• Title/Summary/Keyword: lexicographic order

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A Hypothesis Test under the Generalized Sampling Plan (일반화된 샘플링 계획에서의 가설 검정)

  • 김명수;오근태
    • Journal of the Korean Society for Quality Management
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    • v.26 no.4
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    • pp.79-87
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    • 1998
  • This paper considers the problem of testing a one-sided hypothesis under the generalized sampling plan which is defined by a sequence of independent Bernoulli trials. A certain lexicographic order is defined for the boundary points of the sampling plan. It is shown that the family of probability mass function defined on the boundary points has monotone likelihood ratio, and that the test function is uniformly most powerful.

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DERIVATIONS OF A COMBINATORIAL LIE ALGEBRA

  • Choi, Seul Hee
    • Honam Mathematical Journal
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    • v.36 no.3
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    • pp.493-503
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    • 2014
  • We consider the simple antisymmetrized algebra $N(e^{A_P},n,t)_1^-$. The simple non-associative algebra and its simple subalgebras are defined in the papers [1], [3], [4], [5], [6], [8], [13]. Some authors found all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra in their papers [2], [3], [5], [7], [9], [10], [13], [15], [16]. We find all the derivations of the Lie subalgebra $N(e^{{\pm}x_1x_2x_3},0,3)_{[1]}{^-}$ of $N(e^{A_p},n,t)_k{^-}$ in this paper.

Differential Spatial Modulation with Gray Coded Antenna (그레이 코드화된 안테나 순서의 차등 공간 변조)

  • Kim, Jeong-Su;Lee, Moon Ho
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.17 no.5
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    • pp.51-59
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    • 2017
  • In this paper, we propose a gray code order of antenna index permutations for differential spatial modulation (DSM). To facilitate the implementation, the well-known Trotter-Johnson ranking and unranking algorithms are adopted, which result in similar computational complexity to the existing DSM that uses the lexicographic order. The signal-to-noise ratio gain achieved by the proposed gray code order over the lexicographic order is also analyzed and verified via simulations. Based on the gray coding framework, we further propose a diversity-enhancing scheme named intersected gray (I-gray) code order, where the permutations of active antenna indices are selected directly from the odd (or even) positions of the full permutations in the gray code order. From analysis and simulations, it is shown that the I-gray code order can harvest an additional transmit diversity order with respect to the gray code order.

Gugo Wonlyu of Jeong Yag-yong (정약용의 구고원류)

  • Kim, Young Wook
    • Journal for History of Mathematics
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    • v.32 no.3
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    • pp.97-108
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    • 2019
  • This paper is an outgrowth of a study on recent papers and presentations of Hong Sung Sa, Hong Young Hee and/or Lee Seung On on Gugo Wonlyu which is believed to be written by the famous Joseon scholar Jeong Yag-yong. Most of what is discussed here is already explained in these papers and presentations but due to brevity of the papers it is not understood by most of us. Here we present them in more explicit and mathematical ways which, we hope, will make them more accessible to those who have little background in history of classical Joseon mathematics. We also explain them using elementary projective geometry which allow us to visualize Pythagorean polynomials geometrically.

Mathematical Structures of Jeong Yag-yong's Gugo Wonlyu (정약용(丁若鏞)의 산서(算書) 구고원류(勾股源流)의 수학적(數學的) 구조(構造))

  • HONG, Sung Sa;HONG, Young Hee;LEE, Seung On
    • Journal for History of Mathematics
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    • v.28 no.6
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    • pp.301-310
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    • 2015
  • Since Jiuzhang Suanshu, the main tools in the theory of right triangles, known as Gougushu in East Asia were algebraic identities about three sides of a right triangle derived from the Pythagorean theorem. Using tianyuanshu up to siyuanshu, Song-Yuan mathematicians could skip over those identities in the theory. Chinese Mathematics in the 17-18th centuries were mainly concerned with the identities along with the western geometrical proofs. Jeong Yag-yong (1762-1836), a well known Joseon scholar and writer of the school of Silhak, noticed that those identities can be derived through algebra and then wrote Gugo Wonlyu (勾股源流) in the early 19th century. We show that Jeong reveals the algebraic structure of polynomials with the three indeterminates in the book along with their order structure. Although the title refers to right triangles, it is the first pure algebra book in Joseon mathematics, if not in East Asia.