• Title, Summary, Keyword: generalized fractions

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Some Properties of Generalized Fractions

  • Lee, Dong-Soo;Chung, Sang-Cho
    • Journal of the Chungcheong Mathematical Society
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    • v.7 no.1
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    • pp.153-164
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    • 1994
  • Let A be a commutative ring with identity and M an A-module. When $U_n$ is a triangular subset of $A_n$, Sharp and Zakeri defined a module of generalized fractions $U_n^{-n}M$. In [SZ3], they described a relation of the Monomial Conjecture and a module of generalized fractions under the condition of a Noetherian local ring. In this paper, we investigate some properties of non-zero generalized fractions and give a generalization of results of Sharp and Zakeri for an arbitrary ring.

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SOME EQUALITIES FOR CONTINUED FRACTIONS OF GENERALIZED ROGERS-RAMANUJAN TYPE

  • Li, Yongqun;Wang, Xiantao
    • Journal of the Korean Mathematical Society
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    • v.48 no.5
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    • pp.887-898
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    • 2011
  • In this paper, we first discuss the convergence of the continued fractions of generalized Rogers-Ramanujan type in the modified sense. Then we prove several equalities concerning these continued fractions. The proofs of our main results are mainly based on the Bauer-Muir transformation.

ESSENTIAL SEQUENCES AND GENERALIZED FRACTIONS

  • Chung, Sang-Cho;Lee, Dong-Soo
    • Journal of the Chungcheong Mathematical Society
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    • v.9 no.1
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    • pp.61-68
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    • 1996
  • We investigate associated prime ideals of the module of generalized fractions defined by poor essential sequences and extend the McAdam and Ratliff's criterion of locally unmixed rings.

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TRIANGULAR SUBSETS AND COASSOCIATED PRIME IDEALS

  • Chung, Sang-Cho
    • Journal of the Chungcheong Mathematical Society
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    • v.9 no.1
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    • pp.17-25
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    • 1996
  • We study the relationship between a property of a triangular subset and coassociated prime ideals of the module of generalized fractions induced by the triangular subset, and investigate coassociated prime ideals of modules of generalized fractions defined by some special triangular subsets.

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Optimal fractions in terms of a prediction-oriented measure

  • Lee, Won-Woo
    • Journal of the Korean Statistical Society
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    • v.22 no.2
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    • pp.209-217
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    • 1993
  • The multicollinearity problem in a multiple linear regression model may present deleterious effects on predictions. Thus, its is desirable to consider the optimal fractions with respect to the unbiased estimate of the mean squares errors of the predicted values. Interstingly, the optimal fractions can be also illuminated by the Bayesian inerpretation of the general James-Stein estimators.

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ON DISTRIBUTIONS IN GENERALIZED CONTINUED FRACTIONS

  • AHN, YOUNG-HO
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.6 no.2
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    • pp.1-8
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    • 2002
  • Let $T_{\phi}$ be a generalized Gauss transformation and $[a_1,\;a_2,\;{\cdots}]_{T_{\phi}}$ be a symbolic representation of $x{\in}[0,\;1)$ induced by $T_{\phi}$, i.e., generalized continued fraction expansion induced by $T_{\phi}$. It is shown that the distribution of relative frequency of [$k_1,\;{\cdots},\;k_n$] in $[a_1,\;a_2,\;{\cdots}]_{T_p}$ satisfies Central Limit Theorem where $k_i{\in}{\mathbb{N}}$ for $1{\leq}i{\leq}n$.

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