• Journal of the Korean Statistical Society
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• 제23권1호
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• pp.13-32
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• 1994

Let A(n) and B(n) be sequences of $m \times m$ random matrices with a joint asymptotic distribution as $n \to \infty$. The asymptotic distribution of the ordered roots of $$\mid$A(n) - f B(n)$\mid$ = 0$ depends on the multiplicity of the roots of a determinatal equation involving parameter roots. This paper treats the asymptotic distribution of the roots of the above determinantal equation in the case where some of parameter roots are zero. Furthermore, we apply our results to deriving the asymptotic distributions of the eigenvalues of the MANOVA matrix in the noncentral case when the underlying distribution is not multivariate normal and some parameter roots are zero.

• Industrial Engineering and Management Systems
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• 제12권3호
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• pp.281-287
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• 2013

In this paper, we introduce a roots method that uses the roots inside the unit circle of the associated characteristics equation to evaluate the steady-state system-length distribution at three epochs (pre-arrival, arbitrary, and post-departure) and sojourn-time distribution in GI/PH/1 queueing model. It is very important for an air base to inspect airplane oil because low-quality oil leads to drop or breakdown of an airplane. Since airplane oil inspection is composed of several inspection steps, it sometimes causes train congestion and delay of inventory replenishments. We analyzed interarrival time and inspection (service) time of oil supply from the actual data which is given from one of the ROKAF's (Republic of Korea Air Force) bases. We found that interarrival time of oil follows a normal distribution with a small deviation, and the service time follows phase-type distribution, which was first introduced by Neuts to deal with the shortfalls of exponential distributions. Finally, we applied the GI/PH/1 queueing model to the oil train congestion problem and analyzed the distributions of the number of customers (oil trains) in the queue and their mean sojourn-time using the roots method suggested by Chaudhry for the model GI/C-MSP/1.

• Communications for Statistical Applications and Methods
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• 제15권5호
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• pp.719-726
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• 2008

In this paper we consider a joint test for seasonal cointegrating(CI) ranks that enables us to simultaneously model cointegrated structures across seasonal unit roots in seasonal cointegration. A CI rank test for a single seasonal unit root is constructed and extended to a joint test for multiple seasonal unit roots. Their asymptotic distributions and selected critical values for the joint test are obtained. Through a small Monte Carlo simulation study, we evaluate performances of the tests.

• Journal of the Korean Statistical Society
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• 제28권1호
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• pp.45-55
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• 1999

Knowing the number of unit roots is important in the analysis of k-dimensional multivariate autoregressive process. In this paper we suggest simple multiple unit roots test statistics based on least squares estimator for the multivariate AR(1) process in which some eigenvalues are one and the rest are less than one in magnitude. The empirical distributions are tabulated for suggested test statistics. We have small Monte-Calro studies to compare the powers of the test statistics suggested by Johansen(1988) and in this paper.

• Communications for Statistical Applications and Methods
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• 제4권3호
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• pp.663-676
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• 1997

We obtain the simultaneous unit roots test statistics for both regular and seasonal unit roots in a time series with possible seasonal deterministic trends. The limiting distributions of the proposed test statistics are derived and empirical percentiles of the test statistics are tabulated for some seasonal periods. The power and size of the test statistics are examined for finite samples through a Monte Carlo simulation and Compared with those of the Lagrange multiplier test.

• Journal of the Korean Statistical Society
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• 제24권1호
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• pp.77-90
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• 1995

The Lagrange multiplier test statistics for seasonal unit roots are derived and the asymptotic distributions of the derived statistics are obtained. The relationship between the derived LM test statistics and the "DHF" type regression t statistics are shown.are shown.

• Communications for Statistical Applications and Methods
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• 제12권1호
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• pp.101-115
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• 2005

We propose in this article a procedure for testing unit and fractional orders of integration, with the roots simultaneously occurring in the trend, the seasonal and the cyclical component of the time series. The tests have standard null and local limit distributions. However, finite sample critical values are computed, and several Monte Carlo experiments conducted across the paper show that the rejection frequencies against unit (and fractional) orders of integration are relatively high in all cases. The tests are applied to the UK consumption and income series, the results showing the importance of the roots corresponding to the trend and the seasonal components and, though the unit roots are found to be fairly suitable models, we show that fractional processes (including one for the cyclical component) may also be plausible alternatives in some cases.

• Food Science and Biotechnology
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• 제16권4호
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• pp.636-640
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• 2007

In order to investigate the major metabolite patterns of aged Panax ginseng C.A. Meyer roots, the ginsenoside contents for white ginseng roots of various ages were compared. The 1-year to 6-year old roots were extracted with methanol, and then the methanol-soluble metabolites were analyzed by high performance liquid chromatography (HPLC). The metabolite contents of the 1-year and 2-year roots, including the ginsenosides and minor components, were not different, but the $Rg_1$, Re, and Rc ginsenoside contents between the 2-year and 3-year roots showed significant differences. $Rg_1$ and Rc increased significantly in the 1-year to 2-year roots, and Re increased significantly from the 3-year root age. Rd increased slightly until the 2-year age and decreased from the 3-year age. Based on the ginsenoside distributions and contents at various root ages, we have suggested 2 biogenesis schemes using the ginsenosides that have been isolated from the roots of P. ginseng so far.

• 대한치과교정학회지
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• 제46권4호
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• pp.189-198
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• 2016

Objective: The purpose of this study was to analyze stress distributions in the roots, periodontal ligaments (PDLs), and bones around cylindrical and tapered miniscrews inserted at different angles using a finite element analysis. Methods: We created a three-dimensional (3D) maxilla model of a dentition with extracted first premolars and used 2 types of miniscrews (tapered and cylindrical) with 1.45-mm diameters and 8-mm lengths. The miniscrews were inserted at $30^{\circ}$, $60^{\circ}$, and $90^{\circ}$ angles with respect to the bone surface. A simulated horizontal orthodontic force of 2 N was applied to the miniscrew heads. Then, the stress distributions, magnitudes during miniscrew placement, and force applications were analyzed with a 3D finite element analysis. Results: Stresses were primarily absorbed by cortical bone. Moreover, very little stress was transmitted to the roots, PDLs, and cancellous bone. During cylindrical miniscrew insertion, the maximum von Mises stress increased as insertion angle decreased. Tapered miniscrews exhibited greater maximum von Mises stress than cylindrical miniscrews. During force application, maximum von Mises stresses increased in both groups as insertion angles decreased. Conclusions: For both cylindrical and tapered miniscrew designs, placement as perpendicular to the bone surface as possible is recommended to reduce stress in the surrounding bone.

• 한국유체기계학회 논문집
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• 제16권2호
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• pp.10-14
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• 2013

The present study conducts CFD analyses on the internal flow fields of roots type vacuum pumps of semiconductor fabrication facility, and the computed CFD results for internal pressure and temperature distributions are applied to structural analyses of the pumps. The coupled analysis results between flow and structure show that the deformation of pump structure is mainly resulted from the thermal expansion of gas in pump, and the deformed impeller and housing produce their severe contact and impact phenomena causing mechanical damage and fracture.