• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.81-87
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• 2012

A continuous time risk model is considered, where the premium rate is constant and the claims form a compound Poisson process. We assume that an injection is made, which is an immediate increase of the surplus up to level u > 0 (initial level), when the level of the surplus goes below ${\tau}$(0 < ${\tau}$ < u). We derive the formula of the ruin probability of the surplus by establishing an integro-differential equation and show that an explicit formula for the ruin probability can be obtained when the amounts of claims independently follow an exponential distribution.

• Nuclear Engineering and Technology
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• v.43 no.6
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• pp.531-546
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• 2011

The backward differentiation formula (BDF) method is applied to a three-dimensional reactor kinetics calculation for efficient yet accurate transient analysis with adaptive time step control. The coarse mesh finite difference (CMFD) formulation is used for an efficient implementation of the BDF method that does not require excessive memory to store old information from previous time steps. An iterative scheme to update the nodal coupling coefficients through higher order local nodal solutions is established in order to make it possible to store only node average fluxes of the previous five time points. An adaptive time step control method is derived using two order solutions, the fifth and the fourth order BDF solutions, which provide an estimate of the solution error at the current time point. The performance of the BDF- and CMFD-based spatial kinetics calculation and the adaptive time step control scheme is examined with the NEACRP control rod ejection and rod withdrawal benchmark problems. The accuracy is first assessed by comparing the BDF-based results with those of the Crank-Nicholson method with an exponential transform. The effectiveness of the adaptive time step control is then assessed in terms of the possible computing time reduction in producing sufficiently accurate solutions that meet the desired solution fidelity.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.17 no.12
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• pp.1343-1352
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• 1992

This paper presents a new and easy method to obtain the Fourier transforms of the n-th order cosine-pulses whose maximum amplitudes are uniform. The new method is focused on deriving a formula which is recursively related following their orders and can be well applied to some numerical solutions. On the other hand, this method also offers more compact procedures in view of analytical solutions than the conventional methods because the results are consist of the sum of two functions which are easily calculated. Especially, the formula can be represented as a complete recursion by the separation of coefficients originated by the authors and the resulting difference equation is given by the sum of the original 'sinc' functions shifted by some symmetrical factors and multiplied by some constants. The constants are easily decided from the binomial coefficients and the shifting factors from the corresponding exponential differences in the expansion of $(a+b)^n$.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.27 no.3
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• pp.175-181
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• 2015

In this study, two dimensional wave overtopping tests for vertical wall were performed and overtopping formulas were suggested for impulsive and non-impulsive wave conditions. The test results from this study were compared with those from EurOtop(2007). The wave overtopping formulas were derived and suggested considering the recent research trends, while the existing method used the diagram. The wave overtopping formulas have the form of exponential and power functions using non-dimensional variables for wave overtopping and freeboard heights for non-impulsive and impulsive condition, respectively. The wave overtopping formula and effective parameters for inclined superstructure were also suggested. It is analyzed that the locations of inclined superstructure do not have the significant effects on wave overtopping, that is, the wave overtopping rate were almost same for each locations.

• Korean Journal of Materials Research
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• v.11 no.12
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• pp.1091-1095
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• 2001

Finite element analysis showed that strong magnetic fields were distributed around the arc furnace where the strongest magnetic field was generated around the three phase cables, and followed by the electrodes and the mast arm in decreasing order. Magnetic field decay patterns around the arc furnace could be fitted by introducing exponential formula,$Y=Y_0+Ae^{\frac-{x}{t}}$. These results showed that magnetic field intensities around the arc furnace could be estimated at any 3-dimensional positions using the finite element method (FEM).

• Structural Engineering and Mechanics
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• v.9 no.4
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• pp.375-382
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• 2000

Experimental investigation into the cyclic behaviour of sand plast brick masonry was performed on forty two square panels. The panels were subjected to cyclic uniaxial compression for two cases of loading: normal to bed joint and parallel to bed joint. Experimental data were used to plot the unloading-reloading curves for the entire range of the stress-strain curve. Mathematical expressions to predict the reloading and unloading stress-strain curves at various values of residual strain are proposed. A simple parabola and an exponential type formula are found adequate to model the unloading and reloading curves respectively. The models account for the potential effects of residual strain on these curves. Comparison of test results with the proposed mathematical expression shows good correspondence.

• Structural Engineering and Mechanics
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• v.11 no.5
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• pp.565-574
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• 2001

Experimental investigation into the behaviour of half-scale brick masonry panels were conducted under cyclic loading normal to the bed joint and parallel to the bed joint. For each cycle, full reloading was performed with the cycle peaks coinciding approximately with the envelope curve. Unloading, however, was carried out fully to zero stress level and partially to two different stress levels of 25 percent and 50 percent of peak stress. Stability point limit exhibits a unique stress-strain curve for full unloading but it could not be established for partial unloading. Common point limit was established for all unloading-reloading patterns considered, but its location depends on the stress level at which unloading is carried to. Common point curves were found to follow an exponential formula, while residual strains versus envelope strains can be expressed by a polynomial function of a single term. The relation between residual strain and envelope strain can be used to determine the stress level at which deterioration due to cyclic loading began.

• Journal of Advanced Marine Engineering and Technology
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• v.25 no.2
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• pp.351-356
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• 2001

In this paper, a general one-loop control system was assumed as a model system which has a time-delay element connected with a first order-lag element in series. After the corresponding parameter set causing stability limit condition for the model system was obtained by mathematical procedures, their loci on the parameter space was taken according of frequency change,. The parameter set loci of stability limit showed a specific pattern, and particularly the curves on the Kp-Ti parameter space were able to generalized in the form of an exponential formula. These properties were also compared with the results taken from experimental procedures by Nyquist response method and Ziegler & Nichols method on the time domain, and both results were confirmed to be nearly same.

• Magazine of the Korean Society of Agricultural Engineers
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• v.39 no.2
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• pp.134-142
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• 1997

This study was performed to evaluate the drain runoff characteristics from one paddy field, and to provide the basic data required for the determination of flood discharge and unit drainage water for drainage improvement and farmland consolidation. For this purpose, under the assumption that drain discharge from paddy field was similar to outflow of reservoir, runoff model based on storage equation was applied to the experimental field, and simulated results were compared to the measured discharge at weir point. To estimate effective storage volume of paddy field with water depth, 4 regression formula were examined such as linear, exponential, power, and combined. From the observed runoff characteristics, it was shown to be 3.3~16.3${\ell}$/sec in weir discharge, 57.2~98% in runoff ratio, and relative error of simulated result was 3.0~39.4%, 8.5 ~56.0 % for peak flow and runoff ratio, respectively. Curve number by SCS method was calculated as mean value of 96.4 using measured rainfall and runoff data, it was considered relatively high because paddy field has generally flooding depth contrary to the upland watershed area.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1149-1161
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• 2017

An ($n_1,\;n_2,\;{\ldots},\;n_k$)-colored permutation is a permutation of $n_1+n_2+{\cdots}+n_k$ in which $1,\;2,\;{\ldots},\;n_1$ have color 1, and $n_1+1,\;n_1+2,\;{\ldots},\;n_1+n_2$ have color 2, and so on. We give a bijective proof of Steinhardt's result: the number of colored permutations with no monochromatic cycles is equal to the number of permutations with no fixed points after reordering the first $n_1$ elements, the next $n_2$ element, and so on, in ascending order. We then find the generating function for colored permutations with no monochromatic cycles. As an application we give a new proof of the well known generating function for colored permutations with no fixed colors, also known as multi-derangements.