theory, hydrodynamic forces can be estimated by the summation of the forces acting on each cross-section of the hull. A non-linear strip method for planing hulls was mathematically developed by Zarnick, and his formula has been used to predict the vertical motions of prismatic planing hulls in regular waves. In this study, several improvements were added to Zarnick's formula to predict the vertical motions of warped planing hulls. Based on calm water model test results, the buoyancy force and moment correction coefficients were modified. Further improvements were made in the pile-up correction. Pile-up correction factors were changed according to variations of the deadrise angles using the results found in previous research. Using the same hull form, captive model tests were carried out in other recent research, and the results were compared with the present calculation results. The comparison showed reasonably good agreements between the model tests and present calculations.

Fast computation method for the voltage-current analysis on the rectangular power-ground plane (직사각형의 전력-접지층에 대한 전압전류 특성해석을 위한 빠른 계산방법)

  • Suh, Young-Suk
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.9 no.1
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    • pp.140-145
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    • 2005
  • The existing analytical expression for the voltage between the power and ground plane consist of metal-dielectric-metal board is expressed in the two dimensional infinite series. To reduce the computation time, the two dimensional infinite series is converted to the one dimensional infinite series using the summation formula of Fourier series. We applied these equations to the analysis of voltage between the $9‘{\times}4'$ size power-ground plane. The derived one dimensional infinite series shows the more rapid convergency and the more accurate result than the two dimensional infinite series. This equation can be applied to the power-ground plane analysis which needs a lot of the repeating computation.

The Bias Error due to Windows for the Wigner-Ville Distribution Estimation (위그너-빌 분포함수의 계산시 창문함수의 적용에 의한 바이어스 오차)

  • 박연규;김양한
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 1995.10a
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    • pp.80-85
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    • 1995
  • Too see the effects of finite record on the estimation of WVD in practice, a window which has time varying length is examined. Its length increases linearly with time in the first half of the record, and decreases from the center of the record. The bias error due to this window decreases inversely proportionally to the window length as time increases in the first half. In the second half, the bias error increases and the resolution decreases as time increases. The bias error due to the smoothing of WVD, which is obtained by two-dimensional convolution of the true WVD and the smoothing window, which has fixed lengths along time and frequency axes, is derived for arbitrary smoothing window function. In the case of using a Gaussian window as a smoothing window, the bias error is found to be expressed as an infinite summation of differential operators. It is demonstrated that the derived formula is well applicable to the continuous WVD, but when WVD has some discontinuities, it shows the trend of the error. This is a consequence of the assumption of the derivation, that is the continuity of WVD. For windows other than Gaussian window, the derived equation is shown to be well applicable for the prediction of the bias error.

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The Origin of Newton's Generalized Binomial Theorem (뉴턴의 일반화된 이항정리의 기원)

  • Koh, Youngmee;Ree, Sangwook
    • Journal for History of Mathematics
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    • v.27 no.2
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    • pp.127-138
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    • 2014
  • In this paper we investigate how Newton discovered the generalized binomial theorem. Newton's binomial theorem, or binomial series can be found in Calculus text books as a special case of Taylor series. It can also be understood as a formal power series which was first conceived by Euler if convergence does not matter much. Discovered before Taylor or Euler, Newton's binomial theorem must have a good explanation of its birth and validity. Newton learned the interpolation method from Wallis' famous book ${\ll}$Arithmetica Infinitorum${\gg}$ and employed it to get the theorem. The interpolation method, which Wallis devised to find the areas under a family of curves, was by nature arithmetrical but not geometrical. Newton himself used the method as a way of finding areas under curves. He noticed certain patterns hidden in the integer binomial sequence appeared in relation with curves and then applied them to rationals, finally obtained the generalized binomial sequence and the generalized binomial theorem.

