• Journal of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.959-971
• /
• 1997

In the paper we introduce Hausdorff measures which are suitable or the study of Lipschitz regularity of M-harmonic function in the unit ball B in $C^n$. For an M-harmonic function h which satisfies certain integrability conditions, we show that there is an open set $\Omega$, whose Hausdorff content is arbitrarily small, such that h is Lipschitz smooth on $B \backslash \Omega$.

• Journal of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.731-770
• /
• 1997

We study Diriclet forms and related subjects for the Gibbs measures of classical unbounded sping systems interacting via potentials which are superstable and regular. For any Gibbs measure $\mu$, we construct a Dirichlet form and the associated diffusion process on $L^2(\Omega, d\mu), where \Omega = (R^d)^Z^\nu$. Under appropriate conditions on the potential we show that the Dirichlet operator associated to a Gibbs measure $\mu$ is essentially self-adjoint on the space of smooth bounded cylinder functions. Under the condition of uniform log-concavity, the Gibbs measure exists uniquely and there exists a mass gap in the lower end of the spectrum of the Dirichlet operator. We also show that under the condition of uniform log-concavity, the unique Gibbs measure satisfies the log-Sobolev inequality. We utilize the general scheme of the previous works on the theory in infinite dimensional spaces developed by e.g., Albeverio, Antonjuk, Hoegh-Krohn, Kondratiev, Rockner, and Kusuoka, etc, and also use the equilibrium condition and the regularity of Gibbs measures extensively.

• Journal of applied mathematics & informatics
• /
• v.26 no.1_2
• /
• pp.177-189
• /
• 2008

In this paper, we have considered an investigation on goodness of fit tests based on divergence measures. In the case of categorical data, under certain regularity conditions, we obtained asymptotic distribution of these tests. Also, we have proposed a modified test that improves the rate of convergence. In continuous case, we used our modified entropy estimator [10], for Kullback-Leibler information estimation. A comparative study based on simulation results is discussed also.

• Proceedings of the Korean Statistical Society Conference
• /
• 2003.05a
• /
• pp.287-293
• /
• 2003

In this paper we consider the problem of parameter change based on the cusum test proposed by Lee et al. (2003). The cusum test statistic is constructed utilizing the estimator minimizing density-based divergence measures. It is shown that under regularity conditions, the test statistic has the limiting distribution of the sup of standard Brownian bridge. Simulation results demonstrate that the cusum test is robust when there arc outliers.

• Journal of dental hygiene science
• /
• v.21 no.3
• /
• pp.185-197
• /
• 2021

Background: This study aimed at investigating the meal regularity, health, and oral health habits of single Korean households to understand the impact of these factors on the risk of metabolic syndrome, in addition to preventing and managing metabolic syndrome. Methods: Using raw data from the 8th Korea National Health and Nutrition Examination Survey (2019), 274 study subjects, aged 19 to 64, were selected primarily from single adult households. Complex sample statistical analysis was performed using the Predictive Analytics Software Statistics ver. 18.0 program. Results: Regarding the meal regularity in single-person households in Korea, the younger group outperformed the middle-aged group, and those who drank more than once a month performed better than those who drank less than once a month. In terms of oral health, regardless of the age and the income level, participants who ate three meals a day had a higher rate of speech problems and chewing difficulties than those who ate irregularly or regularly on a regular day. Factors influencing the risk of developing metabolic syndrome were age, speech problems, and frequency of toothbrushing. Compared to the younger group, there were 0.361 times more people in the middle-aged group; and compared to those without speech problems, there were 1.161 more people with speech problem. Compared to those who tooth brushed more than four times a day, there were 1.284 more people who tooth brushed 2 to 3 times a day and there were 5.673 times more people who tooth brushed less than once. Conclusion: Based on the study results, it is necessary to implement a program that can plan and apply customized management measures and prevent metabolic syndrome by improving and correcting the health and oral health behaviors of single-person households in Korea. Therefore, active mediation measures, such as support and publicity at the local or national level, should be planned.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.607-618
• /
• 2017

In this paper, we introduce a quadratic stochastic operators on the set of all probability measures of a measurable space. We study the dynamics of the Lebesgue quadratic stochastic operator on the set of all Lebesgue measures of the set [0, 1]. Namely, we prove the regularity of the Lebesgue quadratic stochastic operators.

• Korean Journal of Mathematics
• /
• v.26 no.2
• /
• pp.271-283
• /
• 2018

In this paper, we generelize the Olsen's density theorem to any measurable set, allowing us to extend the main results of H.K. Baek in (Proc. Indian Acad. Sci. (Math. Sci.) Vol. 118, (2008), pp. 273-279.). In particular, we tried through these results to improve the decomposition theorem of Besicovitch's type for the regularities of multifractal Hausdorff measure and packing measure.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.287-303
• /
• 1999

The general solution of the functional equation f1(pr, qs) + f2(ps, qr) = g(p,q) + h(r,s) for p, q, r, s $\in$] 0, 1[will be investigated without any regularity assumptions on the unknown functions f1, f2, g, h:]0.1[->R.

• Proceedings of the KOSOMBE Conference
• /
• v.1998 no.11
• /
• pp.197-198
• /
• 1998

We tested the capability of Pointwise Correlation Dimension(PD2), Approximate Entropy (ApEn) and LZ complexity, as alternative measures of a biological signal. For this purpose, we analyzed standard data and a healthy child's 24-hour heart rate variability. Our conclusion is as follows. First, PD2, ApEn and LZ complexity can be used for discerning chaotic attractor, white noise, and periodic signal. Second, these measures show different characteristics on day and night. Third, these measures can be used for detecting time-varying characteristics of biological signals.

• Speech Sciences
• /
• v.12 no.3
• /
• pp.19-33
• /
• 2005

Tremor is a main factor of parkinsonism. Voice tremor may be the first, later or the only symptom of a neurological disease and its frequency, amplitude, and regularity may differ among the diseases of different neural subsystems. Differential diagnosis between idiopathic Parkinson's disease (IPD) and multiple system atrophy (MSA) has been difficult. This study included three groups: (1) 6 IPD patients; (2) 6 MSA patients; and (3) 20 ageand sex-matched normal controls. The MDVP (Multidimensional Voice Program) was used to analyze the sustained /a/phonation. The results were as follows: (1) frequency perturbation parameters (jitter, sPPQ, Vf0) and FTRI of tremor parameter of two patient groups were statistically different from those of the controls (p < .01); (2) measures were higher in short-term and long-term f0 and amplitude perturbation in MSA than IPD; (3) however, any acoustic parameters between IPD and MSA were not statistically different; except for the rate of frequency tremor, 4$\sim$5 Hz in IPD, 5$\sim$11 Hz in MSA and (4) the pattern of regularity for voice tremor through histogram indicated that amplitude of IPD was irregular while both f0 and amplitude of MSA were irregular. In conclusion, F0, rate of frequency tremor, and pattern of f0 regularity may be predictors for differential diagnosis. These findings might signify that voice tremor of parkinsonism was resulted from modulation of f0.