• 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.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.47-54
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• 2024

In this paper, we investigate the distribution of the zeros of the Bernoulli-Fibonacci polynomials by using computer.

• Parasites, Hosts and Diseases
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• v.53 no.4
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• pp.501-506
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• 2015

Biting midges belonging to the genus Culicoides (Diptera: Ceratopogonidae) were collected by Mosquito $Magnet^{(R)}$ and black light traps at 5 sites on Jeju-do, Republic of Korea (Korea), from May-November 2013 to determine species diversity and seasonal distribution. A total of 4,267 specimens were collected, of which 99.9% were female. The most common species was Culicoides tainanus (91.8%), followed by C. lungchiensis (7.2%) and C. punctatus (0.6%), while the remaining 4 species accounted for <0.5% of all Culicoides spp. that were collected. High numbers of C. tainanus were collected in May, followed by decreasing numbers through August, and then increasing numbers through November when surveillance was terminated. Peak numbers of C. lungchiensis were collected during September, with low numbers collected from May-August and October-November. The presence of C. lungchiensis in Korea was confirmed by morphological and molecular analyses.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.311-320
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• 2023

In this article, a new penalty and different ranking algorithms are used to find the lowest transportation costs for the fuzzy transportation problem. This approach utilises different ranking techniques when dealing with triangular fuzzy numbers. Also, we find that the fuzzy transportation solution of the proposed method is the same as the Fuzzy Modified Distribution Method (FMODI) solution. Finally, examples are used to show how a problem is solved.

• The Korean Journal of Applied Statistics
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• v.23 no.1
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• pp.189-196
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• 2010

It is never an easy task to physically randomize the sequence of cards. For instance, US 1970 draft lottery resulted in a social turmoil since the outcome sequence of 366 birthday numbers showed a significant relationship with the input order (Wikipedia, "Draft Lottery 1969", Retrieved 2009/05/01). We are motivated by Laplace's 1825 book titled Philosophical Essay on Probabilities that says "Suppose that the numbers 1, 2, ..., 100 are placed, according to their natural ordering, in an urn, and suppose further that, after having shaken the urn, to shuffle the numbers, one draws one number. It is clear that if the shuffling has been properly done, each number will have the same chance of being drawn. But if we fear that there are small differences between them depending on the order in which the numbers were put into the urn, we can decrease these differences considerably by placing these numbers in a second urn in the order in which they are drawn from the first urn, and then shaking the second urn to shuffle the numbers. These differences, already imperceptible in the second urn, would be diminished more and more by using a third urn, a fourth urn, &c." (translated by Andrew 1. Dale, 1995, Springer. pp. 35-36). Laplace foresaw what would happen to us in 150 years later, and, even more, suggested the possible tool to handle the problem. But he did omit the detailed arguments for the solution. Thus we would like to write the supplement in modern terms for Laplace in this research note. We formulate the problem with a lottery box model, to which Markov chain theory can be applied. By applying Markov chains repeatedly, one expects the uniform distribution on k states as stationary distribution. Additionally, we show that the probability of even-number of successes in binomial distribution with trials and the success probability $\theta$ approaches to 0.5, as n increases to infinity. Our theory is illustrated to the cases of truncated geometric distribution and the US 1970 draft lottery.

• Journal of Oriental Neuropsychiatry
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• v.18 no.1
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• pp.37-61
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• 2007

