• Industrial Engineering and Management Systems
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• v.4 no.2
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• pp.123-128
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• 2005

The author derives a general explicit formula and presents an heuristic algorithm for solving Baker’s model. The examples show that this new approximate solution procedure for determining near optimum inspection intervals is more accurate than the ones suggested by Chung (1993) and Vaurio (1994), and is more efficient computationally than the one suggested by Hariga (1996). The construction and solution of the simplest profit model for an exponential failure distribution were presented in Baker (1990), and approximate analytical results were obtained by Chung (1993) and Vaurio (1994). The author will therefore mainly devote the following discussion to the problem of further approximating optimum inspection intervals.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.937-942
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• 2009

In this paper, a continuous-time risk process in an insurance business is considered, where the premium rate is constant and the claim process forms a compound Poisson process. We say that a ruin occurs if the surplus of the risk process becomes negative. It is practically impossible to calculate analytically the ruin probability because the theoretical formula of the ruin probability contains the recursive convolutions and infinite sum. Hence, many authors have suggested approximation formulas of the ruin probability. We introduce a new approximation formula of the ruin probability which extends the well-known De Vylder's and exponential approximation formulas. We compare our approximation formula with the existing ones and show numerically that our approximation formula gives closer values to the true ruin probability in most cases.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.501-510
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• 2008

The distribution of the sum of n independent random variables having exponential distributions with different parameters ${\beta}_i$ ($i=1,2,{\ldots},n$) is given in [2], [3], [4] and [6]. In [1], by using Laplace transform, Jasiulewicz and Kordecki generalized the results obtained by Sen and Balakrishnan in [6] and established a formula for the distribution of this sum without conditions on the parameters ${\beta}_i$. The aim of this note is to present a method to find the distribution of the sum of n independent exponentially distributed random variables with different parameters. Our method can also be used to handle the case when all ${\beta}_i$ are the same.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.273-280
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• 2006

Lipschitzian semigroup is a semigroup of Lipschitz operators which contains $C_0$ semigroup and nonlinear semigroup. In this paper, we establish the cannonical exponential formula of Lipschitzian semigroup from its Lie generator and the approximation theorem by Laplace transform approach to Lipschitzian semigroup.

• Journal of information and communication convergence engineering
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• v.7 no.2
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• pp.182-184
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• 2009

In this letter, we derive a tight closed-form formula for an ergodic capacity of a multiple-input multiple-output (MIMO) for the application of wireless communications. The derived expression is a simple closed-form formula to determine the ergodic capacity of MIMO systems. Assuming the channels are independent and identically distributed (i.i.d.) Rayleigh flat-fading between antenna pairs, the ergodic capacity can be expressed in a closed form as the finite sum of exponential integrals.

• Water Engineering Research
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• v.5 no.1
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• pp.47-54
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• 2004

Several computer programs have been developed to make stochastically generated weather data from observed daily data. But they require fully dataset to run WGEN. Mostly, meterological data frequently have sporadic missing data as well as totally missing data. The modified WGEN has data filling algorithm for incomplete meterological datasets. Any other WGEN models have not the function of data filling. Modified WGEN with data filling algorithm is processing from the equation of Matalas for first order autoregressive process on a multi dimensional state with known cross and auto correlations among state variables. The parameters of the equation of Matalas are derived from existing dataset and derived parameters are adopted to fill data. In case of WGEN (Richardson and Wright, 1984), it is one of most widely used weather generators. But it has to be modified and added. It uses an exponential distribution to generate precipitation amounts. An exponential distribution is easier to describe the distribution of precipitation amounts. But precipitation data with using exponential distribution has not been expressed well. In this paper, generated precipitation data from WGEN and Modified WGEN were compared with corresponding measured data as statistic parameters. The modified WGEN adopted a formula of CLIGEN for WEPP (Water Erosion Prediction Project) in USDA in 1985. In this paper, the result of other parameters except precipitation is not introduced. It will be introduced through study of verification and review soon

• Journal of the Korean Data and Information Science Society
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• v.27 no.1
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• pp.265-274
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• 2016

In this paper, we consider a diffusion risk process, in which, its surplus process behaves like a Brownian motion in-between adjacent epochs of claims. We assume that the claims occur following a Poisson process and their sizes are independent and exponentially distributed with the same intensity. Our main goal is to derive the exact formula of the joint moment generating function of the ruin time and the total amount of aggregated claim sizes until ruin in the diffusion risk process. We also provide a method for computing the related first and second moments using the joint moment generating function and the augmented matrix exponential function.

• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.35-44
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• 1994

In this paper we study exponential growth of Betti numbers over artinian local rings. By the Change of Tor Formula the results in the paper extend to the asymptotic behavior of Betti numbers over Cohen-Macaulay local rings. Using the length function of an artinian ring we calculate an upper bound for the number of generators of modules, this is then used to maximize the number of generators of sygyzy modules. Finally, applying a filtration of an ideal, which we call a Loewy series of an ideal, we derive an invariant B(R) of an artinian local ring R, such that if B(R)>1, then the sequence $b^{R}$$_{i}$ (M) of Betti numbers is strictly increasing and has strong exponential growth for any finitely generated non-free R-module M (Theorem 2.7).).

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.24 no.3
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• pp.228-234
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• 2012

Two-dimensional hydraulic experiments for wave overtopping under non-breaking wave condition are conducted. The wave overtopping formula for vertical structure is suggested and the results are compared with EurOtop (2007). The relative water depth coefficient (${\gamma}_{kh}$) shows that almost the same coefficient is obtained for certain range (kh > 1.55) regardless of relative water depth, that is, although the relative water depth becomes larger, the relative water depth coefficient is almost same. When the wave steepness becomes larger the wave steepness coefficient decreases. The overtopping formula are expressed by relative freeboard(R) and non-dimensional wave overtopping rate(Q) and this formula has the form of exponential function. In this formula, the effects of wave period on wave overtopping are quantitatively investigated and suggested through the relative water depth coefficient(${\gamma}_{kh}$) and wave steepness coefficient(${\gamma}_s$).

• Proceedings of the Korea Contents Association Conference
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• 2004.05a
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• pp.317-322
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• 2004

The improvement of a near-field measurement for an antenna is investigated. We propose the formula of a circular cylindrical scanning based on the Cartesian coordinate. Proposed algorithm for the circular cylindrical scanning is compared with the exact solution for a Hertzian dipole antenna, thus confirming that our approach is useful for most practical measurements.