• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.445-453
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• 2007

This paper deals with the approximate controllability for the nonlinear functional differential equations with time delay and studies a variation of constant formula for solutions of the given equations.

• Industrial Engineering and Management Systems
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• 제4권2호
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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.

• Animal Bioscience
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• 제35권6호
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• pp.804-813
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• 2022

Objective: A formula is needed that is practical for current livestock breeding methods and that predicts the approximate rate of inbreeding (ΔF) in populations where selection is performed according to four-path programs (sires to breed sons, sires to breed daughters, dams to breed sons, and dams to breed daughters). The formula widely used to predict inbreeding neglects selection, we need to develop a new formula that can be applied with or without selection. Methods: The core of the prediction is to incorporate the long-tern genetic influence of the selected parents in four-selection paths executed as sires to breed sons, sires to breed daughters, dams to breed sons, and dams to breed daughters. The rate of inbreeding was computed as the magnitude that is proportional to the sum of squared long-term genetic contributions of the parents of four-selection paths to the selected offspring. Results: We developed a formula to predict the rate of inbreeding in populations undergoing four-path selection on genomically enhanced breeding values and with discrete generations. The new formula can be applied with or without selection. Neglecting the effects of selection led to underestimation of the rate of inbreeding by 40% to 45%. Conclusion: The formula we developed here would be highly useful as a practical method for predicting the approximate rate of inbreeding (ΔF) in populations where selection is performed according to four-path programs.

• Journal of electromagnetic engineering and science
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• 제13권4호
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• pp.240-244
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• 2013

In this paper, we present an improvement of a closed-form formula for mutual impedance computation. Depending on the center-to-center spacing between two rectangular microstrip patch antennas, the mutual impedance formula is separated into two parts. The formula based on synthetic asymptote and variable separation is utilized for spacings of more than 0.5 ${\lambda}_0$. When the spacing is less than 0.5 ${\lambda}_0$, an approximate formula is proposed to improve the computation for closely spaced elements. Simulation results are compared to computational results of mutual impedances and mutual coupling coefficients as functions of normalized center-to-center spacing in both E- and H-plane coupling configurations. A good agreement between simulation and computation is achieved.

• 한국소음진동공학회논문집
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• 제22권1호
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• pp.29-37
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• 2012

This paper is concerned with the natural vibration characteristics of a rectangular plate with a rectangular hole in contact with the water. The addressed problem was solved by using the Rayleigh-Ritz method combined with the Green function method. This study presents the numerical approach, numerical results and experimental results. In addition, the validity of the approximate formula which mainly depends on the so-called non-dimensionalized added virtual mass incremental factor and the natural mode shape change due to the presence of the water were investigated. Experiments were also carried out to validate theoretical results. The theoretical results are in good agreement with the experimental results. It was found that the effect of a square hole on the natural frequencies of the square plate in contact with water is different from the effect of a square hole on the natural frequencies of the square plate in air and the approximate formula can predict lower natural frequencies in water with a good accuracy.

• 한국군사과학기술학회지
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• 제5권3호
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• pp.23-32
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• 2002

We predict the erosion rate of unknown cannon tubes by substituting measured values of the standard cannon, 155㎜ Howitzer M185 and ballistic data for the erosion equation. We know ten measured erosion values of the standard cannon at every 400 rounds. An approximate formula is derived to interpolate six values up to 2,000 rounds. Numerical example is presented and its results are analyzed. The new erosion equation is also suggested. This equation produces more accurate cannon tube erosion rate than the Rauf Imam's empirical approaches. Computer simulations are presented.

• 터널과지하공간
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• 제31권6호
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• pp.480-493
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• 2021

일반화된 Hoek-Brown(GHB) 파괴기준식은 GSI 값을 이용하여 현장 암반조건이 반영된 강도정수 값을 효과적으로 결정할 수 있기 때문에 암반공학 분야에서 표준 파괴기준식의 하나로 인식되고 있다. 그러나 GHB 파괴기준식의 비선형적 형태는 이 식의 수학적 취급을 어렵게 하고 이 식의 적용 범위를 제약하는 요인이 되고 있다. GHB 파괴기준식의 이러한 단점을 극복하기 위한 노력의 하나로 Taylor 다항함수 근사원리를 적용하여 파괴 최대주응력에 대응하는 최소주응력을 근사적으로 계산할 수 있는 명시적, 해석적 수식을 유도하였다. 근사식으로 구한 최소주응력과 수치해석적으로 계산한 정해를 비교하여 이 연구에서 유도한 최소주응력 근사식의 정확성을 검증하였다. 연구결과의 응용사례를 제시하기 위해 근사 최소주응력 계산식을 활용하여 GHB 암반에 굴착된 원형터널 주변에 예상되는 소성영역의 등가 마찰각과 등가 점착력을 계산하였다. 소성영역의 등가 Mohr-Coulomb 강도정수를 정밀하기 산정하기 위해서는 mi, GSI, 초기지압의 크기를 동시에 고려하는 것이 중요한 것으로 나타났다.

• 한국항해학회지
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• 제11권2호
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• pp.73-88
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• 1987

It is well known that the height of tank metacenter above the centroid of fluid in a tank is given by i/v where I is the inertia moment of free surface and v is the fluid volume. It is supposed in this formula that the inclination of ship is small and that the free surface of fluid do not touch the top and the bottom of tank. It the inclination of ship is large, the height of tank metacenter may be possibly greater than that given by i/v. The height of tank metacenter is smaller than i/v when the free surface of fluid touch the top or the bottom of tank. The reasonable method to calculate the height of tank metacenter is presented in this paper and prepared in FORTRAN program by FUNCTION EFFRES. The approximate formula was also developed and given by $g_m=(1+\frac{2}{1}tan^2\theta)[1-EXP\{-12(\frac{\alpha(1-\alpha)k}{tan\theta})^{1.25}\}]\frac{i}{v}$ where $g_m$ is the distance from the centroid of fluid to the tank metacenter, $\theta$ is inclined angle of ship, $\alpha$ is the ratio of filled volume to tank capacity and k is the ratio of the depth to the width of tank. The values calculated by the approximate formula given in this paper were compared with the exact values from the computer program and proved out to be sufficiently precise for practical use.

• 한국통신학회논문지
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• 제25권4A호
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• pp.489-495
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• 2000

In this paper we propose an approximate method to estimate the cell loss probability(CLP) due to buffer overflow in ATM networks. The main idea is to relate the buffer capacity with the CLP target in explicit formula by using the approximate upper bound for the tail distribution of a queue. The significance of the proposition lies in the fact that we can obtain the expected CLP by using only the source traffic data represented by mean rate and its variance. To that purpose we consider the problem of estimating the cell loss measures form the statistical viewpoint such that the probability of cell loss due to buffer overflow does not exceed a target value. In obtaining the exact solution we use a typical matrix analytic method for GI/D/1B queue where B is the queue size. Finally, in order to investigate the accuracy of the result, we present both the approximate and exact results of the numerical computation and give some discussion.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
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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.