• 충청수학회지
• /
• 제27권2호
• /
• pp.183-203
• /
• 2014

We examine fundamental units of quadratic function fields from continued fraction of $\sqrt{D}$. As a consequence, we give another proof of geometric analog of Ankeny-Artin-Chowla-Mordell conjecture and bounds for class number, and study real quadratic function fields of minimal type with quasi-period 4.

• 대한수학회지
• /
• 제54권3호
• /
• pp.877-896
• /
• 2017

In this paper, the complete convergence and complete moment convergence for a class of random variables satisfying the Rosenthal type inequality are investigated. The sufficient and necessary conditions for the complete convergence and complete moment convergence are provided. As applications, the Baum-Katz type result and the Marcinkiewicz-Zygmund type strong law of large numbers for a class of random variables satisfying the Rosenthal type inequality are established. The results obtained in the paper extend the corresponding ones for some dependent random variables.

• 대한수학회지
• /
• 제55권1호
• /
• pp.131-146
• /
• 2018

We generate ring class fields of imaginary quadratic fields in terms of the special values of certain eta-quotients, which are related to the relative norms of Siegel-Ramachandra invariants. These give us minimal polynomials with relatively small coefficients from which we are able to solve certain quadratic Diophantine equations concerning non-convenient numbers.

• 한국식품영양학회지
• /
• 제2권1호
• /
• pp.61-72
• /
• 1989

This study was conducted to gather the baseline data on realities of experimental-practice and opinions toward spot-practice, and to examine how to cope with the problems raised at the Department of Food and Nutrition of Junior Technical College in Korea. Questionnaires were gathered from 42 chairmans of the Department of Food and Nutrition and 140 Present dieticians worked in Seoul, Bucheon am Seongnam area. The results are as follows, First, as a whole, each college had 2~3 experimental laboratory (Lab), in which Cooking Science Lab. Chemistry Lab and Microbiology Lab were occurred at higher frequency as Lab's name. Second, the numbers per experimental-practice class were more than 40 at most colleges. 85% of Present dieticians have answered to feel too much numbers per the class during their college days, whereas professors' opinions toward the numbers per class were suitable at 20~30 persons per class. Third, professors' opinion toward the adquate ratio of the theory subject classes to experimental subject classes was suitable at 60 : 40. Dieticians answered to take the theory subject classes partly or mostly on behalf of the experimental-practice classes. Fourth, the main reasons which inhibited normal experimental-practice class were the class for emphasis on examination, the shortage of experiment budget, the excess of class members, the shortage of experimental Lab Also, this results showed same propensity to present dieticians' opinion toward the same question above. Fifth, among the experimenta1-practice subjects established at the Department of Food and Nutrition, Diet Therapy Lab was highest frequency class emphasized on theory followed by Nutrition Counselling Lab, Food Processing and Storage Lab, Food Hygiene Lab and Food Microbiology Lab in that order. Here, Basic Chemistry Lab, Biochemistry Lab, Food Microbiology Lab were pointed as subjects far from the present task of dieticians. Sixth, Department of Food and Nutrition, as a whole, has conferred with spot-practice arrangement About 50% (all who want to join spot-practice) of second year students took part in spot-practice. In the other way, all colleges except for 2 colleges didn't give the credit for the spot-practice system. Seventh, according to the on analysis on spot-practice places, manufacturing company was at highest frequcney followed by hospitals, elementary school having group feeding system in that order. Especially, 16.7% (5 colleges) of the total colleges sent the students to the research institute related to food industry for spot-practice experience. Eighth, Professors' opinions toward the spot-practice time and period were preferable on summer vacation of second year and for 1~2 weeks, respectively. On the contrary, 74 dieticians answered to the adquate period as for 4 weeks. Ninth, 86 dieticians of the total 140 answered to complete the spot-practice during their college days, which helps the present task of them. Lacks of spot-practice program, Lacks of comprehension of upper personals and lacks of group feeding equipments ranks higher as difficulties in spot-practice management.

