• 한국수학교육학회지시리즈A:수학교육
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• 제62권4호
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• pp.551-567
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• 2023

짝수와 홀수는 초등학교 수학에서 다뤄지는 내용이지만 어느 학년에서 제시하느냐에 따라 도입하는 활동 및 정의 방식, 짝수와 홀수에 대한 합의 성질을 다루는 활동이 달라진다. 이에 본 연구는 우리나라 수학과 교육과정별 교과서에 제시된 짝수와 홀수 관련 활동을 비교 분석하고, 국외 교과서의 관련 활동을 추가적으로 분석하여 짝수와 홀수의 지도 방안에 대한 시사점을 도출하는 것을 목적으로 하였다. 우리나라 교과서에서는 제4차 수학과 교육과정 시기부터 2007 개정 교육과정까지는 5학년 교과서의 배수와 약수 단원에서 짝수와 홀수를 다루었다. 반면 2009 개정 교육과정 이후로는 1학년 교과서에서 50 또는 100까지의 수를 지도하면서 해당 내용을 다루었다. 또한 짝수와 홀수의 정의는 지도하는 학년과 단원의 특성에 따라 달라졌으며 합의 성질을 다루는 활동은 제3차 수학과 교육과정에 따른 교과서와 일부 수학 익힘에만 제시되었다. 국외 교과서에서는 짝수와 홀수의 지도 시기가 1, 2, 5학년으로 다양하게 나타났으며 그에 따라 제시하는 활동이 모두 다르게 나타났다. 이와 같은 연구의 결과를 바탕으로 본 연구에서는 짝수와 홀수의 지도에 대한 시사점을 논의하였다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1996년도 하계학술대회 논문집 C
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• pp.1453-1455
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• 1996

The odd-even effect of the alkyl chain length of rubbed polyimide Langmuir-Blodgett (LB) surfaces on the extrapolation length of 5CB has been successfully evaluated for the first time by measuring polar anchoring strength. The extrapolation length of 5CB for rubbed PI-LB surfaces with even-numbers is small compared with odd-numbers for alkyl chain lengths of greater than 7 carbons. The extrapolation length of 5CB on rubbed PI-LB surfaces with odd-numbers increases gradually as the temperature increases but tends to diverge near the clearing temperature (Tc=$35.3^{\circ}C$). The extrapolation length diverges because of rapidly decreasing surface order near $T_c$. We suggest that the polar anchoring strength on rubbed PI-LB surfaces with even-number is strong because of relatively high surface ordering caused by more crystalline surfaces. Finally, we conclude that the odd-even effects of the polar anchoring strength in NLCs are strongly related to the character of the polymer and observed clearly for long alkyl chain lengths.

• 한국초등수학교육학회지
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• 제5권1호
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• pp.1-18
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• 2001

반복단위와 패턴의 부분 합성을 인식할 때 반복 패턴에 대한 수학적 발전의 잠재성이 충분히 발휘되고, 두 개의 같은 집합으로 분할 활동을 통해서 짝수 홀수의 인식 지도가 필요하며, 수 패턴을 통한 유도전략을 배워서 덧셈계산에서 가속적일 발전을 위한 교수 순서를 제시한다.

• Journal of Astronomy and Space Sciences
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• 제38권1호
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• pp.23-29
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• 2021

Utilizing a new version of the sunspot number and group sunspot number dataset available since 2015, we have statistically studied the relationship between solar activity parameters describing solar cycles and the slope of the linear relationship between the monthly sunspot numbers and the monthly number of active days in percentage (AD). As an effort of evaluating possibilities in use of the number of active days to predict solar activity, it is worthwhile to revisit and extend the analysis performed earlier. In calculating the Pearson's linear correlation coefficient r, the Spearman's rank-order correlation coefficient rs, and the Kendall's τ coefficient with the rejection probability, we have calculated the slope for a given solar cycle in three different ways, namely, by counting the spotless day that occurred during the ascending phase and the descending phase of the solar cycle separately, and during the period corresponding to solar minimum ± 2 years as well. We have found that the maximum solar sunspot number of a given solar cycle and the duration of the ascending phase are hardly correlated with the slope of a linear function of the monthly sunspot numbers and AD. On the other hand, the duration of a solar cycle is found to be marginally correlated with the slope with the rejection probabilities less than a couple of percent. We have also attempted to compare the relation of the monthly sunspot numbers with AD for the even and odd solar cycles. It is inconclusive, however, that the slopes of the linear relationship between the monthly group numbers and AD are subject to the even and odd solar cycles.

• Macromolecular Research
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• 제10권4호
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• pp.230-235
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• 2002

Alternating polyols of oxymethylene and oxyalkylene were synthesized and used as precursors for thermoplastic poly(ether-ester) elastomers (TPEs). The polyols were synthesized by reacting diols having different methylene units with dichloromethane in the presence of a phase transfer catalyst. The number of methylene units in the alkylene oxides was varied from 3 to 6. TPEs were prepared using the polyols as soft segments and poly(butylene terephthalate) units as hard segments. The polyols and TPEs synthesized were characterized using FTIR, NMR, GPC, DSC, and polarized optical microscopy. The polyols showed a profound odd-even effect on the melting (T$_{m}$) and glass transition temperatures (T$_{g}$). Polyols with odd numbers of methylene groups in the alkylene units have higher transition temperatures than polyols with odd number of methylene groups. The tendency is still kept in TPEs, even though the T$_{g}$ of soft segment in TPEs are slightly higher than those of corresponding neat polyols. The T$_{m}$ and T$_{g}$ of soft segments are almost constant in the range of 20 to 60 wt % contents of soft segments. On the other hand, the normalized heat of fusion of hard segment decreased with increasing the content of loft segment.ent.t.ent.

