• 제목/요약/키워드: Asymmetric addition

검색결과 286건 처리시간 0.023초

Organocatalytic Asymmetric Michael Addition of 1,3-Cyclohexanedione to Benzylidenemalonitriles

  • Suh, Chang Won;Kim, Dae Young
    • Bulletin of the Korean Chemical Society
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    • 제35권1호
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    • pp.98-102
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    • 2014
  • The organocatalytic enantioselective Michael addition reaction promoted by chiral binaphthyl-modified squaramide catalyst have been developed, allowing facile synthesis of the corresponding chiral 2-amino-4H-chromenes derivatives with excellent enantioselectivity (up to 99% ee). The method reported represents a practical entry for the preparation of chiral 2-amino-4H-chromenes derivatives.

Construction of bivariate asymmetric copulas

  • Mukherjee, Saikat;Lee, Youngsaeng;Kim, Jong-Min;Jang, Jun;Park, Jeong-Soo
    • Communications for Statistical Applications and Methods
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    • 제25권2호
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    • pp.217-234
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    • 2018
  • Copulas are a tool for constructing multivariate distributions and formalizing the dependence structure between random variables. From copula literature review, there are a few asymmetric copulas available so far while data collected from the real world often exhibit asymmetric nature. This necessitates developing asymmetric copulas. In this study, we discuss a method to construct a new class of bivariate asymmetric copulas based on products of symmetric (sometimes asymmetric) copulas with powered arguments in order to determine if the proposed construction can offer an added value for modeling asymmetric bivariate data. With these newly constructed copulas, we investigate dependence properties and measure of association between random variables. In addition, the test of symmetry of data and the estimation of hyper-parameters by the maximum likelihood method are discussed. With two real example such as car rental data and economic indicators data, we perform the goodness-of-fit test of our proposed asymmetric copulas. For these data, some of the proposed models turned out to be successful whereas the existing copulas were mostly unsuccessful. The method of presented here can be useful in fields such as finance, climate and social science.

A Modified Definition on the Process Capability Index Cpk Based on Median

  • Park, Hyo-Il
    • Communications for Statistical Applications and Methods
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    • 제18권4호
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    • pp.527-535
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    • 2011
  • This study proposes a modified definition about $C_{pk}$ based on median as the centering parameter in order to more easily control the process since the mean does not represent any quantile of the asymmetric process distribution. Then we consider an estimate and derive the asymptotic normality for the estimate of the modified $C_{pk}$. In addition, we provide an example with asymmetric distributions and discuss the estimation for the limiting variance that are followed by some concluding remarks.