• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.299-305
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• 2003

The central limit theorems are obtained for stationary linear processes of the form Xt = (equation omitted), where {$\varepsilon$t} is a strictly stationary sequence of random variables which are either linearly positive quad-rant dependent or associated and {aj} is a sequence of .eat numbers with (equation omitted).

• Journal of the Korean Statistical Society
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• v.7 no.2
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• pp.109-119
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• 1978

When a response surface by a seconde order polynomial regression model, the stationary point is obtained by solving simultaneous linear equations. But the point is a function of random variables. We can find a confidence region for this point as Box and Hunter provided. However, the confidence region is often too large to be useful for the experiments, and it is necessary to augment additional design points in order to obtain a satisfactory confidence region for the stationary point. In this note, the author suggests a method how to augment design points "eficiently", and shows the change of the confidence region of the estimated stationary point in a response surface.e surface.

• Membrane and Water Treatment
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• v.6 no.3
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• pp.225-235
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• 2015

During low-pressure membrane treatments of cyanobacterial cells, including microfiltration (MF) and ultrafiltration (UF), there have reportedly been releases of intracellular compounds including cyanotoxins and compounds with an earthy-musty odor into the water, probably owing to cyanobacterial cell breakage retained on the membrane. However, to our knowledge, no information was reported regarding the effect of growth phase of cyanobacterial cells on the release of the intracellular compounds. In the present study, we used a geosmin-producing cyanobacterium, Anabaena smithii, to investigate the effect of the growth phase of the cyanobacterium on the release of intracellular geosmin during laboratory-scale MF experiments with the cells in either the logarithmic growth or stationary phase. Separate detection of damaged and intact cells revealed that the extent of cell breakage on the MF membrane was almost the same for logarithmic growth and stationary phase cells. However, whereas the geosmin concentration in the MF permeate increased after 3 h of filtration with cells in the logarithmic growth phase, it did not increase during filtration with cells in the stationary phase: the trend in the geosmin concentration in the MF permeate with time was much different between the logarithmic growth and stationary phases. Adsorption of geosmin to algogenic organic matter (AOM) retained on the MF membrane and/or pore blocking with the AOM were greater when the cells were in the stationary phase versus the logarithmic growth phase, the result being a decrease in the apparent release of intracellular geosmin from the stationary phase cells. In actual drinking water treatment plants employing membrane processes, more attention should be paid to the cyanobacterial cells in logarithmic growth phase than in stationary phase from a viewpoint of preventing the leakage of intracellular earthy-musty odor compounds to finished water.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.909-928
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• 1996

In this paper, an empirical law of the iterated logarithm is investigated in the context of a stationary and ergodic martingale differences whose values taking in a measurable space.

• Journal of the Korean Statistical Society
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• v.30 no.1
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• pp.153-161
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• 2001

In this paper, a strong law of large numbers for sums of stationary and ergodic fuzzy random variables is obtained.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.383-392
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• 1998

This paper proposes Generalized Stationary Iterative called GSI method. It is shown that the existing stationary iterative methods are special cases of GSI method. Convergence properties of this method are provided and their numerical experiments for linear systems with symmetric positive definite matrix are also provided.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.281-292
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• 1995

In this paper the concept of strong mixing is extended to random fields, and an invariance principle is obtained for stationary strong mixing random fields.

• Communications for Statistical Applications and Methods
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• v.20 no.3
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• pp.193-197
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• 2013

Almost sure central limit theorems are established for a stationary bootstrap sample mean of strong mixing processes. Both weak and strong consistencies are obtained.

• East Asian mathematical journal
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• v.37 no.1
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• pp.109-122
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• 2021

We establish existence and uniqueness of Green functions for flow velocity of stationary Stokes systems, under a continuity assumption of weak solutions to the system, in a bounded domain such that the divergence equation is solvable there. We also obtain pointwise bounds of the Green functions.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.647-653
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• 2015

Extreme value theory concerns the distributional properties of the maximum of a random sample; subsequently, it has been significantly extended to stationary random sequences satisfying weak dependence restrictions. We focus on distributional mixing condition $D(u_n)$ and the Berman condition based on covariance among weak dependence restrictions. The former is assumed for general stationary sequences and the latter for stationary normal processes; however, both imply the same distributional limit of the maximum of the normal process. In this paper $D(u_n)$ condition is shown weaker than Berman's covariance condition. Examples are given where the Berman condition is satisfied but the distributional mixing is not.