• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1041-1053
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• 2022

In this paper, sharp lower and upper bounds on the third order Hermitian-Toeplitz determinant for the classes of Sakaguchi functions and some of its subclasses related to right-half of lemniscate of Bernoulli, reverse lemniscate of Bernoulli and exponential functions are investigated.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.3
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• pp.279-282
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• 2014

In this paper, we report a new sharp inequality of interpolation type in $\mathbb{R}^n$. This inequality is for controlling weighted average of a function via $L^n$ norm of the gradient of a function together with its' certain exponential norm.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.759-770
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• 2021

The purpose of this paper is to prove unique existence of bounded solution and periodic solution to inhomogeneous linear evolution equations which trajectories of these solutions belong to given admissible Banach function space.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.984-987
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• 2003

This paper discusses the lateral vibration of a bar which has its tip free. The uniform bar has a solution by summation of some simple exponential functions. But if its shape is not uniform, its solution could be by Bessel's function, or mathematical solution could not be existed. Even if the solution of Bessel's function exists. as Bessel function is a series function, we must get the solution by numerical method, Hereof the author proposes the solution of the matrix method by Ritz's method, and proposes a new deflection shape

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.315-315
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• 2000

In this paper, we perform the time series prediction using the SVM(Support Vector Machine). We make use of two different loss functions and two different kernel functions; i) Quadratic and $\varepsilon$-insensitive loss function are used; ii) GRBF(Gaussian Radial Basis Function) and ERBF(Exponential Radial Basis Function) are used. Mackey-Glass time series are used for prediction. For both cases, we compare the results by the SVM to those by ANN(Artificial Neural Network) and show the better performance by SVM than that by ANN.

• Tribology and Lubricants
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• v.20 no.1
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• pp.14-20
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• 2004

In high-speed gas-levitation applications a high compressibility number may bring a numerical difficulty in predicting generated pressure profiles accurately as it causes erroneous sudden pressure overshoot and oscillation in the trailing-edge. To treat the problem, in this study an exact exponential high-order shape function is introduced in the FE lubrication analyses. It is shown by various example applications that the high-order shape function scheme can successfully subdue undesired pressure overshoot and oscillation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.1
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• pp.49-66
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• 2022

The G-Euler process has been proposed to overcome the difficulties of the calculation of the exponential function of the Jacobian. It is an explicit method that uses the exponential function of the scalar skew-symmetric matrix. We define the moving shapes of true solutions and the moving shapes of numerical solutions. It is discussed whether the moving shape of the numerical solution matches the moving shape of the true solution. The match rates of these two kinds of moving shapes are sequentially calculated by the G-Euler process without using the true solution. It is shown that the closer the minimum match rate is to 100%, the more closely the numerical solutions follow the true solutions to the end. The minimum match rate indicates the reliability of the numerical solution calculated by the G-Euler process. The graphs of the Lorenz system in Perko [1] are different from those drawn by the G-Euler process. By the way, there is no basis for claiming that the Perko's graphs are reliable.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.539-557
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• 1998

This article is concerned with the problem of estimating the mean of a one-parameter exponential family through sequential sampling in three stages under quadratic error loss. This more general framework differs from those considered by Hall (1981) and others. The differences are : (i) the estimator and the final stage sample size are dependent; and (ii) second order approximation of a continuously differentiable function of the final stage sample size permits evaluation of the asymptotic regret through higher order moments. In particular, the asymptotic regret can be expressed as a function of both the skewness $\rho$ and the kurtosis $\beta$ of the underlying distribution. The conditions on $\rho$ and $\beta$ for which negative regret is expected are discussed. Further results concerning the stopping variable N are also presented. We also supplement our theoretical findings wish simulation results to provide a feel for the triple sampling procedure presented in this study.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.519-536
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• 2005

The purpose of this paper is to propose several approximating methods to obtain the American option prices under jump-diffusion processes. The first method is to extend an approximating method to the optimal exercise boundary by a multipiece exponential function suggested by Ju [17]. The second approach is to modify the analytical methods of MacMillan [20] and Zhang [25] in a discrete time space. The third approach is to apply the simulation technique of Ibanez and Zapareto [14] to the problem of American option pricing when the jumps are allowed. Finally, we compare the numerical performance of each suggesting method with those of the previous numerical approaches.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.475-477
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• 2014

Lee and Lim (2009) state three characterizations of Loamax, exponential and power function distributions, the proofs of which, are based on the solutions of certain second order non-linear differential equations. For these characterizations, they make the following statement : "Therefore there exists a unique solution of the differential equation that satisfies the given initial conditions". Although the general solution of their first differential equation is easily obtainable, they do not obtain the general solutions of the other two differential equations to ensure their claim via initial conditions. In this very short report, we present the general solutions of these equations and show that the particular solutions satisfying the initial conditions are uniquely determined to be Lomax, exponential and power function distributions respectively.