Objective : By examining EEG status in Korean Traditional Medicine (KTM) from the viewpoint of 'form-qi theory(形氣論)', We wish to prepare for the fundamentals of applicability of KTM diagnoses to EEG. In addition, through reinterpretation of existing Western Medicine reports from the viewpoint of KTM, We tried to find out interrelationship between them. Method : In this paper, a methodology applicable to KTM diagnoses of EEG is presented from the EEG features in waveform characteristics, personalized diversity, and cognitive activity reflection. Results : Frequency bands are assigned to corresponding one of the eight trigrams in terms of yin/yang balance, which is analogous with EEG spectrum analysis mostly used in EEG quantification. The amplitude ratio of each EEG for each frequency band gives meaningful index numbers which can be used in EEG data interpretation, and every index number is named after the sixty four hexagrams. These approaches are adopted through both '4-band classification system and '6-band classification system', and applied to pre-existing reported EEG data obtained from normal adults. These analyses show that changes and distribution pattern in the index numbers are observed as a whole on both left-right line and front-back line connecting EEG measurement cephalic electrodes. And differences in distribution pattern of three index numbers deduced from '6-band classification system' are discussed according to constitution. Conclusion : The index numbers introduced here, which are the spectral power ratio for each EEG, are based on KTM yin/yang balance. These index numbers vary according to cephalic location, so its application in terms of traditional meridian theory is strongly expected. The index number distribution also shows different patterns according to constitution.

• Journal of the Korea Society of Computer and Information
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• v.21 no.7
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• pp.85-92
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• 2016

The law of large numbers, central limit theorem, and connection among binomial distribution, normal distribution, and statistical estimation require dynamics of continuous visualization for students' better understanding of the concepts. During this visualization process, the differences and similarities between statistical probability and mathematical probability that students should observe need to be provided with the intermediate steps in the converging process. We propose a visualization method that can integrate intermediate processes and results through Excel. In this process, students' experiences with dynamic visualization help them to perceive that the results are continuously changed and extracted from multiple situations. Considering modeling as a key process, we developed a classroom exercise using Excel to estimate the population mean and standard deviation by using a sample mean computed from a collection of data out of the population through sampling.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.45-55
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• 2016

Let {$X_n,n{\geq}1$} be a sequence of negatively superadditive dependent random variables. In the paper, we study the strong law of large numbers for general weighted sums ${\frac{1}{g(n)}}{\sum_{i=1}^{n}}{\frac{X_i}{h(i)}}$ of negatively superadditive dependent random variables with non-identical distribution. Some sufficient conditions for the strong law of large numbers are provided. As applications, the Kolmogorov strong law of large numbers and Marcinkiewicz-Zygmund strong law of large numbers for negatively superadditive dependent random variables are obtained. Our results generalize the corresponding ones for independent random variables and negatively associated random variables.

• The Journal of Korean Physical Therapy
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• v.25 no.5
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• pp.260-265
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• 2013

Purpose: This study was conducted in order to evaluate the quantitative effectiveness of region of interest (ROI) setting in MR-DTI analysis with and without fMRI activation results. Methods: Ten right-handed normal volunteers participated in this study. DTI and fMRI datasets for each subject were obtained using a 1.5T MRI system. For neural fiber tracking, ROIs were drawn using two methods: The drawing points were located in the fMRI activation areas or areas randomly selected by users. In this study, the neural fiber tract targeted the corticospinal tract (CST) Quantitative analyses were performed and compared. The pixel numbers passing through the fiber tract in the individual brain volume were counted. The ratios between the ROI pixel numbers and the extracted fiber pixel numbers, and the ratios between the fiber pixel numbers and the whole-brain pixel numbers were also calculated. Results: According to our results, extracted CST fiber tract in which the ROI was drawn with fMRI activation areas showed higher distribution than drawing the ROI by users' hands. In addition, the quantitatively measured values represented higher pixel distribution: The counted average pixel numbers were 4553.8 and 1943.3. The average ratios of the ROI areas were 33.87 and 22.52. The average percentages of the individual whole-brain volume numbers were 2.06 and 0.87. Conclusion: Results of this study appear to indicate that use of this method can allow for more objectives and significant for study of the recovery of neural fiber mechanisms and brain rehabilitation.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.10 no.1
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• pp.12-21
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• 1981

The Enthalpy Model was verified in order to analyze two- dimensional phase change problems. By using the Enthalpy Model, interface locations, frozen fraction rates, heat flux distribution rut cooled surfaces, and surface-integrated heat flux were purely numerically calculated in rectangular thermal storage units, whose initial condition was saturated liquid and phase change material was cooled on its boundaries by convective heat transfer. The calculations were performed for various Stefan numbers and Biot numbers. The effect on those dimensionless numbers were explained.