• 제목/요약/키워드: S series

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CLEANNESS OF SKEW GENERALIZED POWER SERIES RINGS

  • Paykan, Kamal
    • 대한수학회보
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    • 제57권6호
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    • pp.1511-1528
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    • 2020
  • A skew generalized power series ring R[[S, 𝜔]] consists of all functions from a strictly ordered monoid S to a ring R whose support contains neither infinite descending chains nor infinite antichains, with pointwise addition, and with multiplication given by convolution twisted by an action 𝜔 of the monoid S on the ring R. Special cases of the skew generalized power series ring construction are skew polynomial rings, skew Laurent polynomial rings, skew power series rings, skew Laurent series rings, skew monoid rings, skew group rings, skew Mal'cev-Neumann series rings, the "untwisted" versions of all of these, and generalized power series rings. In this paper we obtain some necessary conditions on R, S and 𝜔 such that the skew generalized power series ring R[[S, 𝜔]] is (uniquely) clean. As particular cases of our general results we obtain new theorems on skew Mal'cev-Neumann series rings, skew Laurent series rings, and generalized power series rings.

On the Strong Law of Large Numbers for Arbitrary Random Variables

  • 남은우
    • 한국통계학회:학술대회논문집
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    • 한국통계학회 2002년도 춘계 학술발표회 논문집
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    • pp.49-54
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    • 2002
  • For arbitrary random variables {$X_{n},n{\geq}1$}, the order of growth of the series. $S_{n}\;=\;{\sum}_{j=1}^n\;X_{j}$ is studied in this paper. More specifically, when the series S_{n}$ diverges almost surely, the strong law of large numbers $S_{n}/g_{n}^{-1}$($A_{n}{\psi}(A_{n}))\;{\rightarrow}\;0$ a.s. is constructed by extending the results of Petrov (1973). On the other hand, if the series $S_{n}$ converges almost surely to a random variable S, then the tail series $T_{n}\;=\;S\;-\;S_{n-1}\;=\;{\sum}_{j=n}^{\infty}\;X_{j}$ is a well-defined sequence of random variables and converges to 0 almost surely. For the almost surely convergent series $S_{n}$, a tail series strong law of large numbers $T_{n}/g_{n}^{-1}(B_{n}{\psi}^{\ast}(B_{n}^{-1}))\;{\rightarrow}\;0$ a.s., which generalizes the result of Klesov (1984), is also established by investigating the duality between the limiting behavior of partial sums and that of tail series. In particular, an example is provided showing that the current work can prevail despite the fact that previous tail series strong law of large numbers does not work.

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성인여성의 화장색에 관한 분석 -메이크업 제품을 중심으로- (A Study of Make up Colon Analysis of Adult Women - Focusing on Make up Product -)

  • 한보현;구자명
    • 한국패션뷰티학회지
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    • 제1권1호
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    • pp.27-47
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    • 2003
  • This research is to build the foundation of systematic application of color in cosmetology by analyzing color attributes in women's makeup presentation. The result were as follows. 1. The most popular color series in make up were R then RP and YR. The most popular color tone is 'd' and 'lt'. 2. Colors in make up according to age was as follows. For eye shadow, people aged 18 to 24 used 'lt' tone of the R color series; people aged 25 to 34 used 'lt', 's', 'sf tone of the R color series, 'lt' tone of the PB color series, 'lt' tone of the YR color series; people over 35 'g' tone of the YR color series, 'sf' tone of the P color series. For lipstick, people aged 18 to 24 used 'd' tone of the R color series; people aged 25 to 34 used 'd', 'sf' tone of the R color series; people over 35 used 'd' tone of the R color series. For lip-gloss, people aged 18 to 24 used 'v', 'lt', 'b', 's' tone of the R color series; people aged 25 to 34 used 's' 'd' 'dp' 'sf' tone of the R color series; people over 35 used 'b' tone of the R color series. 3. Make up colors according to marital status was as follows. For eye shadow, while married interviewees used 's', 'dk' tone of the R color series, single interviewees used 'lt', 'sf' tone of the R color series. For lipstick, while married interviewees used 'd', 'g' tone of the R color series, single interviewees preferred to use madder 'd', 'sf' tone of the R color series. For lip-gross, while married interviewees used 'd' tone of the R color series, single interviewees used 'b' tone of the R color series the most.