Development of Tree Stem Weight Equations for Larix kaempferi in Central Region of South Korea (중부지역 일본잎갈나무의 수간중량 추정식 개발)

  • Ko, Chi-Ung;Son, Yeong-Mo;Kang, Jin-Taek;Kim, Dong-Geun
    • Journal of Korean Society of Forest Science
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    • v.107 no.2
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    • pp.184-192
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    • 2018
  • In this study was implemented to develop tree stem weight prediction equation of Larix kaempferi in central region by selecting a standard site, taking into account of diameter and position of the local trees. Fifty five sample trees were selected in total. By utilizing actual data of the sample trees, 11 models were compared and analyzed in order to estimate four different kinds of weights which include fresh weight, ovendry outside bark weight, ovendry inside bark weight and merchantable weight. As to estimate its weight, the study has classified its model according to three parameters: DBH, DBH and height, and volume. The optimal model was chosen by comparing the performance of model using the fit index and standard error of estimate and residual distribution. As a result, the formula utilizing DBH (Variable 1) is $W=a+bD+cD^2$ (3) and its fit index was 90~92%. The formula for DBH and height (Variable 2) is $W=aD^bH^C$ (8) and its fit index was 97~98%. In summation, Variable 2 model showed higher fitness than Variable 1 model. Moreover, fit index of formula for total volume and merchantable volume (W=aV) showed high rate of 98~99%, as well as resulting 7.7-17.5 with SEE and 8.0-10.0 with CV(%) which lead to predominately high fitness in conclusion. This study is expected to provide information on weights for single trees and furthermore, to be used as a basic study for weight of stand unit and biomass estimation equations.

Minimum Weight Design of Oil Tankers Considering Tank Arrangement (Tank 배치를 고려한 유조선의 최소 중량 설계)

  • Jang, Chang-Doo;Na, Seung-Soo
    • Journal of the Society of Naval Architects of Korea
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    • v.33 no.4
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    • pp.97-105
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    • 1996
  • For the minimum weight design of ship structures it is desirable that tank arrangement is predetermined to obtain the minimum weight and then structural arrangement and scanting of each murder is determined to obtain the minimum weight within the given tank arrangement. To carry out the tank arrangement to give minimum weight a minimum weight design program which covers whole ship structures is developed by the combination of minimum weight design program of longitudinal members by classification rules and minimum weight design program of transverse members by generalized slope deflection method which were developed by the authors. The hullweight is estimated by summation of the weight of cargo hold part and the weight except cargo hold part which can be estimated by the empirical formula. In this study, the variation of hullweight is shown with the number of tank, the number of web and the location of longitudinal bulkhead. For the application of actual design alternative designs of tank arrangement which satisfy MARPOL regulation are determined. And several minimum weight designs of whole ship structures are carried out to obtain the tank arrangement which gives minimum weight and then the hullweight is compared with that of existing ship.

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Compound effects of operating parameters on burnup credit criticality analysis in boiling water reactor spent fuel assemblies

  • Wu, Shang-Chien;Chao, Der-Sheng;Liang, Jenq-Horng
    • Nuclear Engineering and Technology
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    • v.50 no.1
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    • pp.18-24
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    • 2018
  • This study proposes a new method of analyzing the burnup credit in boiling water reactor spent fuel assemblies against various operating parameters. The operating parameters under investigation include fuel temperature, axial burnup profile, axial moderator density profile, and control blade usage. In particular, the effects of variations in one and two operating parameters on the curve of effective multiplication factor ($k_{eff}$) versus burnup (B) are, respectively, the so-called single and compound effects. All the calculations were performed using SCALE 6.1 together with the Evaluated Nuclear Data Files, part B (ENDF/B)-VII238-neutron energy group data library. Furthermore, two geometrical models were established based on the General Electric (GE)14 $10{\times}10$ boiling water reactor fuel assembly and the Generic Burnup-Credit (GBC)-68 storage cask. The results revealed that the curves of $k_{eff}$ versus B, due to single and compound effects, can be approximated using a first degree polynomial of B. However, the reactivity deviation (or changes of $k_{eff}$, ${\Delta}k$) in some compound effects was not a summation of the all ${\Delta}k$ resulting from the two associated single effects. This phenomenon is undesirable because it may to some extent affect the precise assessment of burnup credit. In this study, a general formula was thus proposed to express the curves of $k_{eff}$ versus B for both single and compound effects.

