• 대한수학회지
• /
• 제50권1호
• /
• pp.111-125
• /
• 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
• /
• 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
• /
• pp.524-529
• /
• 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.

• 대한자기공명의과학회:학술대회논문집
• /
• 대한자기공명의과학회 2001년도 제6차 학술대회 초록집
• /
• pp.116-116
• /
• 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
• /
• 제14권4호
• /
• pp.46-56
• /
• 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.

• 한국마린엔지니어링학회:학술대회논문집
• /
• 한국마린엔지니어링학회 2000년도 추계학술대회 논문집(Proceeding of the KOSME 2000 Autumn Annual Meeting)
• /
• pp.135-142
• /
• 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.

• 대한수학회보
• /
• 제53권5호
• /
• pp.1497-1530
• /
• 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
• /
• 제8권2호
• /
• pp.79-84
• /
• 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).

• 한국해안·해양공학회논문집
• /
• 제33권6호
• /
• pp.257-264
• /
• 2021

본 연구는 완전비선형 Boussinesq 방정식 모델인 FUNWAVE-TVD 모델을 이용하여 비선형 불규칙파에 의한 해안구조물의 월파량을 산정할 수 있는 수치모형을 수립한 것이다. 여기서는 EurOtop(2018)의 월파량 산정 식 및 Goda(2009)의 경험식을 코딩하여 FUNWAVE-TVD 모델의 서브루틴으로 추가하고 수치모형을 수립하였다. 모형의 검증은 직립구조물에 대한 비선형 불규칙파의 월파량을 수치계산하고 EurOtop(2018)에 제시된 실험 결과와 비교하여 수행하였다. EurOtop 식에 의한 수치계산 결과는 비쇄파 조건의 경우 모든 상대여유고(Rc/Hmo) 구간에서 실험결과와 매우 잘 일치하였으며, 경험식에 의한 수치계산 결과는 R_c/H_mo < 0.8 구간에서는 실험 결과보다 과소평가 되었고 R_c/H_mo < 0.8의 구간에서는 실험 결과보다 과대평가 되었다. 쇄파조건의 경우 본 모형의 결과는 R_c/H_mo ≤ 1.35의 exponential curve나 R_c/H_mo > 1.35의 power curve 구간 모두에서 실험 결과를 잘 재현하였다. 따라서 본 수치모형은 직립구조형식의 호안구조물에서 비선형 불규칙파에 의한 월파량을 정도 높게 모의할 수 있음을 확인하였다.

• 한국농공학회논문집
• /
• 제62권1호
• /
• pp.95-104
• /
• 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.

• 한국지반환경공학회 논문집
• /
• 제12권1호
• /
• pp.5-12
• /
• 2011

본 연구에서는 10개 현장에서 실시한 공내재하시험을 통하여 얻은 변형계수와 RMR과의 상관관계를 분석하여 기존에 사용하고 있는 제안식의 적용성을 평가하였다. RMR이 40보다 작은 경우에는 변형계수와 RMR과의 상관관계가 김교원, Aydan, Serafim과 Pereira의 식과 잘 일치하였지만 RMR이 40보다 큰 경우에는 상관관계가 낮았다. 이것은 RMR 분류 시 일축압축강도나 RQD보다 절리의 상태와 절리의 틈새가 상대적으로 가중치가 크기 때문이며 공학자의 개인적 차이뿐만 아니라 암반의 종류와 다른 풍화도 때문에 정성적으로 평가되는 경향이 있기 때문이다. 퇴적암 중 사암은 제안식과 비교적 잘 일치하지만 다른 사암은 분산이 커서 상관관계가 낮다. 본 연구에서는 현장시험결과를 근거로 새로운 지수함수 형태의 식을 제안하였다.