• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.111-125
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• 2013

In this paper, we consider a continuous time risk model involving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim and the occurrence of by-claim may be delayed depending on associated main claim amount. Using Rouch$\acute{e}$'s theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model from an integro-differential equations system. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit formula for the survival probability. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.524-529
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• 1989

In this paper, an approximate sojourn time distribution is obtained for cyclic service systems. We consider symmetric and limited service systems in which each queue has an infinite capacity. The combined service time is defined which consists of the frame service time and server waiting time that is approximated by two cases of the uniform and exponential distributions. The approximate sojourn time distribution is obtained from the Pollaczek-Khinchine formula where the combined service time is used for the service time in the M/G/I model. And some numerical examples are given to validate the suggested approximate analysis.

• Proceedings of the KSMRM Conference
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• 2001.11a
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• pp.116-116
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• 2001

Purpose： PRESS is one of the representative sequences in MRS, but still, we do not have the formul describing the steady state magnetization of it. So, we derive the equation of th magnetization as a function of the echo time and the repetition time, and compare it wit phantom experiments. Method： PRESS consists of three 180 pulses and the additional crusher gradients whic destroy the unwanted coherences of the magnetization. Using the simple vector model, w derive a formula which describes the behaviour of the magnetization In PRESS and compa the results with the phantom experiment. Also, we explore the results of the T1 from STEAM, PRESS and the simple exponential.

• Journal of Advanced Marine Engineering and Technology
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• v.14 no.4
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• pp.46-56
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• 1990

Stress analysis of axi-symetric body with non-symetric loading and non-symetric given displacements is investigated in this paper using the finite element method. As the non-symetric load and non-symetric given displacements of axi-symetric body are generally periodic functions of angle .theta., the nodal forces and nodal displacements can be expanded in cosine and sine series, that is, Fourier series. Furthermore, using Euler's formula, the cosine and sine series can be converted into exponential series and it is prooved that the related calculus become more clear. Substituting the nodal displacements expanded in Fourier series into the strain components of cylindrical coordinates system, the element strains are expressed in series form and by the principal of virtual work, the element stiffness martix and element load vector are obtained for each order. It is also showed that if the non-symetric loads are even or odd functions of angle ${\theta}$ the stiffness matrix and load vector of the system are composed with only real numbers and relatively small capacity fo computer memory is enough for calculation.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2000.11a
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• pp.135-142
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• 2000

The adjusting parameter set which enable control systems to locate on stability limit can be derived from theoretical or trial methods for an existing real system. The data from the results are much available to keep a system in the Proper stability condition even to site engineers who are inexperienced in the control system. In this paper, a general one loop control system was adopted for a model system the process of which was assumed to consist of a time-delay element and a first order-lag element in series. After obtaining the corresponding parameter set for the model system by mathematical procedures, their loci on the parameter space was taken according to frequency change. The parameter set loci of stability limit showed unique pattern, and particularity , the curves on the Kg-Ti parameter space were able to be generalized in the form of, an unique 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.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1497-1530
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• 2016

External barrier options are two-asset options with stochastic variables where the payoff depends on one underlying asset and the barrier depends on another state variable. The barrier state variable determines whether the option is knocked in or out when the value of the variable is above or below some prescribed barrier level. This paper derives the explicit analytic solution of the chained option with an external single or double barrier by utilizing the probabilistic methods - the reflection principle and the change of measure. Before we do this, we examine the closed-form solution of the external barrier option with a single or double-curved barrier using the methods of image and double Mellin transforms. The exact solution of the external barrier option price enables us to obtain the pricing formula of the chained option with the external barrier more easily.

• Journal of Magnetics
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• v.8 no.2
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• pp.79-84
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• 2003

Finite element analysis showed that strong magnetic fields were distributed around the arc furnace where the strongest magnetic fields were generated around the three phase cables. The second and third strongest fields near the arc furnace were found to be generated around the electrodes and the mast-arms, respectively. The generated field intensities were greatly influenced by the mast arm structure of the arc furnace as well as the phase differences and operation currents of the supplied power, Magnetic field decay patterns around the arc furnace could be smoothly fitted by this equation of exponential formula, H=H$0_$+Ae$^{\frac{r}{t}}$. These results revealed that magnetic field intensities around the arc furnace could be estimated at any 3-dimensional position using finite element method (FEM).

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.33 no.6
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• pp.257-264
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• 2021

This study established a numerical model capable of calculating the wave overtopping rate of coastal structures by nonlinear irregular waves using the FUNWAVE-TVD model, a fully nonlinear Boussinesq equation model. Here, a numerical model was established by coding the mean value approach equations of EurOtop (2018) and empirical formula by Goda (2009), and adding them as subroutines of the FUNWAVE-TVD model. The verification of the model was performed by numerically calculating the wave overtopping rate of nonlinear irregular waves on vertical wall structures and comparing them with the experimental results presented in EurOtop (2018). As a result of the verification, the numerical calculation result according to the EurOtop equation of this model was very well matched with the experimental result in all relative freeboard (R_c/H_mo) range under non-impulsive wave conditions, and the numerical calculation result of empirical formula was evaluated slightly smaller than the experimental result in R_c/H_mo < 0.8 and slightly larger than the experimental result in R_c/H_mo > 0.8. The results of this model were well represented in both the exponential curve and the power curve under impulsive wave conditions. Therefore, it was confirmed that this numerical model can simulate the wave overtopping rate caused by nonlinear irregular waves in an vertical wall structure.

• Journal of The Korean Society of Agricultural Engineers
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• v.62 no.1
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• pp.95-104
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• 2020

The purpose of this study is to develop a pipe type soil sampler that can easily collect soil cross section servey and soil samples to conduct ecological environment surveys while minimizing ecological disturbance in the area subject to soil survey. Furthermore, this study develop the exponential type estimation specific weight formula (ESWF) that uses pipe type soil sampler to easily carry out soil cross section survey and soil sample while estimating the specific weight of the area using water content and soil sample length variation ratio (SLVRs) and to obtain apparent specific gravity, hardness, and max. porosity which are used as growth of corps and ecological environment index. The calibration results of ESWF showed a high degree of significance, with NSE for actual specific weight (γ₀) and calibration estimation specific weight (γ_ec) 0.95, R² for 0.954, and RMSE for 0.051. The verification results of ESWF showed a high significance, with NSE for actual specific weight (γ₀) and verification estimation specific weight (γ_ev) 0.881, R² for 0.978, and RMSE for 0.055.

• Journal of the Korean GEO-environmental Society
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• v.12 no.1
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• pp.5-12
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• 2011

In this study, correlation between measured deformation modulus using pressuremeter and RMR value conducted in 10 sites is analyzed, and applicability of the conventional empirical formulas to the rock masses in Korea are analyzed, It is found that if RMR is below 40, the correlation between deformation modulus and RMR accords Kim Gyo-won's formula and Aydan, Serafim and Pereira's one well, but if the RMR exceeds 40, the correlation was lower than those from the formula. Such results may be attribute to the fact that during classification of RMR, scores are weighed relatively more in joint conditions and apertures than such highly correlational items as uniaxial compression strength or RQD, and RMR would not be evaluated qualitatively due to different weathering degrees and rock mass types as well as engineers' personal errors. Sandstone among sedimentary rocks are quite well accord with suggested equation, but correlation of other rocks are due to large variance. In this study, correlation expressions of various rocks are proposed as the function of exponential based on the field test data.