• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1115-1132
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• 1999

We consider a supercritical multitype age dependent branching process. We define a stochastic process Zf(t) which is a functional of the empirical age distribution. When the limit of the expectation of this functional vanishes we4 find some sufficient conditions for the asymptotic normality of the mean of f with respect to the empirical age distribution at time t.

• The Pure and Applied Mathematics
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• v.1 no.1
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• pp.19-24
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• 1994

Let P be a probability measure on the real line with Lebesque-density f. The usual estimator of the distribution function (≡df) of P for the sample $\chi$$_1$,…, $\chi$$\_$n/ is the empirical df: F$\_$n/(t)=(equation omitted). But this estimator does not take into account the smoothness of F, that is, the existence of a density f. Therefore, one should expect that an estimator which is better adapted to this situation beats the empirical df with respect to a reasonable measure of performance.(omitted)

• Transactions of Materials Processing
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• v.8 no.5
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• pp.520-526
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• 1999

In this study a practical formula based on the experime수 랙 the estimation of load in the non-circular tube extrusion with the mandrel is proposed by using the effective extrusion ratio. Through some experiments for the several shaped sections, the coefficients of the empirical equation are determined by ticine as a model material at room temperature. The proposed empirical formula for the estimation of extrusion load will be applicable to the non-steady state as well as steady state for the extrusion of various shaped tubes from hollow billets.

• Geotechnical Engineering
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• v.6 no.3
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• pp.5-12
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• 1990

In this paper, ground vibration and other properties measurements were conducted to deter mine empirical equation based on careful test blasting with crawler drill(diameter 70-75mm). The empirical euqations for ground vibration are obtained as follows where V is peak particle velocity in cm 1 sec, D is distance in m and W is maximum charge weight per delay in kg

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.1-10
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• 1999

Table of the empirical quantiles for the well known Shapiro-Francia W' goodness of fit statistic is produced which is more accurate than the existing ones. Prediction equation for the quantiles of W' statistic for sample sizes 30 or more we developed. The process of computing the expected values for the standard normal variate is discussed. This work is intended to make the Shapiro-Francia W' statistic more accessible to the practitioner.

• Water for future
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• v.15 no.3
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• pp.37-47
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• 1982

In the past, the design flow of the urban storm drainage systems has been used largely on a basis of empirical and experience, and the rational formula one of empirical method has been widely used for our country, as well as world wide. But the empirical method has insufficient factor because minimal consideration is given to the relationship of the parameters in the equation to the processes being considered, and considerable use of experience and judgment in setting values to the coefficients in the equation is made. The postcomputer era of hydrology has brought an acceleration development of mathematical methods, thus mathematical models are methods which will greatly increase our understanding in hydrology. On this study, a simple mathematical model of urban presented by British Road Research Laboratory is tested on urban watersheds in Ju An Ju Gong Apartment. The basin is located in Kan Seog Dong, Inchon. The model produces a runoff hydrograph by applying rain all to only the directly connected impervious area of the basin. To apply this model the basin is divided into contributing areas or subbasins. With this information the time area for contributing is derived. The rainfall hyetograph to design storm for the basin flow has been obtained by determination of total rainfall and the temporal distribution of that rainfall determined on the basis of Huff's method form historical rainfall data of the basin. The inflows from several subbaisns are successively routed down the network of reaches from the upstream end to the outlet. A simple storage routing technique is used which involves the use of the Manning equation to compute the stage discharge curve for the cross-section in question. To apply the model to a basin, the pattern of impervious areas must be known in detail, as well as the slopes and sizes of all surface and subsurface drains.

• Journal of Astronomy and Space Sciences
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• v.31 no.4
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• pp.303-309
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• 2014

The Earth's outer radiation belt often suffers from drastic changes in the electron fluxes. Since the electrons can be a potential threat to satellites, efforts have long been made to model and predict electron flux variations. In this paper, we describe a prediction model for the outer belt electrons that we have recently developed at Chungbuk National University. The model is based on a one-dimensional radial diffusion equation with observationally determined specifications of a few major ingredients in the following way. First, the boundary condition of the outer edge of the outer belt is specified by empirical functions that we determine using the THEMIS satellite observations of energetic electrons near the boundary. Second, the plasmapause locations are specified by empirical functions that we determine using the electron density data of THEMIS. Third, the model incorporates the local acceleration effect by chorus waves into the one-dimensional radial diffusion equation. We determine this chorus acceleration effect by first obtaining an empirical formula of chorus intensity as a function of drift shell parameter $L^*$, incorporating it as a source term in the one-dimensional diffusion equation, and lastly calibrating the term to best agree with observations of a certain interval. We present a comparison of the model run results with and without the chorus acceleration effect, demonstrating that the chorus effect has been incorporated into the model to a reasonable degree.

• Journal of the Korean Geotechnical Society
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• v.32 no.9
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• pp.5-16
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• 2016

New PHC piles, where short steel pipes are attached to the pile toe, are developed to increase the base load capacity of bored pre-cast piles embedded in weathered rock. In this study, new bored pre-cast piles using the new PHC piles are installed at 7 test sites with different soil conditions, and static and dynamic pile load tests are performed to investigate quantitative characteristics on the base load capacity of new bored pre-cast piles. In addition, based on the static pile load test results, a new empirical equation for estimating the base load capacity of new bored pre-cast piles is proposed. A comparison between predicted and measured base load capacities shows that the proposed empirical equation produces conservative predictions for the new bored pre-cast piles. However, the existing design criterion significantly underestimates the base load capacity of new bored pre-cast piles.

• Journal of the Korean Geotechnical Society
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• v.26 no.8
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• pp.59-66
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• 2010

In this study, an applicability by using the FEM was investigated for the prediction of both the depth of improvement and the vibration effect when dynamic compaction method is applied. The region was modelled by the field conditions applying dynamic compaction method and the rigid body force was applied to the dynamic load model. Predicted depth of improvement calculated by the vertical peak particle acceleration was compared and analyzed with an existing empirical equation, and the effect of groundwave by deducing the peak particle velocity from vibration sources was compared and analyzed with the results of another existing empirical equation. The results showed that the prediction of the depth of improvement has similar tendency to practice, and the vibration effect has some differences in a particular section from existing equation, but it could predict the safety distance to some degree. The analyzed results are expected to be basic data for the development of reliability of dynamic compaction design with existing empirical method.

• Journal of Korean Society on Water Environment
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• v.23 no.6
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• pp.913-919
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• 2007

This study was conducted to develop a model equation to estimate the delivered point and nonpoint pollutant loads, which are critical factor to determine the water quality of watersheds. The model equation was developed by considering various factors such as biological removal and delivered distance of pollutants, basin shape and geomorphic runoff condition. The parameters for the model equation were estimated in 3 periods, which are October to March, April to June, and July to September. As a parameter, ${\alpha}_p$, ${\alpha}_n$, ${\beta}$, a and b for $BOD_5$-delivered pollutant loads were estimated to be 0.010~0.0155, 0.051, -0.033, 0.018~0.050 and 0.93, respectively. For T-N, ${\alpha}_p$, ${\alpha}_n$, ${\beta}$ a and b were estimated to be 0.0060~0.0140, 0.014, -0.02, 0.044~0.079 and 0.93, respectively. The same parameters for T-P were estimated to be 0.0160, 0.014, -0.0250, 0.015 and 1.21, respectively. The relationship, $E^2$ (Model efficiency), between observed and calculated delivered pollutant loads showed 0.65 for $BOD_5$, 0.81 for T-N, and 0.66 for T-P, respectively. Consequently, the model equation is effective to estimate delivered pollutant loads for TMDL.