• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1305-1315
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• 2022

Let u be a function on a connected finite graph G = (V, E). We consider the mean field equation (1) $-{\Delta}u={\rho}\({\frac{he^u}{\int_Vhe^ud{\mu}}}-{\frac{1}{{\mid}V{\mid}}}\),$ where ∆ is 𝜇-Laplacian on the graph, 𝜌 ∈ ℝ\{0}, h : V → ℝ⁺ is a function satisfying min_x∈V h(x) > 0. Following Sun and Wang [15], we use the method of Brouwer degree to prove the existence of solutions to the mean field equation (1). Firstly, we prove the compactness result and conclude that every solution to the equation (1) is uniformly bounded. Then the Brouwer degree can be well defined. Secondly, we calculate the Brouwer degree for the equation (1), say $$d_{{\rho},h}=\{{-1,\;{\rho}>0, \atop 1,\;{\rho}<0.}$$ Consequently, the equation (1) has at least one solution due to the Brouwer degree d_𝜌,h ≠ 0.

• Structural Engineering and Mechanics
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• v.77 no.3
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• pp.355-368
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• 2021

The time-varying mean (TVM) component of non-stationary wind speeds is commonly extracted utilizing empirical mode decomposition (EMD) in practice, whereas the accuracy of the extracted TVM is difficult to be quantified. To deal with this problem, this paper proposes an approach to identify and extract the optimal TVM from several TVM results obtained by the EMD. It is suggested that the optimal TVM of a 10-min time history of wind speeds should meet both the following conditions: (1) the probability density function (PDF) of fluctuating wind component agrees well with the modified Gaussian function (MGF). At this stage, a coefficient p is newly defined as an evaluation index to quantify the correlation between PDF and MGF. The smaller the p is, the better the derived TVM is; (2) the number of local maxima of obtained optimal TVM within a 10-min time interval is less than 6. The proposed approach is validated by a numerical example, and it is also adopted to extract the optimal TVM from the field measurement records of wind speeds collected during a sandstorm event.

• Radiation Oncology Journal
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• v.11 no.1
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• pp.109-117
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• 1993

To analyze biochemical changes of liver function following combined radiotherapy and hyperthermia, we reviewed retrospectively 37 patients with hepatocellular carcinoma treated with radiotherapy and hyperthermia between July 1988 and December 1990 at Department of Radiation Oncology, Yonsei University College of Medicine. Mean age was 52.7 years and male to female ratio was 11:1. The patients were classified as follows; to A and B group by Child's classification, to M and L group by irradiated volume, and subclassified into BM, BL, AM and AL group according to the combination of Child's classification and irradiated volume. Radiation dose to the primary tumor was 3060 cGy with daily 180 cGy, 5 fraction per week using 10 MV or 4 MV linear accelerator. Hyperthermia (Thermotron RF-8) was performed more than 4 times in all patients. Biochemical parameters including albumin (Alb), total bilirubin (T. Bil), aspartate aminotransferase (AST or SGOT), alanine aminotransferase (ALT or SGPT), and alkaline phosphatase (ALP) were regularly followed from 1 week before the treatment to 3 months after the treatment. The results are summerized as follows; 1) In all the patient, mean ALP level peaked at 1 month, decreased at 2 months, slightly increased at 3 months after the treatment. Mean SGOT and SGPT levels peaked at 1 month after the treatment. Mean T. Bil level increased continuously and highest at 3 months after the treatment. Mean Alb level did not show significant changes.; 2) Mean ALP level retured to normal level at 3 month after the treatment in A but increased in B group and the differences were statistically significant (p<0.01). Mean SGOT and SGPT levels peaked 1 month in A and 2 months after the treatment in B group. All the biochemical parameters did not show significant difference between M and L group. Mean ALP level increased at 3 months after the treatment in BM and BL groups and decreased in AM and AL groups. Mean SGOT level increased at 3 months after the treatment in BL groups.; 3) Hepatic failure occurred within 3 months after the treatment in 4 patients, all of whom were in BL group. It is suggested that pre-treatment liver function and irradiated volume influence biochemical changes of liver in patients with hepatocellular carcinoma following combined radiotherapy and hyperthermia, and this treatment modality appears generally to be safe but might cause hepatic failure particularly in patient with poor liver function and large treatment volume.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.2
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• pp.161-170
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• 2022

It is presented a Banach space of functions of bounded mean oscillation BMO type.

• Journal of the Korean Statistical Society
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• v.25 no.4
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• pp.515-527
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• 1996

It has been known for mean field models that the limiting distribution reflecting the asymptotic behavior of the system is non-Gaussian at the critical state. Recently, however, Papangelow showed for the critical Curie-Weiss mean field model that there exist Gaussian structures in the asymptotic behavior of the total magnetization. We construct Gaussian structures existing in the internal fluctuation of the system for the critical case of a generalized Curie-Weiss mean field model.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.789-798
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• 2000

The mean residual function is the expected remaining life of an item at age x. The problem of trend change in the mean residual life is great interest in the reliability and survival analysis. In this paper, we develop a family of test statistics for testing whether or not the mean residual life changes its trend. The asymptotic normality of the test statistics is established. Monte Carlo simulations are conducted to study the performance of our test statistics.