• 전기의세계
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• 제24권6호
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• pp.92-96
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• 1975

A generalized theroretical method is developed to eliminate a given number of harmonics in AC chopper output waves. The results show that halfwave symmetric and sinusoidal symmetric chopping are required to eliminate all even numbers of harmonics and , at least, M+1 times per half cycle chopping is required to eliminate any M odd number of harmonics in the given effective value of the output wave.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.583-590
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• 2008

In this article, we focuss on. sequences of polynomials with {$\pm1$} coefficients constructed by recursive argument that is known as Rudin-Shapiro polynomials. The asymptotic behavior of these polynomials defines as the ratio of their 2q-norm with 2-norm to be dominated by some number depending on q or "the best" by an absolute constant. In this work we first show the conjecture holds for some finite numbers of m and then introduce a technique that give the result for any positive odd integer m whenever it holds for all pervious even numbers.

• 한국학교수학회논문집
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• 제18권1호
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• pp.1-14
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• 2015

본 논문에서는 짝수와 홀수, 수의 합성과 분해, 받아올림과 받아내림이 각각 있는 (몇)+(몇), (십 몇)-(몇)과 관련된 지도 내용의 개선을 위해 ${\ll}$수학 1-1${\gg}$, ${\ll}$수학 1-2${\gg}$에서의 해당 지도 내용을 검토하였다. 이러한 검토를 통해 얻은 시사점은 다음 세 가지이다. 첫째, 짝수와 홀수의 정의를 재고할 필요가 있다. 또, ${\ll}$수학 1-1${\gg}$에서 짝수와 홀수를 취급하는 것이 합리적인지 재고할 필요가 있다. 둘째, 20 이하의 수의 합성 분해를 취급할 필요가 있다. 즉, 10을 기준으로 하여 '10과 (몇)으로 (십 몇)', '(십 몇)으로 10과 (몇)'이라는 합성 분해의 취급을 고려할 필요가 있다. 또, 10의 합성 분해를 (십 몇)의 합성 분해보다 먼저 취급하는 지도 순서를 고려할 필요가 있다. 셋째, 계산 과정에서의 논리적 비약을 해소할 필요가 있다. 즉, 받아올림이 있는 (몇)+(몇)과 받아내림이 있는 (십 몇)-(몇)의 계산에서 10을 기준으로 하여 '10과 (몇)으로 (십 몇)', '(십 몇)으로 10과 (몇)'이라는 수의 합성 분해의 사용을 고려할 필요가 있다. 또, 필산 형식의 지도에서 일관성을 유지할 필요가 있다.

• 대한수학회지
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• 제45권3호
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• pp.835-840
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• 2008

The main result of this paper shows that every reciprocal Littlewood polynomial, one with {-1, 1} coefficients, of odd degree at least 7 has at least five unimodular roots, and every reciprocal Little-wood polynomial of even degree at least 14 has at least four unimodular roots, thus improving the result of Mukunda. We also give a sketch of alternative proof of the well-known theorem characterizing Pisot numbers whose minimal polynomials are in $$A_N=\{[{X^d+ \sum\limits^{d-1}_{k=0} a_k\;X^k{\in} \mathbb{Z}[X]\;:\;a_k={\pm}N,\;0{\leqslant}k{\leqslant}d-1}\}$$ for positive integer $N{\geqslant}2$.

• 복식
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• 제50권7호
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• pp.113-127
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• 2000

The purpose of this study was to examine the symbolic meaning of oriental numbers based on Yin-Yang(陰陽) theory. Based on the thought of Yin-Yang Wu-Hsing(陰陽五行), the number was divided the number of the heaven (positive number) 1, 3. 5, 7, 9 from the number cf the earth(negative number) 2. 4, 6, 8, 10. It was descrived very well in the dress and its ornaments and the folk customs. In the costume of the Court, there were 9, 7, 5, 3 patterns costume for the king and queen. Even though an even number, 12 patterns costume for the emperor symbolized 12 months and made it of the principal of the universe. Korean traditional costume Han-bock(韓服) was formed with the three dimentional principal of circle (圓.$\bigcirc$), square(方.$\square$) and triangularity(角.$\Delta$). In the middle of odd numbers, number 3 was regarded as a holy number of the heaven (天), the earth(地) and a man(人). Taken for a highest number. number 3 had the symbolism of wishes for good fortune. Number 10 and number 100, which meant the fullness and the long life, were used regularly. With Ten longevity patterns(十長生紋), the feast of a hundred-day-old baby, our race prayed for the healthy long life. As mentioned above. the symbolism of the number though the costume prefered the positive number to the negative one. Accommodating to the universal principal and the cycle. The deep meaning and the symbolism of the number has been implied the mental wishes.