• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.815-827
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• 2019

It is well known that the denominator of the Dedekind sum s(c, d) divides 2 gcd(d, 3)d and that no smaller denominator independent of c can be expected. In contrast, here we prove that we usually get a smaller denominator in S(H, d), the sum of the s(c, d)'s over all the c's in a subgroup H of order n > 1 in the multiplicative group $(\mathbb{Z}/d\mathbb{Z})^*$. First, we prove that for p > 3 a prime, the sum 2S(H, p) is a rational integer of the same parity as (p-1)/2. We give an application of this result to upper bounds on relative class numbers of imaginary abelian number fields of prime conductor. Finally, we give a general result on the denominator of S(H, d) for non necessarily prime d's. We show that its denominator is a divisor of some explicit divisor of 2d gcd(d, 3).

• The Korean Journal of Food And Nutrition
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• v.25 no.4
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• pp.719-728
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• 2012

This study focused on the yearly-dietary habits, nutrition status, and health of female students residing in Seoul. A number of classes were assess based on their dietary behaviors in oder to attempt to determine differences in their attitudes to nutrition, according to age. The students of class 2011 (sophomore) ate meals more regularly than the female students of the 2008 class (p<0.05). It was found that sophomore female students of class 2008 consumed higher than average nutrient intake. Sophomore female students of the 2011 class consumed lower than average vitamin $B_2$, C, Ca, and Fe intakes. Folic acid in take was lower than average in both groups. Phosphorus and sodium intakes in both groups were excessive (p<0.05). When surveyed, sophomore female students of the 2008 class believed that the most important thing for health was exercise, whereas students of class 2011 believed that nutrient intake was the most important factor (p<0.05). Female students of the 2008 class exercised 1~2 times a week generally, whereas students of class 2011 exercised three times (43.2%) (p<0.05). Therefore, it is necessary to study changes in dietary habits and health status according to the age of students, and develop specific nutrition education programs for female students.

• Journal of Biomedical Engineering Research
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• v.31 no.4
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• pp.328-334
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• 2010

Over the past few years, a considerable number of methods have been proposed and applied for the classification of photoplethysmography (PPG). Most of the previous studies, however, focused on the qualitative description of the pulse type according to specific disease and thus provided ambiguous criteria to interpreters. In order to screen out this problem, we present a quantitative method for the pulse type classification including the second derivative of photoplethysmography (SDPTG). In the PPG signal, we have classified the signal as 4 types using the position and the presence of the dicrotic wave. In addition, we have categorized the SDPTG signal as 7 types using the position and the presence of "c" and "d" wave and the sign of "c" wave. In order to check the efficacy of the proposed pulse type classification rule, we collected pulse signals from 155 subjects with different ages and sex. From the correlation analysis, Class 1(p<0.01) and Class 2(p<0.01) in the PPG signal are significantly correlated with ages. In a similar manner Class A(p<0.01), Class C(p<0.05), Class D(p<0.01), and Class F(p<0.01) in the SDPTG signal are considerably correlated with the ages. From these observations, and some earlier ones [4], [5], we can conclude that since the newly proposed method has objectivity and clarity in pulse type classification, this method can be used as an alternative of previous classification rules including similar age-related characteristics.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.661-676
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• 2017

Let T be a bounded linear operator acting on a complex Hilbert space ${\mathfrak{H}}$. In this paper we introduce the class, denoted ${\mathcal{Q}}(A(k),m)$, of operators satisfying $T^{m{\ast}}(T^{\ast}{\mid}T{\mid}^{2k}T)^{1/(k+1)}T^m{\geq}T^{{\ast}m}{\mid}T{\mid}^2T^m$, where m is a positive integer and k is a positive real number and we prove basic structural properties of these operators. Using these results, we prove that if P is the Riesz idempotent for isolated point ${\lambda}$ of the spectrum of $T{\in}{\mathcal{Q}}(A(k),m)$, then P is self-adjoint, and we give a necessary and sufficient condition for $T{\otimes}S$ to be in ${\mathcal{Q}}(A(k),m)$ when T and S are both non-zero operators. Moreover, we characterize the quasinilpotent part $H_0(T-{\lambda})$ of class A(k) operator.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.979-991
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• 2022

A special class of exponential dispersion models is the class of Tweedie distributions. This class is very significant in statistical modeling as it includes a number of familiar distributions such as Gaussian, Gamma and compound Poisson. A Tweedie distribution has a power parameter p, a mean m and a dispersion parameter 𝜙. The value of the power parameter lies in identifying the corresponding distribution of the Tweedie family. The basic objective of this research work resides in investigating the existence of the implicit estimator of the power parameter of the Tweedie distribution. A necessary and sufficient condition on the mean parameter m, suggesting that the implicit estimator of the power parameter p exists, was established and we provided some asymptotic properties of this estimator.

• The Mathematical Education
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• v.10 no.2
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• pp.4-8
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• 1972

We consider the class (equation omitted) of all k-degenerate graphs, for k a non-negative integer. The class (equation omitted) and (equation omitted) are exactly the classes of totally disconnected graphs and of forests, respectively; the classes (equation omitted) and (equation omitted) properly contain all outerplanar and planar graphs respectively. The advantage of this view point is that many of the known results for chromatic number and point arboricity have natural extensions, for all larger values of k. The purpose of this note is to show that a graph G is (P$^3$)-realizable if G is planar and 3-degenerate.