• Asian-Australasian Journal of Animal Sciences
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• v.19 no.12
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• pp.1671-1677
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• 2006

A total of two hundred twenty eight half-sib chickens were scored for allele size at 20 microsatellite loci to estimate individual heterozygosity and mean $d^2$. The averages of microsatellite heterozygosity, allele per locus and mean $d^2$ were 0.39, 3.6 and 49, respectively. The body weight was measured biweekly from birth to twelve weeks of age. Gompertz function was assumed to simulate body weight and to estimate the growth model parameters. Due to sex effect on body weight, the regression of body weight on heterozygosity as well as on mean $d^2$ in males and females was analyzed separately in the present study. Positive correlations were found between microsatellite heterozygosity and body weight in males and females (p<0.05). Positive correlation also observed between individual heterozygosity and simulated maximum daily gain estimated from Gompertz function in female chickens (p<0.05). There were no significant correlations between mean $d^2$ and body weight. The results suggest that local effect hypothesis could explain the correlations between heterozygosity and fitness-related traits in the domesticated chicken population, rather than the general effect hypothesis does.

• Journal of the Korean Society of Laryngology, Phoniatrics and Logopedics
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• v.12 no.2
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• pp.121-125
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• 2001

Singing requires exquisite coordination between the respiratory and phonatory system to efficiently control glottal airflow. Respiratory function and vocal aerodynamics were investigated in six female professional sopranos and in six female subjects without vocal training. All sopranos had more than 15 years of formal classic vocal training. Pulmonary function test data on simple pulmonary function, flow volume curve, static lung volumes, maximum inspiratory pressure(MIP), and maximum expiratory pressure(MEP) were obtained from all subjects. Vocal aerodynamic studies of maximum phonation time(MPT), phonation quotient, and mean glottal flow rates (MFR) were also measured in all subjects. Simple pulmonary function in professional sopranos was generally the same as that of other female subjects without vocal training. However, MIP and MEP showing respiratory muscle forces were significantly elevated in professional sopranos, compared to those of other female subjects without vocal training. Maximum phonation times and phonation quotient in sopranos are longer than those of other female subjects even though there were no differences in simple pulmonary function. High-pitched tones were made with significantly higher mean glottal flow rates(GFR) in normal subjects than low-pitched tones, whereas no changes in GFR were found in sopranos. The result indicated that sopranos demonstrated significant improvements in aerodynamic measures of GFR, maximum phonation time, suggesting an increase in glottal efficiency.

• The Journal of Internal Korean Medicine
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• v.31 no.1
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• pp.113-117
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• 2010

Objectives : in recent years, there have been some case reports about liver injuries suspected to be caused by Heshouwu, the root of Polygonum multiflorum. So, I investigated liver function tests of patients who had taken Heshouwu, to know whether Heshouwu was hepatotoxic. Methods : I surveyed whether Heshouwu caused liver injury in patients, who had been admitted and taken Heshouwu at Dongguk University International Hospital, from May 2005 to July 2008. I looked over all the liver function tests of those patients, done during medication and 30 days after. Results : Among 1,449 inpatients, there were 124 patients who had taken Heshouwu. Among those 124 patients, 14 cases whose liver function tests were abnormal before medication were excluded. 69 cases who did not take liver function test 30 days after were also excluded. As a result, 41 patients were enrolled, and their mean dosage was 14.04(8-24) g/day, and the mean medication period was 13.8 (1-89) days. During and after medication, there were no abnormal liver function test results at all, in the enrolled cases. Conclusions : Roughly speaking, according to the above results, it seems that taking Heshouwu for about two weeks as per the commonly taken dosage did not cause hepatotoxicity, though we needs more laboratory and clinical research to reach a more definitive conclusion.

• International Journal of Contents
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• v.13 no.4
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• pp.23-28
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• 2017

Of the total economic loss caused by disasters, 40% are due to floods and floods have a severe impact on human health and life. So, it is important to monitor the water level of a river and to issue a flood warning during unfavorable circumstances. In this paper, we propose a modified error function to improve a hydrological modeling using a multi-layer perceptron (MLP) neural network. When MLP's are trained to minimize the conventional mean-squared error function, the prediction performance is poor because MLP's are highly tunned to training data. Our goal is achieved by preventing overspecialization to training data, which is the main reason for performance degradation for rare or test data. Based on the modified error function, an MLP is trained to predict the water level with rainfall data at upper reaches. Through simulations to predict the water level of Nakdong River near a UNESCO World Heritage Site "Hahoe Village," we verified that the prediction performance of MLP with the modified error function is superior to that with the conventional mean-squared error function, especially maximum error of 40.85cm vs. 55.51cm.