• 대한수학회보
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• 제54권1호
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• pp.343-358
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• 2017

Let {$X_i$} be a sequence of stationary ${\alpha}-mixing$ random variables with probability density function f(x). The recursive kernel estimators of f(x) are defined by $$\hat{f}_n(x)={\frac{1}{n\sqrt{b_n}}{\sum_{j=1}^{n}}b_j{^{-\frac{1}{2}}K(\frac{x-X_j}{b_j})\;and\;{\tilde{f}}_n(x)={\frac{1}{n}}{\sum_{j=1}^{n}}{\frac{1}{b_j}}K(\frac{x-X_j}{b_j})$$, where 0 < $b_n{\rightarrow}0$ is bandwith and K is some kernel function. Under appropriate conditions, we establish the Berry-Esseen bounds for these estimators of f(x), which show the convergence rates of asymptotic normality of the estimators.

• 대한수학회지
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• 제61권5호
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• pp.853-874
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• 2024

Let {X, X_n; n ≥ 1} be a 𝛽-mixing sequence of identical nonnegative random variables with super-heavy tailed distributions and S_n = X₁ + X₂ + · · · + X_n. For 𝜀 > 0, b > 1 and appropriate values of x, we obtain the logarithmic asymptotics behaviors for the tail probabilities ℙ(S_n > e^𝜀nx) and P(S_n > e^𝜀bn). Moreover, our results are applied to the log-Pareto distribution and the distribution for the super-Petersburg game.

• 대한수학회지
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• 제45권2호
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• pp.355-365
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• 2008

Let ${Y_i;-\infty<i<\infty}$ be a doubly infinite sequence of identically distributed and $\phi$-mixing random variables with zero means and finite variances and ${a_i;-\infty<i<\infty}$ an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of ${{\sum}_{k=1}^{n}\;{\sum}_{i=-\infty}^{\infty}\;a_{i+k}Y_i/n^{1/p};n\geq1}$ under some suitable conditions.

• 산업경영시스템학회지
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• 제46권3호
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• pp.139-147
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• 2023

The metal bush assembling process is a process of inserting and compressing a metal bush that serves to reduce the occurrence of noise and stable compression in the rotating section. In the metal bush assembly process, the head diameter defect and placement defect of the metal bush occur due to metal bush omission, non-pressing, and poor press-fitting. Among these causes of defects, it is intended to prevent defects due to omission of the metal bush by using signals from sensors attached to the facility. In particular, a metal bush omission is predicted through various data mining techniques using left load cell value, right load cell value, current, and voltage as independent variables. In the case of metal bush omission defect, it is difficult to get defect data, resulting in data imbalance. Data imbalance refers to a case where there is a large difference in the number of data belonging to each class, which can be a problem when performing classification prediction. In order to solve the problem caused by data imbalance, oversampling and composite sampling techniques were applied in this study. In addition, simulated annealing was applied for optimization of parameters related to sampling and hyper-parameters of data mining techniques used for bush omission prediction. In this study, the metal bush omission was predicted using the actual data of M manufacturing company, and the classification performance was examined. All applied techniques showed excellent results, and in particular, the proposed methods, the method of mixing Random Forest and SA, and the method of mixing MLP and SA, showed better results.

• 한국운동역학회지
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• 제30권4호
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• pp.301-309
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• 2020

Objective: This study aimed to investigate the effect of white noise on dynamic balance in patients with stroke during walking. Method: Nineteen patients with chronic stroke (age: 61.2±9.8 years, height: 164.4±7.4 cm, weight: 61.1±9.4 kg, paretic side (R/L): 11/8, duration: 11.6±4.9 years) were included as study participants. Auditory stimulus used white noise, and all participants listened for 40 minutes mixing six types of natural sounds with random sounds. The dynamic balancing ability was evaluated while all participants walked before and after listening to white noise. The variables were the center of pressure (CoP), the center of mass (CoM), CoP-CoM inclined angle. Results: There is a significant increase in the antero-posterior (A-P) CoP range, A-P inclination angle, and gait speed on the paretic and non-paretic sides following white noise intervention (p<.05). Conclusion: Our findings confirmed the positive effect of using white noise as auditory stimulus through a more objective and quantitative assessment using CoP-CoM inclination angle as an evaluation indicator for assessing dynamic balance in patients with chronic stroke. The A-P and M-L inclination angle can be employed as a useful indicator for evaluating other exercise programs and intervention methods for functional enhancement of patients with chronic stroke in terms of their effects on dynamic balance and effectiveness.

• 한국지반신소재학회논문집
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• 제17권4호
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• pp.53-64
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• 2018

본 연구에서는 안정성과 위험도 평가의 중요성이 증대되고 있는 DCM(Deep Cement Mixing, 이하 DCM) 보강 지반상의 항만 구조물에 대하여 위험도 평가를 위한 파괴확률을 산정하였다. DCM 개량 지반의 위험도에 영향을 미치는 확률변수로 개량체의 설계기준강도와 시공중첩, 원지반의 강도 및 내부마찰각, 개량지반의 단위중량을 선정하고 관련 통계치를 산정하여 적용하였다. 또한, 상시 조건과 지진시 조건에서의 전체 시스템에 대한 파괴확률을 분석하였다. 본 연구를 통해 DCM 개량지반의 위험도 평가를 위한 확률변수에서 변동계수가 가장 큰 것은 설계기준강도이나 안전율의 변동성 즉, 시스템의 위험도에는 큰 영향을 미치지는 않는 것을 알 수 있었다. DCM 보강 지반에 대한 시스템의 파괴확률 영향인자 즉, 주된 위험요소는 상시 및 지진시 모두 외적안정의 경우 수평활동, 내적안정의 경우 압축파괴인 것으로 평가되었다. 또한, 수평활동에 대해서는 상시 파괴확률이 지진시 파괴확률보다 높고 압축파괴에 대해서는 상시 파괴확률이 지진시 파괴확률보다 낮은 것으로 나타났다. 전체 시스템의 상시 파괴확률과 지진시 파괴확률은 유사하지만, 본 사례의 경우 지진시 위험도가 다소 높은 것으로 나타났다.