• 충청수학회지
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• 제23권1호
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• pp.169-176
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• 2010

Let $k={\mathbb{F}}_q(T)$ and ${\mathbb{A}}={\mathbb{F}}_q[T]$. In this paper, we obtain the the criterion for the parity of the ideal class number h(${\mathcal{O}}_K$) of the real biquadratic function field $K=k(\sqrt{P_1},\;\sqrt{P_2})$, where $P_1$, $P_2{\in}{\mathbb{A}}$ be two distinct monic primes of even degree.

• 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.

• Korean Journal of Mathematics
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• 제30권2호
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• pp.361-362
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• 2022

It is shown that the p-part of the class number of the lower layers of a cyclotomic ℤ_p-extension can grow exponentially.

• 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 $1{\leq}i{\leq}{\ell}-1$.

• 보건행정학회지
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• 제13권4호
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• pp.99-114
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• 2003

This study was performed to determine the effect of social class distribution as measured by lower social class rate on all cause and cause specific mortality in Korea. I obtained data on social class, fiscal autonomy of municipalities, number of medical doctors, region(Si/Gun) from 1955 Korea Census Data and Regional Statistics Data. And all of the data on mortality adjusted for age for 1995 for each district from the National Statistics Office. Lower social class rate ranged from 18.9％ for Kangnam gu to 85.7％ for Imsil gun and age standardized mortality ranged from 385/100,000 population for Kangnam go to 803/100,000 population for Sinan gun. Lower social class showed had a significant correlation with total mortality adjusted for age(r=0.81, p<0.0001). The association of the rate to total mortality remained highly significant after adjusted for number of medical doctors per 1,000 population, fiscal autonomy of municipalities and region(p<0.0001). Effects of the lower social class were also found for neoplasm (p=0.0008)； cardiovascular disease (p<0.0001)； infectious disease(p=0.0115)； respiratory disease(p=0.0085)； gastrointestinal disease(p<0.0001)； accident ＆ poisoning (p<0.0001). The findings suggest that policies that deal with the inequality in social class may have an important impact on the health of the population.

• 호남수학학술지
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• 제44권1호
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• pp.146-147
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• 2022

Let 𝔹_p,n be the n-th layer of the cyclotomic ℤ_p-extension over the rationals. In this note, we will prove that the p-class group of 𝔹_p,n is trivial for all n by elementary method.

• 대한수학회논문집
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• 제16권4호
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• pp.595-606
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• 2001

Using p-adic class number formula, we derive a congru-ence relation for class numbers of the simplest cubic fields which can be considered as a cubic analogue of Ankeny-Artin-Chowlas theo-rem, Furthermore, we give an elementary proof for an upper bound for the class numbers of the simplest cubic fields.

• Restorative Dentistry and Endodontics
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• 제38권2호
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• pp.79-84
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• 2013

Objectives: This study aimed to investigate the effect of clinical clerkship-associated achievements, such as performance of procedures at the student clinic, observation, and attitude towards a clerkship, on the objective structured clinical examination (OSCE) scores of dental students graduating in restorative dentistry. Materials and Methods: The OSCEs consisted of two stations designed to assess students' clinical skills regarding cavity preparation for a class II gold inlay and a class IV composite restoration. The clerkship achievements, consisting of the number of student clinical procedures performed, observation-related OSCE, and scores of their attitudes towards a conservative dentistry clerkship, were assessed. Correlation and multiple regression analyses were conducted. Results: The correlation coefficient between the OSCE scores for cavity preparation for a class II gold restoration and clerkship attitude scores was 0.241 (p < 0.05). Regarding a class IV composite restoration, OSCE scores showed statistically significant correlations with the observation (r = 0.344, p < 0.01) and attitude (r = 0.303, p < 0.01) scores. In a multiple regression analysis, attitudes towards a clerkship (p = 0.033) was associated with the cavity preparation for a class II gold inlay OSCE scores, while the number of procedure observations (p = 0.002) was associated with the class IV composite restoration OSCE scores. Conclusions: The number of clinical procedures performed by students, which is an important requirement for graduation, showed no correlation with either of the OSCEs scores.

• 대한수학회지
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• 제48권6호
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• pp.1249-1268
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• 2011

For imaginary quadratic number fields F = $\mathbb{Q}(\sqrt{{\varepsilon}p_1{\ldots}p_{t-1}})$, where ${\varepsilon}{\in}${-1,-2} and distinct primes $p_i{\equiv}1$ mod 4, we give condition of 8-ranks of class groups C(F) of F equal to 1 or 2 provided that 4-ranks of C(F) are at most equal to 2. Especially for F = $\mathbb{Q}(\sqrt{{\varepsilon}p_1p_2)$, we compute densities of 8-ranks of C(F) equal to 1 or 2 in all such imaginary quadratic fields F. The results are stated in terms of congruence relation of $p_i$ modulo $2^n$, the quartic residue symbol $(\frac{p_1}{p_2})4$ and binary quadratic forms such as $p_2^{h+(2_{p_1})/4}=x^2-2p_1y^2$, where $h+(2p_1)$ is the narrow class number of $\mathbb{Q}(\sqrt{2p_1})$. The results are also very useful for numerical computations.

• 대한수학회논문집
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• 제13권2호
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• pp.233-242
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• 1998

Let $k = Q(\sqrt{m})$ be a real quadratic field. In this paper, the following theorems on p-divisibility of the class number h of k are studied for each prime pp. Theorem 1. If the discriminant of k has at least three distinct prime divisors, then 2 divides h. Theorem 2. If an odd prime p divides h, then p divides $B_{a,\chi\omega^{-1}}$, where $\chi$ is the nontrivial character of k, and $\omega$ is the Teichmuller character for pp. Theorem 3. Let $h_n$ be the class number of $k_n$, the nth layer of the $Z_p$-extension $k_\infty$ of k. If p does not divide $B_{a,\chi\omega^{-1}}$, then $p \notmid h_n$ for all $n \geq 0$.