• 대한수학교육학회지:수학교육학연구
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• 제22권1호
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• pp.53-68
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• 2012

본 연구는 아이들이 문장제 또는 수식 형태의 나눗셈의 결과를 여러 타입의 분수들-진분수, 가분수, 대분수-과 연관시키면서 분수가 가지는 여러 하위 개념 중 몫에 대한 개념 도식을 어떻게 구성해 가는지에 대하여 미국의 5학년 초등학생 네 명을 대상으로 이루어졌다. 실험 결과는 다음과 같았다. 균등분배 상황에서, 아이들은 나눗셈을 두 가지 방식으로 개념화하였다. 첫째, 아이들이 나눗셈을 통해 대분수 형태의 몫을 산출했을 경우, 이 대분수 형태의 몫은 진분수와 가분수 형태의 분수들을 부분-전체의 하위개념이 아니라 몫이라는 하위개념으로 이해하는데 개념적인 기초가 되었다. 둘째, 진분수 형태의 몫을 얻은 경우, 아이들은 그 몫을 곱셈구조의 예로 보려는 경향이 있었다. 즉, $a{\times}b=c$ ; $a{\div}c=\frac{1}{b}$ ; $b{\div}c=\frac{1}{a}$. 하지만, 장제법 계산은 소수 형태의 몫을 생산함으로써 아이들이 이 구조를 깨닫는 것을 어렵게 했다.

• 한국학교수학회논문집
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• 제16권3호
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• pp.583-600
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• 2013

본 연구에서는 무리지수에 대한 현직교사들의 인식과 오류에 대해 조사하기 위하여 K 광역시 관내에 있는 중 고등학교에 재직하고 있는 수학 교사를 대상으로 선정하여 무리지수에 대한 인식과 오류에 대하여 조사하였다. 또한, 무리지수에 대한 현직교사와 예비교사의 인식의 차이를 분석하였다. 그 결과 다음과 같은 결론을 얻었다. 첫째, 현직교사의 정답률은 문제의 유형에 따라 다르게 나타났다. 둘째, 현직교사들은 논리적으로 판단하기 보다는 직관에 의존하여 판단하였다. 셋째, 현직교사들의 판단의 근거는 밑의 형태보다는 지수의 형태에 의존하여 판단하였다.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권4호
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• pp.481-491
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• 2006

Diffy is a simple mathematical puzzle that provides elementary-school students with subtraction practice. The idea appears to have originated in the late nineteenth century with E. Ducci of Itali. Thirty years ago Professor J. Copley of the University of Houston introduced the diffy game to teachers in elementary schools and it widely spreaded out. During the diffy activity we naturally guess many interesting conjectures. First, does diffy always end? Second, does the head of diffy always exist? Third, for an arbitrary given natural number n, is there any possible method to find the diffy with the given length n? In this study I give the necessary and sufficient condition for the existence of the head of diffy. Using this condition I classify all possible heads of diffy and provide an algorithm to find the diffy with any given length n. With this algorithm I find four natural numbers with diffy length 200. To ensure my numbers are correct, I make a diffy program for Mathematica and check they are correct. I suggest the diffy game is good for enlarging the mathematical thinking to all graded students, especially gifted and talented students, It will produce rational consideration and synthetic judgement.

• 한국실내디자인학회논문집
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• 제19권6호
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• pp.141-149
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• 2010

This thesis is designed to take a close look into the characteristics of architectural space through the standard of beauty, which has been created apart from our desires at certain cultural or historical periods of time. It will try to construct the outline of conception about the beauty throughout many centuries. First of all, contents of the research will focus on the aspects, which people have been considering as beauty eversince the ancient time without having any assumptions on its concept. For example, if the beauty of art has been accepted by the theories of modern aesthetics while degrading the beauty of nature, its value could have possibly been much more appreciated. The standard of beauty has been going through the process of change in such history of mankind. The general standard of beauty, which was established in the ancient time was the proportion and harmony between many elements. Afterwards, beauty was expressed as colors and light in medieval times. Expression of beauty using ugly features such as monsters or demons also existed at the time. Beauty has been periodically developing from supernatural to gracious, rational, noble, romantic, religious, mechanical, and today's media. The concept of beauty established from the above has been appearing throughout various culture such as dress and decoration at the given period of time. It would later affect the formation of space as well as decoration for architectures and styles. It will be analyzed throughout the five design elements; style, composition, materials, components, and form. The thesis would like to find the spatial order of beauty from the result of the analysis. The analysis will examine the possibility for which the recomposition of beauty will be provided as a design process for the new era. The Greek beauty represents a shape. The shape represents proportion and the proportion represents given numbers. However, beauty is being expressed by the opposite process at the present time. In other words, computers will arrange the numbers, which would formalize the proportion between the numbers. Beauty would be presented when the shape is presented as certain forms.

