• 대한수학회보
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• 제60권2호
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• pp.315-323
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• 2023

First, we recall the results for prime-producing polynomials related to class number one problem of quadratic fields. Next, we give the relation between prime-producing cubic polynomials and class number one problem of the simplest cubic fields and then present the conjecture for the relations. Finally, we numerically compare the ratios producing prime values for several polynomials in some interval.

• East Asian mathematical journal
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• 제37권5호
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• pp.613-617
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• 2021

Abstract. For a positive square-free integer m, let K = ℚ($\sqrt{m}$) be a real quadratic field. The relative class number H_d(f) of K of discriminant d is the ratio of class numbers 𝒪_K and 𝒪_f, where 𝒪_K is the ring of integers of K and 𝒪_f is the order of conductor f given by ℤ + f𝒪_K. In 1856, Dirichlet showed that for certain m there exists an infinite number of f such that the relative class number H_d(f) is one. But it remained open as to whether there exists such an f for each m. In this paper, we give a result for existence of real quadratic field ℚ($\sqrt{m}$) with relative class number one where the period of continued fraction expansion of $\sqrt{m}$ is 6.

• 대한수학회보
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• 제45권2호
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• pp.375-384
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• 2008

Let $k={\mathbb{F}}_q(T)$ and ${\mathbb{A}}={\mathbb{F}}_q[T]$. Fix a prime divisor ${\ell}$ q-1. In this paper, we consider a ${\ell}$-cyclic real function field $k(\sqrt[{\ell}]P)$ as a subfield of the imaginary bicyclic function field K = $k(\sqrt[{\ell}]P,\;(\sqrt[{\ell}]{-Q})$, which is a composite field of $k(\sqrt[{\ell}]P)$ wit a ${\ell}$-cyclic totally imaginary function field $k(\sqrt[{\ell}]{-Q})$ of class number one. und give various conditions for the class number of $k(\sqrt[{\ell}]{P})$ to be one by using invariants of the relatively cyclic unramified extensions $K/F_i$ over ${\ell}$-cyclic totally imaginary function field $F_i=k(\sqrt[{\ell}]{-P^iQ})$ for $1{\leq}i{\leq}{\ell}-1$.

• 대한수학회보
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• 제58권6호
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• pp.1463-1481
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• 2021

Divisibility properties of harmonic numbers by a prime number p have been a recurrent topic. However, finding the exact p-adic orders of them is not easy. Using class numbers of number fields and Bernoulli numbers, we compute the exact p-adic orders of harmonic type sums. Moreover, we obtain an asymptotic formula for generalized harmonic numbers whose p-adic orders are exactly one.

• 대한치과기공학회지
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• 제29권2호
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• pp.197-211
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• 2007

With the development of orthodontics and increasing concerns on physical appearance, the number of patients has been steadily increasing. It is quite important not only to make effective cure plans and accurate diagnoses but also to have a thorough grasp of patients' malocclusion types and their occurrence frequency, in addition to patients' personality in order to cure the patients appropriately. This study is based on 946 malocclusion patients who had visited Chong-A Dental Hospital from 1999 to 2004 and investigated their aspects of malocclusion and characteristics of their gender, age and residence. The results are as follows. 1. The number of patients per year had been decreased until 2001, after which year the number had fluctuated. The number was the largest in 1999, 169 and the smallest in 2001, 140. Female occupied 68.0% of the total, twice as many as male, 32.0%) 2. Based on the Angle's classification, 19 or over year - old group was the largest of the total, 59.3% and 6 or younger year - old group, the smallest, 0.5%. The 19 or over year old group was less than a half of the total (47.4%) in 2003 and there were no patients who belonged to the 6 or younger year - old group in 2003 and 2004. 3. Distributions on the types of malocclusion have shown that 39.9 % of the total are in the Class I, the largest, 31.0% in the Class I and 29.2 in the Class II, the smallest. 1) The number of the ClassI was 73, the largest, that of the Class III being 35, the smallest in 1999. On the whole, the number of the Class I accounted for the largest part of the total. 2) The number of male patients in the Class II was the smallest, generally being the largest in the Class I. In case of female, that of the Class III was the smallest. 3) Based on the age, the Class I was the highest in between 7 and 13 age group, the Class III the lowest. The Class I occupied the largest around 40%. 4) In the shape of physiognomy, the meso occupied the largest part among all the Class, of which the Class II was the highest, 64.2%. The bracy was the largest in the Class I, and the dolicho in the Class III. 5) In the profile, the convex shape was the largest in the Class I and II, and especially in the Class II, over 3/4 of the total, 75.4%. In contrast, the direct shape was the largest in the Class III and the sunken shape occupied 33.3%, which was nearly ten times more than the case of the Class I and III. 6) In the asymmetry of physiognomy, the number of patients of the Class IIIwas the largest, 34.1% and that of the Class II, the smallest, 19.5%. It was found that about one fourth of the malocclusion patients were under the asymmetry of physiognomy. 4. In the distribution of patients' residence, 81.4% were from the Seoul Metropolis and 48.2% from Gangnam-Gu where Chong-A Dental Hospital is located and Seocho-Gu and Songpa-Gu which are adjacent to Gangnam-Gu.

