• Bulletin of the Korean Chemical Society
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• v.16 no.4
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• pp.344-348
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• 1995

As an effort to elucidate the chiral recognition mechanisms exerted by the (S)-naproxen-derived CSP bearing both π-acidic and π-basic sites, a homologues series of π-basic N-acyl-α-(1-naphthyl)alkylamines and π-acidic N-(3,5-dinitrobenzoyl)-α-amino esters were prepared and resolved. Based on the chromatographic resolution trends of the homologues series of analytes on the (S)-naproxen-derived chiral stationary phase, we proposed chiral recognition mechanisms which demonstrate that the intercalation of the substituent in the analyte molecule between the strands of bonded phase does significantly influence the enantioselectivity for resolving N-acyl-α-(1-naphthyl)alkylamines but the intercalation process is not involved in resolving N-(3,5-dinitrobenzoyl)-α-amino esters.

• Communications for Statistical Applications and Methods
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• v.29 no.2
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• pp.151-160
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• 2022

The total system is composed of the main system (MS) and the failure detection equipment (FDE) which detects failures of MS. The analysis of system reliability is performed when the failure of FDE is possible. Several repair policies are considered to determine the order of repair of failed systems, which are sequential repair (SQ), priority repair (PR), independent repair (ID), and simultaneous repair (SM). The states of MS-FDE systems are represented by Markov models according to repair policies and the main purpose of this paper is to derive the system availabilities of the Markov models. Analytical solutions of the stationary equations are derived for the Markov models and the system availabilities are immediately determined using the stationary solutions. A simple illustrative example is discussed for the comparison of availability values of the repair policies considered in this paper.

• The Korean Journal of Applied Statistics
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• v.7 no.1
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• pp.103-112
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• 1994

An asymptotic property of the estimated eigenvalues for multivariate AR(p) process which consists of vector of nonstationary process and vector of stationary process is developed. All components of the nonstationary process are assumed to reveal random walk behavior. The asymptotic property is helpful in understanding multiple unit roots. In this paper we show the stationay part in multivariate AR(p) process does not affect the limiting distribution of estimated eigenvalues associated with the nonstationary process. A test statistic based on the ordinary least squares estimator for testing a certain number of multiple unit roots is suggested.

• Wind and Structures
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• v.1 no.2
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• pp.161-174
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• 1998

Wind forces on structures are usually schematized by the sum of their mean static part and a nil mean fluctuation generally treated as a stationary process randomly varying in space and time. The multi-variate and multi-dimensional nature of such a process requires a considerable quantity of numerical procedures to carry out the dynamic analysis of the structural response. With the aim of drastically reducing the above computational burden, this paper introduces a method by means of which the external fluctuating wind forces on slender structures and structural elements are schematized by an equivalent process identically coherent in space. This process is identified by a power spectral density function, called the Generalized Equivalent Spectrum, whose expression is given in closed form.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.483-498
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• 1994

Suppose that a stationary process ${X_t}$ has a marginal distribution whose support consists of sufficiently large integers. We are concerned with some analogous law of large numbers for such distribution function F. In particular, we determine a weak law of large numbers for maximum queueing length in $M/M\infty$ system. We also present a limiting behavior for the maxima based on AR(1) process with binomial thining and poisson marginals (INAR(1)) introduced by E. Mckenzie. It turns out that the result of AR(1) process is the same as that of $M/M/\infty$ queueing process in limit when we observe the queues at regularly spaced intervals of time.

• Industrial Engineering and Management Systems
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• v.12 no.1
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• pp.2-8
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• 2013

Uncertainty theory is a branch of mathematics based on normolity, duality, subadditivity and product axioms. Uncertain process is a sequence of uncertain variables indexed by time. Canonical Liu process is an uncertain process with stationary and independent increments. And the increments follow normal uncertainty distributions. Uncertain differential equation is a type of differential equation driven by the canonical Liu process. Stability analysis on uncertain differential equation is to investigate the qualitative properties, which is significant both in theory and application for uncertain differential equations. This paper aims to study stability properties of linear uncertain differential equations. First, the stability concepts are introduced. And then, several sufficient and necessary conditions of stability for linear uncertain differential equations are proposed. Besides, some examples are discussed.

• Journal of the Korea Society for Simulation
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• v.5 no.2
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• pp.59-72
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• 1996

The purpose of this study is to make an improvement to the batch-means method, which is a procedure to construct a confidence interval(c.i.) for the steady-state process mean of a stationary simulation output process. In the batch-means method, the data in the output process are grouped into batches. The sequence of means of the data included in individual batches is called a batch-menas process and can be treated as an independently and identically distributed set of variables if each batch includes sufficiently large number of observations. The traditional batch-means method, therefore, uses a batch size as large as possible in order to. destroy the autocovariance remaining in the batch-means process. The c.i. prodedure developed and empirically tested in this study uses a small batch size which can be well fitted by a simple ARMA model, and then utilizes the dependence structure in the fitted model to correct for bias in the variance estimator of the sample mean.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.739-751
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• 1995

Let ${X(t) : 0 \leq t < \infty}$ be an almost surely continuous Gaussian process with X(0) = 0, E{X(t)} = 0 and stationary increments $E{X(t) - X(s)}^2 = \sigma^2($\mid$t - s$\mid$)$, where $\sigma(y)$ is a function of $y \geq 0(e.g., if {X(t);0 \leq t < \infty}$ is a standard Wiener process, then $\sigma(t) = \sqrt{t})$. Assume that $\sigma(t), t > 0$, is a nondecreasing continuous, regularly varying function at infinity with exponent $\gamma$ for some $0 < \gamma < 1$.

• The Korean Journal of Applied Statistics
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• v.26 no.2
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• pp.335-347
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• 2013

There are various types of real world signals. For example, an electrocardiogram(ECG) represents myocardium activities (contraction and relaxation) according to the beating of the heart. ECG can be expressed as the fluctuation of ampere ratings over time. A signal is a composite of various types of signals. An orchestra (which boasts a beautiful melody) consists of a variety of instruments with a unique frequency; subsequently, each sound is combined to form a perfect harmony. Various research on how to to decompose mixed stationary signals have been conducted. In the case of non-stationary signals, there is a limitation to use methodologies for stationary signals. Huang et al. (1998) proposed empirical mode decomposition(EMD) to deal with non-stationarity. EMD provides a data-driven approach to decompose a signal into intrinsic mode functions according to local oscillation through the identification of local extrema. However, due to the repeating process in the construction of envelopes, EMD algorithm is not efficient and not robust to a noise, and its computational complexity tends to increase as the size of a signal grows. In this research, we propose a new method to extract a local oscillation embedded in a signal by utilizing the second derivative.

• Ocean Systems Engineering
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• v.4 no.4
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• pp.293-308
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• 2014

Unlike the traditional displacement type vessels, the high speed planing crafts are supported by the lift forces which are highly non-linear. This non-linear phenomenon causes their motions in an irregular seaway to be non-Gaussian. In general, it may not be possible to express the probability distribution of such processes by an analytical formula. Also the process might not be stationary or ergodic in which case the statistical behavior of the motion to be constantly changing with time. Therefore the extreme values of such a process can no longer be calculated using the analytical formulae applicable to Gaussian processes. Since closed form analytical solutions do not exist, recourse is taken to fitting a distribution to the data and estimating the statistical properties of the process from this fitted probability distribution. The peaks over threshold analysis and fitting of the Generalized Pareto Distribution are explored in this paper as an alternative to Weibull, Generalized Gamma and Rayleigh distributions in predicting the short term extreme value of a random process.