• 대한수학회보
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• 제53권1호
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• pp.1-20
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• 2016

The general number field sieve (GNFS) is asymptotically the fastest known factoring algorithm. One of the most important steps of GNFS is to select a good polynomial pair. A standard way of polynomial selection (being used in factoring RSA challenge numbers) is to select a nonlinear polynomial for algebraic sieving and a linear polynomial for rational sieving. There is another method called a nonlinear method which selects two polynomials of the same degree greater than one. In this paper, we generalize Montgomery's method [12] using geometric progression (GP) (mod N) to construct a pair of nonlinear polynomials. We also introduce GP of length d + k with $1{\leq}k{\leq}d-1$ and show that we can construct polynomials of degree d having common root (mod N), where the number of such polynomials and the size of the coefficients can be precisely determined.

• 한국실내디자인학회논문집
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• 제20호
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• pp.62-70
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• 1999

Today's economic environment, which has reached to an unlimitedly competitive edge, is producing numbers of economical values and new type of knowledges under the paradigm of "globalization". With the increasing demands of the values and knowledges, enterprises have to deal with larger amount of information and to utilize it in organized ways than any other time, to adjust to the global economic circumstances. And they have to cope with the changes to the office environment, too. Now every corporation has been laid to the point of time that needs more rational and effective ways of business management and providing work environment. Therefore, this research aims at understanding the basic of new corporate culture and office environment by analyzing the factors that caused changes to that of advanced countries, and providing knowledges for proper reaction and acceptance for these changes.e changes.

• 대한수학회지
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• 제54권2호
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• pp.479-491
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• 2017

We investigate the zeros of Epstein zeta functions associated with positive definite quadratic forms with rational coefficients in the vertical strip ${\sigma}_1$ < ${\Re}s$ < ${\sigma}_2$, where 1/2 < ${\sigma}_1$ < ${\sigma}_2$ < 1. When the class number h of the quadratic form is bigger than 1, Voronin gave a lower bound and Lee gave an asymptotic formula for the number of zeros. Recently Gonek and Lee improved their results by providing a new upper bound for the error term when h > 3. In this paper, we consider the cases h = 2, 3 and provide an upper bound for the error term, smaller than the one for the case h > 3.

• 호남수학학술지
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• 제34권2호
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• pp.279-287
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• 2012

Let $k$ be a field containing the field $\mathbb{Q}$ of rational numbers and let $R=k[x_{ij}{\mid}1{\leq}i{\leq}m,\;1{\leq}j{\leq}n]$ be the polynomial ring over a field $k$ with indeterminates $x_{ij}$. Let $I_t(X)$ be the determinantal ideal generated by the $t$-minors of an $m{\times}n$ matrix $X=(x_{ij})$. Eagon and Hochster proved that $I_t(X)$ is a perfect ideal of grade $(m-t+1)(n-t+1)$. We give a structure theorem for a class of determinantal ideals of grade 3. This gives us a characterization that $I_t(X)$ has grade 3 if and only if $n=m+2$ and $I_t(X)$ has the minimal free resolution $\mathbb{F}$ such that the second dierential map of $\mathbb{F}$ is a matrix defined by complete matrices of grade $n+2$.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.247-262
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• 2006

The main objective of this paper is to study the boundedness character, the periodic character and the global stability of the positive solutions of the following difference equation $x_{n+1}=\frac{{\alpha}x_n+{\beta}x_{n-1}+{\gamma}x_{n-2}+{\delta}x_{n-3}}{Ax_n+Bx_{n-1}+Cx_{n-2}+Dx{n-3}}$, n=0, 1, 1, ... where the coefficients A, B, C, D, ${\alpha},\;{\beta},\;{\gamma},\;{\delta}$ and the initial conditions x-3, x-2, x-1, x0 are arbitrary positive real numbers.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.251-263
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• 2004

In this paper, algorithms for computing the minimal polynomial and the common minimal polynomial of resultant matrices over any field are presented by means of the approach for the Grobner basis of the ideal in the polynomial ring, respectively, and two algorithms for finding the inverses of such matrices are also presented. Finally, an algorithm for the inverse of partitioned matrix with resultant blocks over any field is given, which can be realized by CoCoA 4.0, an algebraic system over the field of rational numbers or the field of residue classes of modulo prime number. We get examples showing the effectiveness of the algorithms.