• 보건행정학회지
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• 제14권1호
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• pp.148-168
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• 2004

To investigate the effect of parents' social class on birthweight in Korea during the period of transition to a market economy, 1995-2001. Methods: All births resulting from pregnacies reported in 1995-22001(n=4,298,374) were studied with respect to social variation in birthweight. The results were adjusted for maternal age, parity, parents' education, gestational age, total births, the dead births among total births, the number of births in one delivery. Results: Between 1995 and 2001, mean birth weight was 3271g and low birth rate was 3.41%. Maternal education, faternal education, parents' occupation, the number of birth in one delivery, total births, gestational age, and the number of deaths among. total births were all independently related to the birthweight. Parents with lower education showed higher low-birthweight rates compared with parents with university level of education(OR: 2.16 for mother and 1.68 for father). Especially, mother's education showed stronger relationship with birthweight than fathers' education. The differences in birth weight by parents' social class, especially parents' educational level became stronger between 1995 and 2001. Discussion: This study suggests that the social differences of birth weight were increasing in order 1995 to 2001. Especially, this increasing tendency in variation in birth weight by social class was shown after economic crisis, 1998.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.121-123
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• 2016

In this paper, we compute the number of distinct centralizers and commutativity degree of a class of finite groups. These computations produce a further class of examples of groups answering one question raised by Belcastro and Sherman and another one raised by Lescot.

• 지역사회간호학회지
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• 제30권4호
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• pp.449-459
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• 2019

Purpose: The aim of this study is to explore different types of self-rated health trajectories among one-person households in Korea. Methods: We used five time-point data derived from Korea Health Panel (2011~2015). A latent growth curve modeling was used to assess the overall feature of self-rated health trajectory in one-person households, and a latent class growth modeling was used to determine the number and shape of trajectories. We then applied multinomial logistic regression on each class to explore the predicting variables. Results: We found that the overall slope of self-rated health in one-person households decreases. In addition, latent class analysis demonstrated three classes: 1) High-Decreasing class (i.e., high intercept, significantly decreasing slope), 2) Moderate-Decreasing class (i.e., average intercept, significantly decreasing slope), and 3) Low-Stable class (i.e., low intercept, flat and nonsignificant slope). The multinomial logistic regression analysis showed that the predictors of each class were different. Especially, one-person households with poor health condition early were at greater risk of being Low-Stable class compared with High-Decreasing class group. Conclusion: The findings of this study demonstrate that more attentions to one-person households are needed to promote their health status. Policymakers may develop different health and welfare programs depending on different characteristics of one-person household trajectory groups in Korea.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2005년도 학술발표회 논문집
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• pp.578-582
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• 2005

In this study, the conceptual foundation and development process of the Antecedent soil Moisture Condition(AMC) in SCS runoff curve number method are reviewed. Although the runoff volume is very sensitive with AMC condition, the AMC class limits developed in SCS(1972) are used in rainfall-runoff analysis without careful consideration. Tn this study, following the SCS curve number development process, rainfall-runoff characteristics of the Jang-Pyung subbasin subject to the Pyung-Chang River basin are analyzed to evaluate the reasonability of the AMC class limits at present. The New AMC class limits are proposed by the sensitive analysis of the antecedent rainfall - curve number value. As a result, the classification value of AMC-I with II is 22mm of antecedent 5-day rainfall amount, and the classification of AMC-II with III is 117mm in growing season. When the New AMC class limits are applied to Jang-Pyung subbasin, AMC probability distribution shows that the AMC-II has increased remarkably even though the AMC-I has a little higher value. But the AMC-III has the smallest one. According to the conceptual basis of the curve number method, the AMC probability distribution, the New AMC class limits adopted, gives reasonable results.

• 대한수학회논문집
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• 제28권4호
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• pp.735-740
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• 2013

In this paper, we will introduce the notion of the real quadratic function fields of minimal type, which is a function field analogue to Kawamoto and Tomita's notion of real quadratic fields of minimal type. As number field cases, we will show that there are exactly 6 real quadratic function fields of class number one that are not of minimal type.