Calculation of Unit Hydrograph from Discharge Curve, Determination of Sluice Dimension and Tidal Computation for Determination of the Closure curve (단위유량도와 비수갑문 단면 및 방조제 축조곡선 결정을 위한 조속계산)

  • 최귀열
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.7 no.1
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    • pp.861-876
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    • 1965
  • During my stay in the Netherlands, I have studied the following, primarily in relation to the Mokpo Yong-san project which had been studied by the NEDECO for a feasibility report. 1. Unit hydrograph at Naju There are many ways to make unit hydrograph, but I want explain here to make unit hydrograph from the- actual run of curve at Naju. A discharge curve made from one rain storm depends on rainfall intensity per houre After finriing hydrograph every two hours, we will get two-hour unit hydrograph to devide each ordinate of the two-hour hydrograph by the rainfall intensity. I have used one storm from June 24 to June 26, 1963, recording a rainfall intensity of average 9. 4 mm per hour for 12 hours. If several rain gage stations had already been established in the catchment area. above Naju prior to this storm, I could have gathered accurate data on rainfall intensity throughout the catchment area. As it was, I used I the automatic rain gage record of the Mokpo I moteorological station to determine the rainfall lntensity. In order. to develop the unit ~Ydrograph at Naju, I subtracted the basic flow from the total runoff flow. I also tried to keed the difference between the calculated discharge amount and the measured discharge less than 1O~ The discharge period. of an unit graph depends on the length of the catchment area. 2. Determination of sluice dimension Acoording to principles of design presently used in our country, a one-day storm with a frequency of 20 years must be discharged in 8 hours. These design criteria are not adequate, and several dams have washed out in the past years. The design of the spillway and sluice dimensions must be based on the maximun peak discharge flowing into the reservoir to avoid crop and structure damages. The total flow into the reservoir is the summation of flow described by the Mokpo hydrograph, the basic flow from all the catchment areas and the rainfall on the reservoir area. To calculate the amount of water discharged through the sluiceCper half hour), the average head during that interval must be known. This can be calculated from the known water level outside the sluiceCdetermined by the tide) and from an estimated water level inside the reservoir at the end of each time interval. The total amount of water discharged through the sluice can be calculated from this average head, the time interval and the cross-sectional area of' the sluice. From the inflow into the .reservoir and the outflow through the sluice gates I calculated the change in the volume of water stored in the reservoir at half-hour intervals. From the stored volume of water and the known storage capacity of the reservoir, I was able to calculate the water level in the reservoir. The Calculated water level in the reservoir must be the same as the estimated water level. Mean stand tide will be adequate to use for determining the sluice dimension because spring tide is worse case and neap tide is best condition for the I result of the calculatio 3. Tidal computation for determination of the closure curve. During the construction of a dam, whether by building up of a succession of horizontael layers or by building in from both sides, the velocity of the water flowinii through the closing gapwill increase, because of the gradual decrease in the cross sectional area of the gap. 1 calculated the . velocities in the closing gap during flood and ebb for the first mentioned method of construction until the cross-sectional area has been reduced to about 25% of the original area, the change in tidal movement within the reservoir being negligible. Up to that point, the increase of the velocity is more or less hyperbolic. During the closing of the last 25 % of the gap, less water can flow out of the reservoir. This causes a rise of the mean water level of the reservoir. The difference in hydraulic head is then no longer negligible and must be taken into account. When, during the course of construction. the submerged weir become a free weir the critical flow occurs. The critical flow is that point, during either ebb or flood, at which the velocity reaches a maximum. When the dam is raised further. the velocity decreases because of the decrease\ulcorner in the height of the water above the weir. The calculation of the currents and velocities for a stage in the closure of the final gap is done in the following manner; Using an average tide with a neglible daily quantity, I estimated the water level on the pustream side of. the dam (inner water level). I determined the current through the gap for each hour by multiplying the storage area by the increment of the rise in water level. The velocity at a given moment can be determined from the calcalated current in m3/sec, and the cross-sectional area at that moment. At the same time from the difference between inner water level and tidal level (outer water level) the velocity can be calculated with the formula $h= \frac{V^2}{2g}$ and must be equal to the velocity detertnined from the current. If there is a difference in velocity, a new estimate of the inner water level must be made and entire procedure should be repeated. When the higher water level is equal to or more than 2/3 times the difference between the lower water level and the crest of the dam, we speak of a "free weir." The flow over the weir is then dependent upon the higher water level and not on the difference between high and low water levels. When the weir is "submerged", that is, the higher water level is less than 2/3 times the difference between the lower water and the crest of the dam, the difference between the high and low levels being decisive. The free weir normally occurs first during ebb, and is due to. the fact that mean level in the estuary is higher than the mean level of . the tide in building dams with barges the maximum velocity in the closing gap may not be more than 3m/sec. As the maximum velocities are higher than this limit we must use other construction methods in closing the gap. This can be done by dump-cars from each side or by using a cable way.e or by using a cable way.

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