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Banach 공간에서 독립인 확률요소들의 Tail 합에 대한 대수의 법칙에 대하여 (On the Tail Series Laws of Large Numbers for Independent Random Elements in Banach Spaces)

  • 남은우
    • 한국콘텐츠학회논문지
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    • 제6권5호
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    • pp.29-34
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    • 2006
  • 본 연구에서는, Banach 공간의 값을 갖는 확률요소들의 합 $S_n=\sum_{i=1}^nV-i$ 수렴하는 경우에, Tail 합 $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}V-i$에 대한 대수의 법칙을 고찰하여 $S_n$이 하나의 확률변수 S로 수렴하는 속도를 연구한다. 좀 더 구체적으로 말하자면, 확률변수들의 Tail 합과 확률요소들의 Tail 합에 대한 극한 성질의 유사성을 연구하여, Banach 공간에서 독립인 확률요소들의 Tail 합에 대한 약 대수의 법칙과 하나의 수렴법칙이 동등함을 기술하는 기존의 정리를 다른 대체적인 방법으로 증명한다.

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ZERO DIVISOR GRAPHS OF SKEW GENERALIZED POWER SERIES RINGS

  • MOUSSAVI, AHMAD;PAYKAN, KAMAL
    • 대한수학회논문집
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    • 제30권4호
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    • pp.363-377
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    • 2015
  • Let R be a ring, (S,${\leq}$) a strictly ordered monoid and ${\omega}$ : S ${\rightarrow}$ End(R) a monoid homomorphism. The skew generalized power series ring R[[S,${\omega}$]] is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal'cev-Neumann Laurent series rings. In this paper, we investigate the interplay between the ring-theoretical properties of R[[S,${\omega}$]] and the graph-theoretical properties of its zero-divisor graph ${\Gamma}$(R[[S,${\omega}$]]). Furthermore, we examine the preservation of diameter and girth of the zero-divisor graph under extension to skew generalized power series rings.

독립인 확률변수들의 Tail 합의 극한 성질에 대하여 (Limiting Behavior of Tail Series of Independent Random Variable)

  • 장윤식;남은우
    • 한국콘텐츠학회논문지
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    • 제6권4호
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    • pp.63-68
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    • 2006
  • 본 연구에서는, 서로 독립인 확률변수들의 합 $S_n$이 수렴하는 경우에, 확률변수들의 Tail 합 $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}X_i$의 극한 성질을 연구함으로써, $S_n$이 하나의 확률변수 S로 수렴하는 속도를 연구한다. 좀 더 구체적으로 말하자면, 유사-단조감소(Quasi-monotone decreasing)하는 상수(Norming constants)의 수열에 대하여, 확률변수들의 Tail 합에 대한 약대수법칙과 하나의 수렴법칙이 동등함을 정리로 기술하고 증명하여, 기존의 연구 결과를 더 넓은 부류의 상수들의 경우에 적용할 수 있도록 확장한다.

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화학처리(化學處理) Silica의 SBR에 대한 보강효과(補强效果)에 관(關)한 연구(硏究) (Study on the Chemical Treatment of Silica for SBR Reinforcement)

  • 박건록;유종선;최세영
    • Elastomers and Composites
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    • 제29권1호
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    • pp.18-29
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    • 1994
  • The purpose of this study is to investigate reinforced effect between silica treated by coupling agents and rubber matrix under the configuration chemical bonds, and the effect of silica particles coated by organic polymers using aluminum chloride as the catalyst. In vulcanization characteristies were tested by Curastometer. The M-series vulcanizates were reached to the fastest optimum cure $time(t_{90})$ and R-series vulcanizates with the same formula had the shorted optimum cure times. Tensile characteristics measuring with a tensile tester revealed that the M-series vulcanizate was the best in the physical properties, such as tensile strength. In 100% modulus, however, the S-series vulcanizates appeared to be better than the other vulcanizates. Also, hardness showed the following order : S-series>R-series>M-series with the order of elongation R-series>M-series>S-series. In SEM test, shapes of chemical treated silicas were observed. The dispersion of filler in the SBR composite appeard uniformly. In RDS test for the dynamic characteristics, G' indicates that S-3 shows the highest value with the next order M-3>R-3, and the order of damping values are as followe: M-3>M-3>R-3.

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APPLICATIONS OF GENERALIZED KUMMER'S SUMMATION THEOREM FOR THE SERIES 2F1

  • Kim, Yong-Sup;Rathie, Arjun K.
    • 대한수학회보
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    • 제46권6호
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    • pp.1201-1211
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    • 2009
  • The aim of this research paper is to establish generalizations of classical Dixon's theorem for the series $_3F_2$, a result due to Bailey involving product of generalized hypergeometric series and certain very interesting summations due to Ramanujan. The results are derived with the help of generalized Kummer's summation theorem for the series $_2F_1$ obtained earlier by Lavoie, Grondin, and Rathie.