• 대한수학회보
• /
• 제52권5호
• /
• pp.1559-1568
• /
• 2015

The relative class number $H_d(f)$ of a real quadratic field $K=\mathbb{Q}(\sqrt{m})$ of discriminant d is the ratio of class numbers of $O_f$ and $O_K$, where $O_K$ denotes the ring of integers of K and $O_f$ is the order of conductor f given by $\mathbb{Z}+fO_K$. In a recent paper of A. Furness and E. A. Parker the relative class number of $\mathbb{Q}(\sqrt{m})$ has been investigated using continued fraction in the special case when $(\sqrt{m})$ has a diagonal form. Here, we extend their result and show that there exists a conductor f of relative class number 1 when the continued fraction of $(\sqrt{m})$ is non-diagonal of period 4 or 5. We also show that there exist infinitely many real quadratic fields with any power of 2 as relative class number if there are infinitely many Mersenne primes.

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

• 한국도서관정보학회지
• /
• 제24권
• /
• pp.449-484
• /
• 1996

The purpose of this study is to analyze the structural model of classification, to compare enumerative schemes with faceted schemes and finding the facted schems used in the Dewey Decimal Classification. The Structural model of classifications can be divided to enumerrative schemes and facted schemes(analytico-synthetic schemes). Enumerative schemes represent the various kind of subject in different ways and have to not only list all existing combinations of subjects but also any of potential subjects. Faceted schemes is the decomposition of concepts into all possible characteristics which are known as facets. DDC was originally created as enumerative, but over 20 editions has moved increasing towards synthetic features such as the add instructions, and the seven auxiliary tables. Many DDC class numbers found in the Schedules may be subdivied by another number(or part of it) that has been drawn from the Schedules or auxiliary tables. This process of subdividing class numbers is called number building and it can be done only when there are number building instruction in the Schedules or Tables.

• 한국경영과학회지
• /
• 제32권3호
• /
• pp.1-15
• /
• 2007

In this paper, the return link of interactive GEO satellite network providing multimedia services is considered. First, we classify data by delay characteristics, and analyze the numbers of expected lost packets and expected delay packets for each data class of each terminal. Next we mathematically formulate optimal rate scheduling model to minimize the weighted sum of the numbers of expected lost packets and expected delay packets considering priority of each data class. We also suggest a dynamic rate scheduling scheme based on Lagrangean relaxation technique and subgradient technique to solve the proposed model in a fast time. Extensive experiments show that the proposed scheme provides encouraging results.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제47권1호
• /
• pp.27-47
• /
• 2008

In this paper, we study the effect of writing activity as mathematical communication on the students's mathematics achievement, learning attitude, and mathematical tendency. For this purpose, we construct a experimental class and then analyze the students' change in those aspects after applying three-divided-note writing activity and colleague feedback on their works those students are in the experimental class. As a result of the experiment, we find that three-divided-note writing activity and colleague feedback made some significant changes on the students achievement in mathematics, learning attitude, but does not affect on mathematical tendency. We also offer some suggestions for further research. Firstly, the mathematical communication ability must be stressed in mathematics education. For this purpose, we need to develop the teaching and the evaluation method to use not only writing but also reading, speaking, and listening skills so that many teachers can apply this method easily to their classes. Second, we need to fix some realistic problems such as fair evaluation , the numbers of students per class, the numbers of lesson, and too much extra-work, and so on. Thirdly, we suggest to explore some methods for extending three- divided-note writing activity to evaluate mathematical essay and to study educational effects of colleague feedback on mathematics performance assessment.

• 대한수학회보
• /
• 제33권3호
• /
• pp.397-409
• /
• 1996

Let X be a connected compact polyhedron and $f : X \to X$ a selfmap of X. The Reidemeister number of f is denoted by R(f).