• Journal of Korean Home Economics Education Association
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• v.14 no.1
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• pp.87-95
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• 2002

The purposel of this study was to examine the effects which the direct and the indirect instructions at a Home Economics class have on improving the learning achievements and attitudes. To accomplish these goals. 90 students. the number of two classes of the first tirade at p high school at Anyang city of Kyonggi province were selected. They are composed of the experimental group and the comparative group. Each group contained 40 students. The former was implemented by indirect instructions and the latter direct instructions. The 'Family and Domestic Life' unit of the first tirade was selected as the study subject to take effects and 30 periods of class were enforced. For the experimental measure of this study. the researcher used a pre-learning test. a learning attitude test. and a learning achievement test as means of measure. The two groups were confirmed as the group having the same quality, So after the experimental measure, the results of the post tests(included a learning achievement test and a learning attitude test) were verified by T-test in order to research the problematic subject. and SPSS/win statistics package was used for the processing of the statistics. The results are following: 1. The direct and the indirect instructions represented the meaningful differences in the learning achievements (p <.05). They represented the meaningful differences in improving the learning achievements of knowledge and understanding(p <.05). It was verified that the (order is more effective than the latter in improving the learning achievements of knowledge and understanding, and They represented the meaningful differences in the improving learning achievements of application (p <.05) 2. They represented the meaningful differences in the learning attitudes at a domestic class(p <.05) The latter is more effective than the former in changing into the positive learning attitudes. In the light of these result7. the direct instructions are effective in improving the learning achievements of knowledge and understanding. and the indirect instructions are effective in improving the learning achievements of application. Also the indirect instructions are more effective than the direct instructions in changing into the positive learning attitude.

• The Korean Journal of Ecology
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• v.27 no.2
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• pp.115-120
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• 2004

Coarse woody debris (CWD, $\ge$ 5 cm in maximum diameter) is an important functional component, especially to nutrient cycling in forest ecosystems. To compare mass and nutrient dynamics of CWD in natural oak forests, a two-year study was conducted at Quercus serrata and Q. variabilis stands in Yangpyeong, Kyonggi Province. Total CWD (snag, stump, log and large branch) and annual decomposition mass (Mg/ha) were 1.9 and 0.4 for the Q. serrata stand and 7.5 and 0.5 for the Q. variabilis stand, respectively. Snags covered 72% of total CWD mass for the Q. variabilis stand and 42% for the Q. serrata stand. Most of CWD was classified into decay class 1 for both stands. CWD N and P concentrations for the Q. variabilis stand significantly increased along decay class and sampling time, except for P concentration in 2002. There were no differences in CWD N concentration for the Q. serrata stand along decay class and sampling time. However, CWD P concentration decreased along sampling time. CWD N and P contents (kg/ha) ranged from 3.5∼4.7 and 0.8∼1.3 for the Q. serrata stand to 22.8∼23.6 and 3.7∼4.7 for the Q. variabilis stand. Nitrogen and P inputs (kg/ha/yr) into mineral soil through the CWD decomposition were 0.7 and 0.3 for the Q. serrata stand and 1.6 and 0.3 for the Q. variabilis stand, respectively. The number of CWD and decay rate were main factors influencing the difference in CWD mass and nutrient dynamics between both stands.

• The korean journal of orthodontics
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• v.35 no.6 s.113
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• pp.420-432
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• 2005

Bolton analysis is widely used to predict tooth size discrepancy. but its accuracy has been challenged. The purpose of this study was to describe true anterior tooth size discrepancies among orthodontic patients and to evaluate the factors that affect true anterior tooth size discrepancies. The subjects consisted of 80 patients with varying malocclusions (Class I. Class II. Class III. and Class III surgery) who were treated orthodontically. Pre-treatment models. set-up models from post-treatment models. and lateral cephalometric radiographs were analyzed The results were as follows. The means. the standard deviations. and ranges of anterior Bolton ratio in the present study were somewhat higher than those of Bolton's samples and Korean normal samples. The number of patients showing maxillary deficiency was larger than that of patients showing maxillary excess in view of true anterior discrepancies. There was a significant difference between anterior Bolton discrepancy from pre-treatment models and true anterior discrepancy from set-up models (p < 0.05) There was no significant difference in true anterior discrepancies among malocclusion groups (p > 0.05). And there was also no significant difference between the male and female groups (p> 0.05). Overbite and the incisal edge thickness of maxillary anterior teeth have little relationship with true anterior discrepancies. Multiple regression analysis showed that true anterior discrepancy was mainly determined by anterior Bolton ratio, upper incisor to occlusal plane angle after treatment. interincisal angle after treatment. and upper right lateral incisor width.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.379-388
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• 2017

Self-dual codes of lengths less than 5 over ${\mathbb{Z}}_p$ are completely classified by the second author [The classification of self-dual modular codes, Finite Fields Appl. 17 (2011), 442-460]. The number of such self-dual codes are also determined. In this article we will extend the results to classify self-dual codes over ${\mathbb{Z}}_{p^2}$ of length less than 5 and give the number of codes in each class. Explicit and complete classifications for small p's are also given.